(cache)minimal-elements-of-the-prime-numbers/README.md at main · xayahrainie4793/minimal-elements-of-the-prime-numbers

(Note: I do not offer links to the OEIS Wiki (https://oeis.org/wiki/Main_Page) or the PrimeGrid Wiki (http://primegrid.wikia.com/wiki/PrimeGrid_Wiki) or the Rechenkraft Wiki (https://www.rechenkraft.net/wiki/Willkommen_beim_Verein_Rechenkraft.net_e.V.), with the only one exception: the page "OEIS sequences needing factors" (https://oeis.org/wiki/OEIS_sequences_needing_factors) in the OEIS Wiki, since fewer people contribute the OEIS Wiki and the PrimeGrid Wiki, and most things in the Rechenkraft Wiki are out of date)

A Prime Game:

Write down a multidigit prime number (i.e. a prime number > 10), and I can always strike out 0 or more digits to get a prime in this list:

{11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}

e.g.

Write down the prime 149 → I can strike out the digit 4, to get the prime 19
Write down the prime 439 → I can strike out the digit 9, to get the prime 43
Write down the prime 857 → I can strike out zero digits, to get the prime 857
Write down the prime 2081 → I can strike out the digit 0, to get the prime 281
Write down the largest known double Mersenne prime 170141183460469231731687303715884105727 (2¹²⁷−1) → I can strike out all digits except the third-leftmost 1 and the second-rightmost 3, to get the prime 13 (also I can choose to strike out all digits except the second-leftmost 4 and the third-rightmost 7, to get the prime 47)
Write down the largest known Fermat prime 65537 → I can strike out the 6 and the 3, to get the prime 557 (also I can choose to strike out the 6 and two 5's, to get the prime 37) (also I can choose to strike out two 5's and the 3, to get the prime 67) (also I can choose to strike out the 6, one 5, and the 7, to get the prime 53)
Write down the famous repunit prime 1111111111111111111 (with 19 1's) → I can strike out 17 1's, to get the prime 11
Write down the prime 1000000000000000000000000000000000000000000000000000000000007 (which is the next prime after 10⁶⁰) → I can strike out all 0's, to get the prime 17
Write down the prime 95801 → I can strike out the 9, to get the prime 5801
Write down the prime 946969 → I can strike out the first 9 and two 6's, to get the prime 499
Write down the prime 90000000581 → I can strike out five 0's, the 5, and the 8, to get the prime 9001
Write down the prime 8555555555555555555551 → I can strike out the 8 and nine 5's, to get the prime 555555555551

These primes are called minimal primes.

Let b > 1 be a natural number (https://en.wikipedia.org/wiki/Natural_number, https://www.rieselprime.de/ziki/Natural_number, https://mathworld.wolfram.com/NaturalNumber.html). A minimal prime base b is a prime number (https://en.wikipedia.org/wiki/Prime_number, https://t5k.org/glossary/xpage/Prime.html, https://www.rieselprime.de/ziki/Prime, https://mathworld.wolfram.com/PrimeNumber.html, https://www.numbersaplenty.com/set/prime_number/, http://www.numericana.com/answer/primes.htm#definition, http://irvinemclean.com/maths/pfaq2.htm, https://oeis.org/A000040, https://t5k.org/lists/small/1000.txt, https://t5k.org/lists/small/10000.txt, https://t5k.org/lists/small/100000.txt, https://t5k.org/lists/small/millions/) greater than (https://en.wikipedia.org/wiki/Greater_than, https://mathworld.wolfram.com/Greater.html) b whose base-b (i.e. the positional numeral system (https://en.wikipedia.org/wiki/Positional_numeral_system) with radix (https://en.wikipedia.org/wiki/Radix, https://t5k.org/glossary/xpage/Radix.html, https://www.rieselprime.de/ziki/Base, https://mathworld.wolfram.com/Radix.html) b) representation has no proper subsequence (https://en.wikipedia.org/wiki/Subsequence, https://mathworld.wolfram.com/Subsequence.html) which is also a prime number greater than b.

For example, 857 is a minimal prime in decimal (base b = 10) because there is no prime > 10 among the shorter subsequences of the digits: 8, 5, 7, 85, 87, 57. The subsequence does not have to consist of consecutive digits, so 149 is not a minimal prime in decimal (base b = 10) (because 19 is prime and 19 > 10). But it does have to be in the same order; so, for example, 991 is still a minimal prime in decimal (base b = 10) even though a subset of the digits can form the shorter prime 19 > 10 by changing the order.

Now we extend minimal primes to bases b other than 10.

A string (https://en.wikipedia.org/wiki/String_(computer_science), https://mathworld.wolfram.com/String.html) x is a subsequence (https://en.wikipedia.org/wiki/Subsequence, https://mathworld.wolfram.com/Subsequence.html) of another string y, if x can be obtained from y by deleting zero or more of the characters (https://en.wikipedia.org/wiki/Character_(computing)) (in this project, digits (https://en.wikipedia.org/wiki/Numerical_digit, https://www.rieselprime.de/ziki/Digit, https://mathworld.wolfram.com/Digit.html)) in y. For example, 514 is a subsequence of 352148, "STRING" is a subsequence of "MEISTERSINGER". In contrast, 758 is not a subsequence of 378259, "ABC" is not a subsequence of "CBACACBA", since the characters (in this project, digits) must be in the same order. The empty string (https://en.wikipedia.org/wiki/Empty_string) 𝜆 is a subsequence of every string. There are 2ⁿ subsequences of a string with length n, e.g. the subsequences of 123456 are (totally 2⁶ = 64 subsequences):

𝜆, 1, 2, 3, 4, 5, 6, 12, 13, 14, 15, 16, 23, 24, 25, 26, 34, 35, 36, 45, 46, 56, 123, 124, 125, 126, 134, 135, 136, 145, 146, 156, 234, 235, 236, 245, 246, 256, 345, 346, 356, 456, 1234, 1235, 1236, 1245, 1246, 1256, 1345, 1346, 1356, 1456, 2345, 2346, 2356, 2456, 3456, 12345, 12346, 12356, 12456, 13456, 23456, 123456

"The set of strings ordered by subsequence" is a partially ordered set (https://en.wikipedia.org/wiki/Partially_ordered_set, https://mathworld.wolfram.com/PartialOrder.html, https://mathworld.wolfram.com/PartiallyOrderedSet.html), since this binary relation (https://en.wikipedia.org/wiki/Binary_relation, https://mathworld.wolfram.com/BinaryRelation.html) is reflexive (https://en.wikipedia.org/wiki/Reflexive_relation, https://mathworld.wolfram.com/Reflexive.html), antisymmetric (https://en.wikipedia.org/wiki/Antisymmetric_relation), and transitive (https://en.wikipedia.org/wiki/Transitive_relation), and thus we can draw its Hasse diagram (https://en.wikipedia.org/wiki/Hasse_diagram, https://mathworld.wolfram.com/HasseDiagram.html) and find its greatest element (https://en.wikipedia.org/wiki/Greatest_element), least element (https://en.wikipedia.org/wiki/Least_element), maximal elements (https://en.wikipedia.org/wiki/Maximal_element, https://mathworld.wolfram.com/MaximalElement.html), and minimal elements (https://en.wikipedia.org/wiki/Minimal_element), however, the greatest element and least element may not exist, and for an infinite set (such as the set of the "prime numbers > b" strings in base b (for a given base b ≥ 2), for the proofs for that there are infinitely many primes, see https://en.wikipedia.org/wiki/Euclid%27s_theorem, https://mathworld.wolfram.com/EuclidsTheorems.html, http://www.numericana.com/answer/primes.htm#euclid, https://t5k.org/notes/proofs/infinite/, https://t5k.org/notes/proofs/infinite/euclids.html, https://t5k.org/notes/proofs/infinite/topproof.html, https://t5k.org/notes/proofs/infinite/goldbach.html, https://t5k.org/notes/proofs/infinite/kummers.html, https://t5k.org/notes/proofs/infinite/Saidak.html)), the maximal elements also may not exist, thus we are only interested on finding the minimal elements of these sets, and we define "minimal set" of a set as the set of the minimal elements of this set, under a given partially ordered binary relation (this binary relation is "is a subsequence of" in this project))

Two strings x and y are comparable (https://en.wikipedia.org/wiki/Comparability, https://mathworld.wolfram.com/ComparableElements.html) if either x is a subsequence of y, or y is a subsequence of x. A surprising result from formal language theory (https://en.wikipedia.org/wiki/Formal_language_theory) is that every set of pairwise incomparable strings is finite (https://en.wikipedia.org/wiki/Finite_set, https://mathworld.wolfram.com/FiniteSet.html) (which is proved by M. Lothaire), i.e. there are no infinite (https://en.wikipedia.org/wiki/Infinite_set, https://t5k.org/glossary/xpage/Infinite.html, https://mathworld.wolfram.com/InfiniteSet.html) antichains (https://en.wikipedia.org/wiki/Antichain, https://mathworld.wolfram.com/Antichain.html) for the subsequence (https://en.wikipedia.org/wiki/Subsequence, https://mathworld.wolfram.com/Subsequence.html) ordering (https://en.wikipedia.org/wiki/Partially_ordered_set, https://mathworld.wolfram.com/PartialOrder.html, https://mathworld.wolfram.com/PartiallyOrderedSet.html).

By the theorem that there are no infinite (https://en.wikipedia.org/wiki/Infinite_set, https://t5k.org/glossary/xpage/Infinite.html, https://mathworld.wolfram.com/InfiniteSet.html) antichains (https://en.wikipedia.org/wiki/Antichain, https://mathworld.wolfram.com/Antichain.html) (i.e. a subset of a partially ordered set such that any two distinct elements in the subset are incomparable (https://en.wikipedia.org/wiki/Comparability, https://mathworld.wolfram.com/ComparableElements.html)) for the subsequence (https://en.wikipedia.org/wiki/Subsequence, https://mathworld.wolfram.com/Subsequence.html) ordering (https://en.wikipedia.org/wiki/Partially_ordered_set, https://mathworld.wolfram.com/PartialOrder.html, https://mathworld.wolfram.com/PartiallyOrderedSet.html) (i.e. the set of the minimal elements of any set under the subsequence ordering must be finite, even if this set is infinite, such as the set of the "prime numbers > b" strings in base b (for a given base b ≥ 2), for the proofs for that there are infinitely many primes, see https://en.wikipedia.org/wiki/Euclid%27s_theorem, https://mathworld.wolfram.com/EuclidsTheorems.html, http://www.numericana.com/answer/primes.htm#euclid, https://t5k.org/notes/proofs/infinite/, https://t5k.org/notes/proofs/infinite/euclids.html, https://t5k.org/notes/proofs/infinite/topproof.html, https://t5k.org/notes/proofs/infinite/goldbach.html, https://t5k.org/notes/proofs/infinite/kummers.html, https://t5k.org/notes/proofs/infinite/Saidak.html), there must be only finitely such minimal elements in every base b.

In this project, we want to find the set of the minimal strings of the "prime number > b" digit strings in bases 2 ≤ b ≤ 36, since decimal (base 10) is not special in mathematics, there is no reason to only find this set in decimal (base 10), also, finding this set in decimal (base 10) is too easy to be researched in an article (only harder than bases 2, 3, 4, 6), thus it is necessary to research this set in other bases b.

Equivalently, a string x in a set of strings S is a minimal string if and only if any proper subsequence of x (subsequence of x which is unequal to x, like proper subset (https://en.wikipedia.org/wiki/Proper_subset, https://mathworld.wolfram.com/ProperSubset.html)) is not in S.

The minimal set M(L) of a language (https://en.wikipedia.org/wiki/Formal_language, https://mathworld.wolfram.com/FormalLanguage.html) L is interesting, this is because it allows us to compute two natural and related languages, defined as follows:

sub(L) = {x ∈ Σ* : there exists y ∈ L such that x is a subsequence of y}
sup(L) = {x ∈ Σ* : there exists y ∈ L such that y is a subsequence of x}

An amazing fact is that sub(L) and sup(L) are always regular. This follows from the classical theorem that every set of pairwise incomparable strings is finite, for the proof see https://www.sciencedirect.com/science/article/pii/S0021980069801110 (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_329.pdf).

Although the minimal set M(L) is necessary finite even for infinite set L, but computing (https://en.wikipedia.org/wiki/Computing) the minimal set M(L) is undecidable (https://en.wikipedia.org/wiki/Undecidable_problem, https://mathworld.wolfram.com/Undecidable.html) in general and can be very difficult to compute even for simple languages, and can lead to some strange behaviour ...

The minimal set of the primes > 7 in base b = 7 has 71 elements, but the largest of which has only 17 digits.
The minimal set of the primes > 5 in base b = 5 has only 22 elements, but the largest of which has 96 digits!

And ...

The minimal set of the primes > 10 in base b = 10 has 77 elements, but the largest of which has only 31 digits.
The minimal set of the primes > 12 in base b = 12 has 106 elements, but the largest of which has only 42 digits.
The minimal set of the primes > 8 in base b = 8 has only 75 elements, but the largest of which has 221 digits!

Also, more strange ...

The minimal set of the primes > 15 in base b = 15 has 1284 elements, but the largest of which has only 157 digits.
The minimal set of the primes > 9 in base b = 9 has only 151 elements, but the largest of which has 1161 digits!
The minimal set of the primes > 18 in base b = 18 has only 549 elements, but the largest of which has 6271 digits!
The minimal set of the primes > 14 in base b = 14 has only 650 elements, but the largest of which has 19699 digits!

And ...

The minimal set of the primes > 20 in base b = 20 has 3314 elements, and the largest of which also has 6271 digits.
The minimal set of the primes > 24 in base b = 24 has 3409 elements, and the largest of which has 8134 digits.

And the finales ...

The minimal set of the primes > 11 in base b = 11 has only 1068 elements, but the largest of which has 62669 digits! (technically, probable primality tests were used to show this (which have a very small chance of making an error) because all known primality tests run far too slowly to run on a number of this size)
The minimal set of the primes > 16 in base b = 16 has only 2347 elements, but the largest of which has 116139 digits! (technically, probable primality tests were used to show this (which have a very small chance of making an error) because all known primality tests run far too slowly to run on a number of this size)
The minimal set of the primes > 13 in base b = 13 has only 3197 elements, but the largest of which has 592199 digits! (technically, probable primality tests were used to show this (which have a very small chance of making an error) because all known primality tests run far too slowly to run on a number of this size)

In this project, we will find the sets of the minimal elements of these 35 sets under the subsequence (https://en.wikipedia.org/wiki/Subsequence, https://mathworld.wolfram.com/Subsequence.html) ordering (https://en.wikipedia.org/wiki/Partially_ordered_set, https://mathworld.wolfram.com/PartialOrder.html, https://mathworld.wolfram.com/PartiallyOrderedSet.html):

b	the base b representations of the prime numbers (https://en.wikipedia.org/wiki/Prime_number, https://t5k.org/glossary/xpage/Prime.html, https://www.rieselprime.de/ziki/Prime, https://mathworld.wolfram.com/PrimeNumber.html, https://www.numbersaplenty.com/set/prime_number/, http://www.numericana.com/answer/primes.htm#definition, http://irvinemclean.com/maths/pfaq2.htm, https://oeis.org/A000040, https://t5k.org/lists/small/1000.txt, https://t5k.org/lists/small/10000.txt, https://t5k.org/lists/small/100000.txt, https://t5k.org/lists/small/millions/) > b (only list the first 1000 elements in the sets)
2	11, 101, 111, 1011, 1101, 10001, 10011, 10111, 11101, 11111, 100101, 101001, 101011, 101111, 110101, 111011, 111101, 1000011, 1000111, 1001001, 1001111, 1010011, 1011001, 1100001, 1100101, 1100111, 1101011, 1101101, 1110001, 1111111, 10000011, 10001001, 10001011, 10010101, 10010111, 10011101, 10100011, 10100111, 10101101, 10110011, 10110101, 10111111, 11000001, 11000101, 11000111, 11010011, 11011111, 11100011, 11100101, 11101001, 11101111, 11110001, 11111011, 100000001, 100000111, 100001101, 100001111, 100010101, 100011001, 100011011, 100100101, 100110011, 100110111, 100111001, 100111101, 101001011, 101010001, 101011011, 101011101, 101100001, 101100111, 101101111, 101110101, 101111011, 101111111, 110000101, 110001101, 110010001, 110011001, 110100011, 110100101, 110101111, 110110001, 110110111, 110111011, 111000001, 111001001, 111001101, 111001111, 111010011, 111011111, 111100111, 111101011, 111110011, 111110111, 111111101, 1000001001, 1000001011, 1000011101, 1000100011, 1000101101, 1000110011, 1000111001, 1000111011, 1001000001, 1001001011, 1001010001, 1001010111, 1001011001, 1001011111, 1001100101, 1001101001, 1001101011, 1001110111, 1010000001, 1010000011, 1010000111, 1010001101, 1010010011, 1010010101, 1010100001, 1010100101, 1010101011, 1010110011, 1010111101, 1011000101, 1011001111, 1011010111, 1011011101, 1011100011, 1011100111, 1011101111, 1011110101, 1011111001, 1100000001, 1100000101, 1100010011, 1100011101, 1100101001, 1100101011, 1100110101, 1100110111, 1100111011, 1100111101, 1101000111, 1101010101, 1101011001, 1101011011, 1101011111, 1101101101, 1101110001, 1101110011, 1101110111, 1110001011, 1110001111, 1110010111, 1110100001, 1110101001, 1110101101, 1110110011, 1110111001, 1111000111, 1111001011, 1111010001, 1111010111, 1111011111, 1111100101, 1111110001, 1111110101, 1111111011, 1111111101, 10000000111, 10000001001, 10000001111, 10000011001, 10000011011, 10000100101, 10000100111, 10000101101, 10000111111, 10001000011, 10001000101, 10001001001, 10001001111, 10001010101, 10001011101, 10001100011, 10001101001, 10001111111, 10010000001, 10010001011, 10010010011, 10010011101, 10010100011, 10010101001, 10010110001, 10010111101, 10011000001, 10011000111, 10011001101, 10011001111, 10011010101, 10011100001, 10011101011, 10011111101, 10011111111, 10100000011, 10100001001, 10100001011, 10100010001, 10100010101, 10100010111, 10100011011, 10100100111, 10100101001, 10100101111, 10101010001, 10101010111, 10101011101, 10101100101, 10101110111, 10110000001, 10110001111, 10110010011, 10110010101, 10110011001, 10110011111, 10110100111, 10110101011, 10110101101, 10110110011, 10110111111, 10111001001, 10111001011, 10111001111, 10111010001, 10111010101, 10111011011, 10111100111, 10111110011, 10111111011, 11000000111, 11000001101, 11000010001, 11000010111, 11000011111, 11000100011, 11000101011, 11000101111, 11000111101, 11001000001, 11001000111, 11001001001, 11001001101, 11001010011, 11001010101, 11001011011, 11001100101, 11001111001, 11001111111, 11010000011, 11010000101, 11010011101, 11010100001, 11010100011, 11010101101, 11010111001, 11010111011, 11011000101, 11011001101, 11011010011, 11011011001, 11011011111, 11011110001, 11011110111, 11011111011, 11011111101, 11100001001, 11100010011, 11100011111, 11100100111, 11100110111, 11101000101, 11101001011, 11101001111, 11101010001, 11101010101, 11101010111, 11101100001, 11101101101, 11101110011, 11101111001, 11110001011, 11110001101, 11110011101, 11110011111, 11110110101, 11110111011, 11111000011, 11111001001, 11111001101, 11111001111, 11111010011, 11111011011, 11111100001, 11111101011, 11111101101, 11111110111, 100000000101, 100000001111, 100000010101, 100000100001, 100000100011, 100000100111, 100000101001, 100000110011, 100000111111, 100001000001, 100001010001, 100001010011, 100001011001, 100001011101, 100001011111, 100001101001, 100001110001, 100010000011, 100010011011, 100010011111, 100010100101, 100010101101, 100010111101, 100010111111, 100011000011, 100011001011, 100011011011, 100011011101, 100011100001, 100011101001, 100011101111, 100011110101, 100011111001, 100100000101, 100100000111, 100100011101, 100100100011, 100100100101, 100100101011, 100100101111, 100100110101, 100101000011, 100101001001, 100101001101, 100101001111, 100101010101, 100101011001, 100101011111, 100101101011, 100101110001, 100101110111, 100110000101, 100110001001, 100110001111, 100110011011, 100110100011, 100110101001, 100110101101, 100111000111, 100111011001, 100111100011, 100111101011, 100111101111, 100111110101, 100111110111, 100111111101, 101000010011, 101000011111, 101000100001, 101000110001, 101000111001, 101000111101, 101001001001, 101001010111, 101001100001, 101001100011, 101001100111, 101001101111, 101001110101, 101001111011, 101001111111, 101010000001, 101010000101, 101010001011, 101010010011, 101010010111, 101010011001, 101010011111, 101010101001, 101010101011, 101010110101, 101010111101, 101011000001, 101011001111, 101011011001, 101011100101, 101011100111, 101011101101, 101011110001, 101011110011, 101100000011, 101100010001, 101100010101, 101100011011, 101100100011, 101100101001, 101100101101, 101100111111, 101101000111, 101101010001, 101101010111, 101101011101, 101101100101, 101101101111, 101101111011, 101110001001, 101110001101, 101110010011, 101110011001, 101110011011, 101110110111, 101110111001, 101111000011, 101111001011, 101111001111, 101111011101, 101111100001, 101111101001, 101111110101, 101111111011, 110000000111, 110000001011, 110000010001, 110000100101, 110000101111, 110000110001, 110001000001, 110001011011, 110001011111, 110001100001, 110001101101, 110001110011, 110001110111, 110010000011, 110010001001, 110010010001, 110010010101, 110010011101, 110010110011, 110010110101, 110010111001, 110010111011, 110011000111, 110011100011, 110011100101, 110011101011, 110011110001, 110011110111, 110011111011, 110100000001, 110100000011, 110100001111, 110100010011, 110100011111, 110100100001, 110100101011, 110100101101, 110100111101, 110100111111, 110101001111, 110101010101, 110101101001, 110101111001, 110110000001, 110110000101, 110110000111, 110110001011, 110110001101, 110110100011, 110110101011, 110110110111, 110110111101, 110111000111, 110111001001, 110111001101, 110111010011, 110111010101, 110111011011, 110111100101, 110111100111, 110111110011, 110111111101, 110111111111, 111000001001, 111000010111, 111000011101, 111000100001, 111000100111, 111000101111, 111000110101, 111000111011, 111001001011, 111001010111, 111001011001, 111001011101, 111001101011, 111001110001, 111001110101, 111001111101, 111010000111, 111010001111, 111010010101, 111010011011, 111010110001, 111010110111, 111010111001, 111011000011, 111011010001, 111011010101, 111011011011, 111011101101, 111011101111, 111011111001, 111100000111, 111100001011, 111100001101, 111100010111, 111100100101, 111100101001, 111100110001, 111101000011, 111101000111, 111101001101, 111101001111, 111101010011, 111101011001, 111101011011, 111101100111, 111101101011, 111101111111, 111110010101, 111110100001, 111110100011, 111110100111, 111110101101, 111110110011, 111110110101, 111110111011, 111111010001, 111111010011, 111111011001, 111111101001, 111111101111, 111111111011, 111111111101, 1000000000011, 1000000001111, 1000000011111, 1000000100001, 1000000100101, 1000000101011, 1000000111001, 1000000111101, 1000000111111, 1000001010001, 1000001101001, 1000001110011, 1000001111001, 1000001111011, 1000010000101, 1000010000111, 1000010010001, 1000010010011, 1000010011101, 1000010100011, 1000010100101, 1000010101111, 1000010110001, 1000010111011, 1000011000001, 1000011001001, 1000011100111, 1000011110001, 1000011110011, 1000011111101, 1000100000101, 1000100001011, 1000100010101, 1000100100111, 1000100101101, 1000100111001, 1000101000101, 1000101000111, 1000101011001, 1000101011111, 1000101100011, 1000101101001, 1000101101111, 1000110000001, 1000110000011, 1000110001101, 1000110011011, 1000110100001, 1000110100101, 1000110100111, 1000110101011, 1000111000011, 1000111000101, 1000111010001, 1000111010111, 1000111100111, 1000111101111, 1000111110101, 1000111111011, 1001000001101, 1001000011101, 1001000011111, 1001000100011, 1001000101001, 1001000101011, 1001000110001, 1001000110111, 1001001000001, 1001001000111, 1001001010011, 1001001011111, 1001001110001, 1001001110011, 1001001111001, 1001001111101, 1001010001111, 1001010010111, 1001010101111, 1001010110011, 1001010110101, 1001010111001, 1001010111111, 1001011000001, 1001011001101, 1001011010001, 1001011011111, 1001011111101, 1001100000111, 1001100001101, 1001100011001, 1001100100111, 1001100101101, 1001100110111, 1001101000011, 1001101000101, 1001101001001, 1001101001111, 1001101010111, 1001101011101, 1001101100111, 1001101101001, 1001101101101, 1001101111011, 1001110000001, 1001110000111, 1001110001011, 1001110010001, 1001110010011, 1001110011101, 1001110011111, 1001110101111, 1001110111011, 1001111000011, 1001111010101, 1001111011001, 1001111011111, 1001111101011, 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1011000110011, 1011000111001, 1011000111101, 1011001000101, 1011001001111, 1011001010101, 1011001101001, 1011001101101, 1011001101111, 1011001110101, 1011010010011, 1011010010111, 1011010011111, 1011010101001, 1011010101111, 1011010110101, 1011010111101, 1011011000011, 1011011001111, 1011011010011, 1011011011001, 1011011011011, 1011011100001, 1011011100101, 1011011101011, 1011011101101, 1011011110111, 1011011111001, 1011100001001, 1011100001111, 1011100100011, 1011100100111, 1011100110011, 1011101000001, 1011101011101, 1011101100011, 1011101110111, 1011101111011, 1011110001101, 1011110010101, 1011110011011, 1011110011111, 1011110100101, 1011110110011, 1011110111001, 1011110111111, 1011111001001, 1011111001011, 1011111010101, 1011111100001, 1011111101001, 1011111110011, 1011111110101, 1011111111111, 1100000000111, 1100000010011, 1100000011101, 1100000110101, 1100000110111, 1100000111011, 1100001000011, 1100001001001, 1100001001101, 1100001010101, 1100001100111, 1100001110001, 1100001110111, 1100001111101, 1100001111111, 1100010000101, 1100010001111, 1100010011011, 1100010011101, 1100010100111, 1100010101101, 1100010110011, 1100010111001, 1100011000001, 1100011000111, 1100011010001, 1100011010111, 1100011011001, 1100011011111, 1100011100101, 1100011101011, 1100011110101, 1100011111101, 1100100010101, 1100100011011, 1100100110001, 1100100110011, 1100101000101, 1100101001001, 1100101010001, 1100101011011, 1100101111001, 1100110000001, 1100110010011, 1100110010111, 1100110011001, 1100110100011, 1100110101001, 1100110101011, 1100110110001, 1100110110101, 1100111000111, 1100111001111, 1100111011011, 1100111101101, 1100111111101, 1101000000011, 1101000000101, 1101000010001, 1101000010111, 1101000100001, 1101000100011, 1101000101101, 1101000101111, 1101000110101, 1101000111111, 1101001001101, 1101001010001, 1101001101001, 1101001101011, 1101001111011, 1101001111101, 1101010000111, 1101010001001, 1101010010011, 1101010100111, 1101010101011, 1101010101101, 1101010110001, 1101010111001, 1101011001001, 1101011001111, 1101011010101, 1101011010111, 1101011100011, 1101011110011, 1101011111011, 1101011111111, 1101100000101, 1101100100011, 1101100100101, 1101100101111, 1101100110001, 1101100110111, 1101100111011, 1101101000001, 1101101000111, 1101101001111, 1101101010101, 1101101011001, 1101101100101, 1101101101011, 1101101110011, 1101101111111, 1101110000011, 1101110010001, 1101110011101, 1101110100111, 1101110111111, 1101111000101, 1101111010001, 1101111010111, 1101111011001, 1101111101111, 1101111110111, 1110000001001, 1110000010011, 1110000011001, 1110000100111, 1110000101011, 1110000101101, 1110000110011, 1110000111101, 1110001000101, 1110001001011, 1110001001111, 1110001010101, 1110001110011, 1110010000001, 1110010001011, 1110010001101, 1110010011001, 1110010100011, 1110010100101, 1110010110101, 1110010110111, 1110011001001, 1110011100001, 1110011110011, 1110011111001, 1110100001001, 1110100011011, 1110100100001, 1110100100011, 1110100110101, 1110100111001, 1110100111111, 1110101000001, 1110101001011, 1110101010011, 1110101011101, 1110101100011, 1110101101001, 1110101110001, 1110101110101, 1110101111011, 1110101111101, 1110110000111, 1110110001001, 1110110010101, 1110110011001, 1110110011111, 1110110100101, 1110110100111, 1110110110011, 1110110110111, 1110111000101, 1110111010111, 1110111011011, 1110111100001, 1110111110101, 1110111111001, 1111000000001, 1111000000111, 1111000001011, 1111000010011, 1111000010111, 1111000100101, 1111000101011, 1111000101111, 1111000111101, 1111001001001, 1111001001101, 1111001001111, 1111001101101, 1111001110001, 1111010001001, 1111010001111, 1111010010101, 1111010100001, 1111010101101, 1111010111011, 1111011000001, 1111011000101, 1111011000111, 1111011001011, 1111011011101, 1111011100011, 1111011101111, 1111011110111, ...
3	12, 21, 102, 111, 122, 201, 212, 1002, 1011, 1101, 1112, 1121, 1202, 1222, 2012, 2021, 2111, 2122, 2201, 2221, 10002, 10022, 10121, 10202, 10211, 10222, 11001, 11012, 11201, 11212, 12002, 12011, 12112, 12121, 12211, 20001, 20012, 20102, 20122, 20201, 21002, 21011, 21022, 21101, 21211, 22021, 22102, 22111, 22122, 22212, 22221, 100022, 100112, 100202, 100222, 101001, 101021, 101102, 101111, 101212, 102101, 102112, 102121, 102202, 110021, 110111, 110212, 110221, 111002, 111022, 111121, 111211, 112001, 112012, 112102, 112201, 112212, 120011, 120112, 120121, 120222, 121001, 121021, 121102, 121122, 121221, 122002, 122011, 122022, 122202, 200001, 200012, 200111, 200122, 200212, 201022, 201101, 202001, 202021, 202122, 202212, 210002, 210011, 210101, 210202, 210222, 211012, 211021, 211111, 211201, 211212, 211221, 212101, 212202, 212211, 212222, 220012, 220102, 220111, 220221, 221002, 221022, 221121, 221222, 222021, 222122, 222221, 1000011, 1000101, 1000112, 1000211, 1001001, 1001012, 1001111, 1001122, 1002011, 1002112, 1002222, 1010001, 1010102, 1010111, 1010122, 1010201, 1011002, 1011121, 1011202, 1011211, 1011222, 1012111, 1012122, 1012201, 1012212, 1020121, 1020202, 1021001, 1021102, 1021201, 1021212, 1022002, 1022022, 1022211, 1022222, 1100012, 1100102, 1100201, 1100221, 1101101, 1101112, 1101202, 1101211, 1102012, 1102021, 1102111, 1102212, 1102221, 1110022, 1110101, 1110121, 1111021, 1111102, 1111111, 1111122, 1111212, 1112002, 1112101, 1112121, 1112211, 1120122, 1120201, 1121002, 1121101, 1121202, 1121222, 1122012, 1122111, 1122221, 1200002, 1200022, 1200112, 1200121, 1200211, 1201021, 1201122, 1202022, 1202101, 1202112, 1202202, 1202211, 1210001, 1210012, 1210021, 1210102, 1210212, 1210221, 1211011, 1212102, 1212122, 1212212, 1220011, 1220211, 1221012, 1221201, 1221212, 1221221, 1222002, 1222022, 1222121, 1222202, 1222211, 2000001, 2000111, 2000212, 2000221, 2001002, 2001011, 2001022, 2001112, 2001222, 2002102, 2002201, 2010011, 2010101, 2010112, 2010202, 2011001, 2011012, 2011111, 2011122, 2012011, 2012022, 2012112, 2012121, 2012202, 2012222, 2020001, 2020021, 2020122, 2021101, 2021121, 2021202, 2021211, 2022201, 2022212, 2022221, 2100022, 2100202, 2100211, 2101012, 2101111, 2101201, 2101221, 2102011, 2102211, 2110001, 2110012, 2110021, 2110201, 2111002, 2111112, 2111211, 2112102, 2112221, 2120011, 2120022, 2120101, 2120112, 2120121, 2120222, 2121102, 2121122, 2121212, 2122112, 2122121, 2200012, 2200021, 2201002, 2201022, 2201121, 2201211, 2201222, 2202001, 2202012, 2202111, 2202201, 2210002, 2210011, 2210112, 2211001, 2211102, 2211122, 2212002, 2212011, 2212022, 2212101, 2212202, 2220012, 2220021, 2220212, 2220221, 2221011, 2221022, 2221101, 2221202, 2222001, 2222201, 10000121, 10000202, 10000222, 10001021, 10001212, 10001221, 10002002, 10002101, 10002222, 10010001, 10010012, 10010111, 10010201, 10010221, 10011002, 10011112, 10011121, 10012102, 10012122, 10012201, 10012221, 10020002, 10020022, 10020211, 10021001, 10021012, 10021021, 10021111, 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12111221, 12112011, 12112222, 12120001, 12120021, 12120212, 12121002, 12121112, 12121121, 12121211, 12122021, 12122212, 12122221, 12200002, 12200022, 12200211, 12200222, 12201001, 12201201, 12202121, 12202222, 12210012, 12210021, 12210122, 12210201, 12211002, 12211011, 12211112, 12211202, 12211211, 12212012, 12212021, 12212122, 12212212, 12220011, 12221021, 12221122, 12221201, 12222002, 12222101, 12222121, 12222222, 20000122, 20000212, 20001022, 20001202, 20001211, 20002111, 20002201, 20002212, 20010002, 20010022, 20010222, 20011001, 20011102, 20011221, 20012011, 20012022, 20012101, 20012112, 20020102, 20020111, 20020221, 20021011, 20021202, 20022001, 20022021, 20022111, 20100011, 20100202, 20100211, 20100222, 20101012, 20101021, 20101111, 20101201, 20102002, 20102022, 20102202, 20110012, 20110212, 20110221, 20111011, 20111022, 20111222, 20112021, 20120011, 20120022, 20120101, 20120112, 20120202, 20120211, 20121021, 20121102, 20121221, 20200001, 20200102, 20200122, 20201002, 20201121, 20201211, 20202012, 20202122, 20202201, 20202212, 20210002, 20210101, 20210121, 20210222, 20211001, 20211012, 20211201, 20211221, 20212011, 20212022, 20212112, 20212121, 20212222, 20220001, 20220122, 20221002, 20221101, 20222001, 20222012, 20222102, 20222212, 20222221, 21000011, 21000101, 21000121, 21001122, 21001212, 21002101, 21002112, 21002211, 21010012, 21010111, 21010221, 21011121, 21011202, 21011211, 21011222, 21012212, 21020022, 21020112, 21020121, 21021012, 21021102, 21021122, 21022011, 21022112, 21100001, 21100012, 21101022, 21101112, 21101202, 21101222, 21102021, 21102111, 21102122, 21102201, 21110011, 21110101, 21110112, 21110121, 21110211, 21111122, 21111212, 21111221, 21112002, 21112202, 21112211, 21112222, 21120102, 21120111, 21120201, 21120212, 21121211, 21122001, 21122021, 21122102, 21122201, 21200002, 21201021, 21201212, 21201221, 21202011, 21202022, 21202101, 21202112, 21202121, 21202222, 21210111, 21210201, 21210212, 21211011, 21211112, 21211202, 21212111, 21212122, 21212201, 21212221, 21221001, 21221012, 21221111, 21221212, 21222002, 21222022, 21222121, 21222211, 22000021, 22000102, 22000122, 22000201, 22000221, 22001002, 22001022, 22001101, 22001202, 22001211, 22002102, 22002122, 22010101, 22010112, 22010222, 22011111, 22012112, 22012202, 22020111, 22020122, 22021022, 22021121, 22021211, 22021222, 22022012, 22022201, 22022221, 22100011, 22100112, 22100121, 22100222, 22101102, 22101201, 22102002, 22102011, 22102112, 22102211, 22110021, 22110122, 22111112, 22111121, 22111202, 22112001, 22112021, 22112102, 22112201, 22120101, 22120202, 22120222, 22121012, 22121021, 22121111, 22121212, 22122022, 22122101, 22122202, 22122222, 22200012, 22200102, 22200201, 22200221, 22201022, 22201112, 22201121, 22201211, 22202001, 22202021, 22202122, 22202221, 22210211, 22211001, 22211212, 22211221, 22212121, 22212202, 22220001, 22220102, 22221112, 22221211, 22222111, 22222122, 22222201, 100000002, 100000022, 100000101, 100000121, 100000202, 100001102, 100001201, 100002011, 100002211, 100010102, 100010122, 100010201, 100011011, 100011101, 100011202, 100011211, 100012012, 100012021, 100012111, 100012212, 100020101, 100020112, 100021102, 100021111, 100022002, 100022011, 100022112, 100022121, 100022222, 100100201, 100100212, 100100221, 100101002, 100101101, 100101222, 100102012, 100102102, 100102111, 100102221, 100110112, 100110211, 100110222, 100111012, 100112022, 100112101, 100112202, 100112211, 100120001, 100120012, 100120102, 100120122, 100120221, 100121011, 100121022, 100121202, 100121222, 100122021, 100122201, 100122212, 100200101, 100200211, 100201012, 100202002, 100202022, 100202202, 100202222, 100210001, 100210212, 100211011, 100211211, 100212012, 100212102, 100212221, 100220002, 100220011, 100220101, 100220202, 100221001, 100221021, 100221102, 100221122, 100222202, 101000021, 101000122, 101000201, 101001011, 101001112, 101001121, 101002012, 101002021, 101002221, 101010211, 101011111, 101011201, 101012022, 101012222, 101020012, 101020021, 101020221, 101021002, 101021022, 101021101, 101021202, 101022001, 101022102, 101022122, 101022212, 101100011, 101100022, 101100112, 101100121, 101100222, 101101001, 101101111, 101101122, 101101212, 101102002, 101102011, 101102121, 101102202, 101110021, 101110221, 101111002, 101111022, 101112001, 101112012, 101112111, 101112201, 101112212, 101120011, 101120022, 101120211, 101121001, 101121012, 101121201, 101122011, 101122022, 101122101, 101200111, 101200122, 101201112, 101201202, 101201222, 101202102, 101202212, 101210101, 101210121, 101210202, 101210211, 101210222, 101211122, 101211212, 101212022, 101212121, 101212211, ...
4	11, 13, 23, 31, 101, 103, 113, 131, 133, 211, 221, 223, 233, 311, 323, 331, 1003, 1013, 1021, 1033, 1103, 1121, 1201, 1211, 1213, 1223, 1231, 1301, 1333, 2003, 2021, 2023, 2111, 2113, 2131, 2203, 2213, 2231, 2303, 2311, 2333, 3001, 3011, 3013, 3103, 3133, 3203, 3211, 3221, 3233, 3301, 3323, 10001, 10013, 10031, 10033, 10111, 10121, 10123, 10211, 10303, 10313, 10321, 10331, 11023, 11101, 11123, 11131, 11201, 11213, 11233, 11311, 11323, 11333, 12011, 12031, 12101, 12121, 12203, 12211, 12233, 12301, 12313, 12323, 13001, 13021, 13031, 13033, 13103, 13133, 13213, 13223, 13303, 13313, 13331, 20021, 20023, 20131, 20203, 20231, 20303, 20321, 20323, 21001, 21023, 21101, 21113, 21121, 21133, 21211, 21221, 21223, 21313, 22001, 22003, 22013, 22031, 22103, 22111, 22201, 22211, 22223, 22303, 22331, 23011, 23033, 23113, 23131, 23203, 23213, 23233, 23311, 23321, 30001, 30011, 30103, 30131, 30221, 30223, 30311, 30313, 30323, 30331, 31013, 31111, 31121, 31123, 31133, 31231, 31301, 31303, 31313, 32023, 32033, 32113, 32201, 32221, 32231, 32303, 32321, 33013, 33023, 33101, 33113, 33133, 33211, 33301, 33311, 33323, 33331, 100013, 100021, 100033, 100121, 100123, 100211, 100213, 100231, 100333, 101003, 101011, 101021, 101033, 101111, 101131, 101203, 101221, 101333, 102001, 102023, 102103, 102131, 102203, 102221, 102301, 102331, 103001, 103013, 103031, 103033, 103111, 103201, 103223, 103331, 103333, 110003, 110021, 110023, 110101, 110111, 110113, 110123, 110213, 110221, 110233, 111101, 111113, 111131, 111211, 111313, 112001, 112033, 112103, 112111, 112121, 112133, 112213, 112223, 112231, 112303, 112333, 113021, 113023, 113033, 113101, 113111, 113123, 113213, 113303, 113323, 120013, 120031, 120101, 120113, 120133, 120203, 120223, 120233, 120331, 121001, 121013, 121021, 121031, 121103, 121111, 121123, 121211, 121321, 121333, 122003, 122011, 122131, 122201, 122203, 122231, 122321, 122323, 123011, 123031, 123103, 123121, 123133, 123301, 123313, 123323, 123331, 130021, 130103, 130133, 130213, 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5	12, 21, 23, 32, 34, 43, 104, 111, 122, 131, 133, 142, 203, 214, 221, 232, 241, 243, 304, 313, 324, 342, 401, 403, 412, 414, 423, 1002, 1011, 1022, 1024, 1044, 1101, 1112, 1123, 1132, 1143, 1204, 1211, 1231, 1233, 1242, 1244, 1321, 1343, 1402, 1404, 1413, 1424, 1431, 2001, 2012, 2023, 2034, 2041, 2102, 2111, 2113, 2133, 2212, 2221, 2223, 2232, 2311, 2322, 2342, 2344, 2403, 2414, 2432, 2443, 3004, 3013, 3024, 3042, 3101, 3114, 3134, 3141, 3211, 3213, 3224, 3233, 3244, 3312, 3321, 3323, 3332, 3404, 3422, 3431, 3444, 4003, 4014, 4041, 4043, 4131, 4142, 4212, 4223, 4234, 4241, 4302, 4322, 4333, 4344, 4401, 4412, 4423, 4432, 4434, 10011, 10031, 10033, 10042, 10103, 10114, 10121, 10143, 10202, 10213, 10231, 10301, 10314, 10334, 10402, 10413, 10424, 10433, 11001, 11012, 11021, 11034, 11043, 11122, 11142, 11214, 11221, 11241, 11243, 11302, 11304, 11324, 11403, 11412, 11414, 11423, 12002, 12011, 12013, 12022, 12112, 12121, 12134, 12204, 12222, 12231, 12242, 12303, 12332, 12341, 12402, 12413, 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6	11, 15, 21, 25, 31, 35, 45, 51, 101, 105, 111, 115, 125, 135, 141, 151, 155, 201, 211, 215, 225, 241, 245, 251, 255, 301, 305, 331, 335, 345, 351, 405, 411, 421, 431, 435, 445, 455, 501, 515, 521, 525, 531, 551, 1011, 1015, 1021, 1025, 1035, 1041, 1055, 1105, 1115, 1125, 1131, 1141, 1145, 1151, 1205, 1231, 1235, 1241, 1245, 1311, 1321, 1335, 1341, 1345, 1355, 1411, 1421, 1431, 1435, 1445, 1501, 1505, 1521, 1535, 1541, 1555, 2001, 2011, 2015, 2025, 2041, 2045, 2051, 2055, 2115, 2131, 2135, 2151, 2155, 2205, 2225, 2231, 2301, 2311, 2325, 2335, 2345, 2351, 2401, 2415, 2425, 2435, 2441, 2451, 2501, 2505, 2511, 2531, 2545, 2551, 2555, 3005, 3015, 3021, 3041, 3045, 3055, 3111, 3125, 3141, 3155, 3211, 3221, 3231, 3235, 3251, 3301, 3305, 3321, 3325, 3351, 3405, 3425, 3431, 3445, 3451, 3455, 3501, 3515, 3541, 3545, 3551, 3555, 4021, 4025, 4031, 4035, 4111, 4115, 4131, 4145, 4201, 4205, 4215, 4225, 4251, 4255, 4305, 4315, 4331, 4341, 4401, 4405, 4415, 4421, 4435, 4441, 4451, 4505, 4511, 4525, 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23225, 23231, 23251, 23255, 23315, 23321, 23335, 23341, 23405, 23411, 23435, 23445, 23521, 23545, 24001, 24005, 24011, 24015, 24021, 24055, 24111, 24131, 24141, 24155, 24201, 24205, 24215, 24221, 24231, 24245, 24251, 24311, 24325, 24331, 24345, 24411, 24421, 24425, 24435, 24451, 24501, 24511, 24535, 24555, 25001, 25005, 25031, 25041, 25045, 25101, 25115, 25131, 25141, 25151, 25225, 25235, 25241, 25255, 25321, 25325, 25335, 25405, 25411, 25425, 25451, 25455, 25501, 25515, 25541, 25545, 30001, 30031, 30035, 30045, 30051, 30055, 30105, 30111, 30131, 30135, 30211, 30245, 30305, 30311, 30315, 30325, 30335, 30341, 30351, 30425, 30431, 30441, 30505, 30515, 30535, 30541, 30551, 31011, 31035, 31041, 31045, 31055, 31121, 31125, 31131, 31201, 31241, 31255, 31305, 31311, 31325, 31331, 31345, 31351, 31405, 31415, 31421, 31435, 31441, 31455, 31505, 31521, 32011, 32025, 32031, 32045, 32101, 32111, 32125, 32155, 32205, 32225, 32245, 32251, 32321, 32331, 32335, 32345, 32355, 32425, 32431, 32445, 32511, 32521, 32525, 32531, 32535, 33015, 33021, 33041, 33051, 33115, 33131, 33141, 33151, 33221, 33245, 33251, 33255, 33305, 33311, 33321, 33331, 33345, 33355, 33415, 33435, 33505, 33511, 33521, 33525, 33555, 34011, 34051, 34055, 34101, 34105, 34115, 34121, 34141, 34145, 34211, 34301, 34315, 34325, 34345, 34411, 34421, 34435, 34455, 34501, 34505, 34515, 34531, 34541, 34555, 35001, 35005, 35031, 35041, 35051, 35055, 35105, 35111, 35125, 35131, 35155, 35215, 35231, 35301, 35305, 35315, 35335, 35341, 35351, 35401, 35411, 35455, 35505, 35531, 35535, 35551, 40005, 40021, 40041, 40111, 40115, 40121, 40125, 40205, 40225, 40235, 40241, 40305, 40315, 40325, 40351, 40405, 40431, 40435, 40525, 40535, 40545, 40555, 41011, 41021, 41025, 41031, 41051, 41101, 41105, 41111, 41121, 41155, 41205, 41211, 41215, 41245, 41251, 41255, 41315, 41321, 41331, 41335, 41421, 41431, 41441, 41445, 41501, 41515, 42011, 42035, 42041, 42051, 42055, 42101, 42105, 42111, 42125, 42151, 42201, 42205, 42221, 42235, 42245, 42321, 42325, 42331, 42341, 42431, 42435, 42451, 42505, 42515, 42525, 42541, 42551, 43011, 43015, 43025, 43031, 43041, 43045, 43055, 43101, 43115, 43121, 43145, 43155, 43231, 43235, 43255, 43321, 43405, 43415, 43451, 43455, 43525, 43541, 43551, 43555, 44005, 44031, 44041, 44051, 44105, 44111, 44125, 44145, 44201, 44215, 44221, 44235, 44251, 44311, 44325, 44405, 44411, 44415, 44431, 44441, 44445, 44501, 44531, 44545, 44555, 45005, 45011, 45021, 45035, 45055, 45101, 45115, 45125, 45135, 45145, 45201, 45211, 45225, 45235, 45241, 45251, 45301, 45311, 45325, 45341, 45421, 45431, 45505, 45511, 45541, 45545, 50001, 50015, 50105, 50121, 50151, 50155, 50201, 50215, 50225, 50231, 50241, 50245, 50315, 50331, 50351, 50421, 50445, 50455, 50501, 50521, 50531, 50545, 50551, 51005, 51011, 51021, 51035, 51101, 51105, 51145, 51151, 51215, 51221, 51235, 51241, 51255, 51331, 51335, 51341, 51345, 51401, 51425, 51435, 51445, 51451, 51511, 51535, 51551, 51555, 52005, 52055, 52101, 52115, 52121, 52131, 52135, 52145, 52155, 52211, 52221, 52225, 52245, 52255, 52311, 52331, 52335, 52401, 52421, 52435, 52515, 52525, 52545, 52555, 53001, 53035, 53051, 53121, 53135, 53145, 53211, 53215, 53221, 53231, 53245, 53301, 53311, 53315, 53325, 53415, 53441, 53455, 53501, 53521, 53535, 53541, 54005, 54011, 54041, 54121, 54151, 54201, 54225, 54255, 54305, 54311, 54341, 54345, 54355, 54401, 54415, 54431, 54445, 54455, 54505, 54521, 54525, 54535, 54541, 54555, 55001, 55021, 55025, 55035, 55045, 55051, 55111, 55115, 55141, 55211, 55215, 55225, 55301, 55305, 55321, 55331, 55335, 55351, 55355, 55421, 55431, 55435, 55501, 55521, 55525, 55531, 100021, 100025, 100105, 100115, 100125, 100145, 100205, 100231, 100241, 100245, 100251, 100255, 100325, 100335, 100355, 100411, 100421, 100425, ...
7	14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 104, 113, 115, 124, 131, 133, 142, 146, 155, 166, 203, 205, 212, 214, 221, 241, 245, 254, 256, 302, 304, 313, 322, 326, 335, 344, 346, 362, 364, 401, 403, 421, 436, 443, 445, 452, 461, 463, 506, 515, 524, 533, 535, 544, 551, 553, 566, 616, 623, 625, 632, 652, 661, 1004, 1006, 1013, 1022, 1033, 1042, 1051, 1055, 1064, 1105, 1112, 1123, 1136, 1141, 1154, 1156, 1165, 1202, 1211, 1222, 1226, 1231, 1235, 1253, 1264, 1301, 1312, 1316, 1325, 1343, 1345, 1402, 1411, 1424, 1433, 1442, 1444, 1453, 1466, 1505, 1514, 1516, 1525, 1534, 1541, 1543, 1561, 1604, 1606, 1613, 1622, 1631, 1633, 1651, 1655, 1664, 2005, 2021, 2032, 2045, 2056, 2065, 2104, 2111, 2122, 2131, 2135, 2146, 2153, 2203, 2216, 2234, 2236, 2252, 2254, 2261, 2263, 2306, 2326, 2333, 2335, 2342, 2362, 2366, 2401, 2405, 2434, 2441, 2452, 2465, 2506, 2513, 2522, 2531, 2551, 2555, 2564, 2603, 2614, 2623, 2641, 2645, 2654, 2656, 3002, 3004, 3013, 3026, 3031, 3044, 3046, 3055, 3112, 3116, 3121, 3125, 3134, 3143, 3154, 3163, 3202, 3233, 3235, 3251, 3262, 3305, 3314, 3323, 3334, 3352, 3356, 3365, 3404, 3406, 3415, 3433, 3446, 3503, 3505, 3512, 3521, 3523, 3532, 3536, 3541, 3545, 3563, 3565, 3604, 3653, 3662, 4001, 4012, 4036, 4052, 4102, 4106, 4111, 4115, 4124, 4135, 4142, 4144, 4153, 4201, 4214, 4216, 4223, 4225, 4232, 4241, 4256, 4304, 4315, 4333, 4342, 4346, 4355, 4366, 4403, 4414, 4421, 4441, 4445, 4454, 4456, 4463, 4502, 4504, 4513, 4526, 4555, 4564, 4601, 4603, 4636, 4643, 4645, 4661, 5006, 5011, 5024, 5035, 5044, 5053, 5062, 5116, 5125, 5132, 5134, 5152, 5165, 5213, 5224, 5246, 5266, 5305, 5312, 5314, 5321, 5323, 5336, 5354, 5363, 5402, 5426, 5431, 5453, 5455, 5516, 5525, 5536, 5545, 5552, 5554, 5561, 5602, 5611, 5624, 5626, 5642, 5662, 6005, 6014, 6032, 6034, 6041, 6043, 6056, 6104, 6106, 6131, 6133, 6142, 6146, 6151, 6164, 6205, 6232, 6265, 6302, 6311, 6322, 6344, 6346, 6353, 6364, 6416, 6421, 6425, 6436, 6445, 6454, 6461, 6506, 6511, 6542, 6551, 6553, 6562, 6566, 6605, 6625, 6634, 6641, 6643, 6652, 6656, 6665, 10013, 10022, 10031, 10051, 10055, 10064, 10112, 10123, 10132, 10136, 10204, 10231, 10244, 10255, 10262, 10301, 10303, 10312, 10343, 10361, 10363, 10415, 10426, 10433, 10451, 10501, 10514, 10516, 10523, 10534, 10543, 10552, 10556, 10561, 10565, 10604, 10615, 10622, 10624, 10633, 10646, 10651, 10664, 11005, 11012, 11032, 11045, 11063, 11065, 11104, 11111, 11113, 11135, 11155, 11162, 11201, 11212, 11221, 11225, 11252, 11263, 11306, 11315, 11324, 11335, 11351, 11366, 11416, 11423, 11432, 11441, 11443, 11513, 11515, 11531, 11542, 11546, 11566, 11603, 11614, 11632, 11641, 11656, 11663, 12002, 12031, 12044, 12046, 12101, 12136, 12143, 12145, 12163, 12202, 12206, 12224, 12233, 12244, 12251, 12262, 12323, 12325, 12332, 12334, 12352, 12422, 12424, 12433, 12442, 12451, 12455, 12464, 12466, 12514, 12521, 12536, 12541, 12554, 12556, 12611, 12613, 12635, 12644, 13003, 13025, 13036, 13043, 13045, 13052, 13054, 13115, 13126, 13144, 13153, 13166, 13201, 13205, 13214, 13216, 13225, 13241, 13243, 13261, 13304, 13306, 13322, 13342, 13351, 13355, 13364, 13405, 13414, 13423, 13445, 13463, 13465, 13502, 13522, 13531, 13535, 13546, 13562, 13603, 13612, 13621, 13652, 13661, 13663, 14006, 14026, 14033, 14042, 14066, 14101, 14114, 14134, 14141, 14143, 14156, 14206, 14213, 14224, 14251, 14255, 14264, 14266, 14303, 14312, 14314, 14332, 14336, 14365, 14426, 14444, 14446, 14453, 14462, 14501, 14503, 14512, 14543, 14545, 14554, 14606, 14615, 14633, 14635, 14644, 14662, 15014, 15016, 15023, 15032, 15052, 15056, 15061, 15115, 15151, 15164, 15203, 15205, 15221, 15223, 15236, 15241, 15254, 15263, 15265, 15311, 15313, 15326, 15335, 15346, 15421, 15434, 15436, 15452, 15463, 15502, 15515, 15542, 15551, 15566, 15614, 15616, 15643, 15652, 15656, 15665, 16004, 16031, 16033, 16046, 16066, 16105, 16112, 16114, 16121, 16154, 16156, 16204, 16213, 16235, 16246, 16255, 16264, 16321, 16343, 16345, 16352, 16361, 16363, 16402, 16411, 16424, 16433, 16451, 16466, 16523, 16525, 16534, 16541, 16565, 16606, 16642, 16646, 16651, 16655, 16664, 16666, 20014, 20021, 20041, 20113, 20126, 20135, 20153, 20203, 20212, 20225, 20243, 20245, 20252, 20261, 20302, 20311, 20324, 20326, 20333, 20353, 20362, 20401, 20405, 20414, 20416, 20432, 20434, 20456, 20504, 20515, 20542, 20546, 20555, 20603, 20605, 20614, 20623, 20632, 21002, 21011, 21031, 21035, 21046, 21062, 21103, 21121, 21145, 21152, 21154, 21161, 21224, 21242, 21251, 21253, 21305, 21314, 21323, 21343, 21356, 21406, 21413, 21455, 21464, 21503, 21512, 21523, 21532, 21536, 21541, 21556, 21565, 21602, 21604, 21613, 21644, 21653, 21655, 21662, 22016, 22021, 22025, 22043, 22045, 22054, 22061, 22126, 22135, 22144, 22151, 22162, 22205, 22252, 22304, 22306, 22315, 22322, 22324, 22331, 22333, 22346, 22366, 22405, 22412, 22423, 22436, 22445, 22504, 22511, 22513, 22522, 22564, 22601, 22612, 22625, 22634, 22643, 22654, 22663, 23011, 23015, 23024, 23026, 23035, 23042, 23051, 23053, 23066, 23101, 23123, 23132, 23161, 23165, 23213, 23233, 23303, 23312, 23341, 23345, 23402, 23413, 23422, 23426, 23435, 23455, 23464, 23503, 23516, 23521, 23534, 23552, 23563, 23606, 23611, 23624, 23635, 23653, 23666, 24032, 24034, 24041, 24052, 24061, 24065, 24106, 24133, 24146, 24155, 24164, 24166, 24205, 24221, 24236, 24241, 24254, 24263, 24302, 24311, 24322, 24331, 24344, 24353, 24355, 24364, 24403, 24412, 24425, 24436, 24502, 24511, 24542, 24544, 24601, 24605, 24616, 24632, 25004, 25015, 25042, 25046, 25051, 25064, 25103, 25105, 25114, 25121, 25145, 25156, 25204, 25231, 25253, 25262, 25264, 25312, 25321, 25334, 25336, 25352, 25354, 25363, 25406, 25426, 25433, 25466, 25501, 25523, 25525, 25541, 25543, 25556, 25615, 25622, 25624, 25631, 25642, 25664, 26003, 26012, 26014, 26032, 26054, 26065, 26102, 26111, 26153, 26155, 26201, 26203, 26212, 26216, 26225, 26234, 26245, 26254, 26261, 26306, 26315, 26326, 26344, 26351, 26401, 26416, 26432, 26465, 26504, 26522, 26531, 26533, 26564, 26605, 26632, 26645, 26654, 30004, 30011, 30013, 30022, 30035, 30046, 30055, 30062, 30101, 30143, 30163, 30206, 30211, 30226, 30242, 30244, 30266, 30301, 30325, 30361, 30415, 30424, 30446, 30503, 30512, 30514, 30541, 30545, 30554, 30556, 30602, 30613, 30626, 30635, 30644, 30655, 30662, 31001, 31003, 31016, 31021, 31036, 31043, 31052, 31061, 31063, 31111, 31115, 31135, 31162, 31166, 31205, 31234, 31241, 31252, 31261, 31265, 31306, 31313, 31333, 31342, 31346, 31366, 31414, 31421, 31423, 31465, 31502, 31535, 31544, 31553, 31601, 31616, 31636, 31645, 31652, 31654, 31661, 32015, 32024, 32042, 32053, 32062, 32066, 32114, ...
8	13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 103, 107, 111, 117, 123, 131, 141, 145, 147, 153, 155, 161, 177, 203, 211, 213, 225, 227, 235, 243, 247, 255, 263, 265, 277, 301, 305, 307, 323, 337, 343, 345, 351, 357, 361, 373, 401, 407, 415, 417, 425, 431, 433, 445, 463, 467, 471, 475, 513, 521, 533, 535, 541, 547, 557, 565, 573, 577, 605, 615, 621, 631, 643, 645, 657, 661, 667, 673, 701, 711, 715, 717, 723, 737, 747, 753, 763, 767, 775, 1011, 1013, 1035, 1043, 1055, 1063, 1071, 1073, 1101, 1113, 1121, 1127, 1131, 1137, 1145, 1151, 1153, 1167, 1201, 1203, 1207, 1215, 1223, 1225, 1241, 1245, 1253, 1263, 1275, 1305, 1317, 1327, 1335, 1343, 1347, 1357, 1365, 1371, 1401, 1405, 1423, 1435, 1451, 1453, 1465, 1467, 1473, 1475, 1507, 1525, 1531, 1533, 1537, 1555, 1561, 1563, 1567, 1613, 1617, 1627, 1641, 1651, 1655, 1663, 1671, 1707, 1713, 1721, 1727, 1737, 1745, 1761, 1765, 1773, 1775, 2007, 2011, 2017, 2031, 2033, 2045, 2047, 2055, 2077, 2103, 2105, 2111, 2117, 2125, 2135, 2143, 2151, 2177, 2201, 2213, 2223, 2235, 2243, 2251, 2261, 2275, 2301, 2307, 2315, 2317, 2325, 2341, 2353, 2375, 2377, 2403, 2411, 2413, 2421, 2425, 2427, 2433, 2447, 2451, 2457, 2521, 2527, 2535, 2545, 2567, 2601, 2617, 2623, 2625, 2631, 2637, 2647, 2653, 2655, 2663, 2677, 2711, 2713, 2717, 2721, 2725, 2733, 2747, 2763, 2773, 3007, 3015, 3021, 3027, 3037, 3043, 3053, 3057, 3075, 3101, 3107, 3111, 3115, 3123, 3125, 3133, 3145, 3171, 3177, 3203, 3205, 3235, 3241, 3243, 3255, 3271, 3273, 3305, 3315, 3323, 3331, 3337, 3361, 3367, 3373, 3375, 3411, 3423, 3437, 3447, 3467, 3505, 3513, 3517, 3521, 3525, 3527, 3541, 3555, 3563, 3571, 3613, 3615, 3635, 3637, 3665, 3673, 3703, 3711, 3715, 3717, 3723, 3733, 3741, 3753, 3755, 3767, 4005, 4017, 4025, 4041, 4043, 4047, 4051, 4063, 4077, 4101, 4121, 4123, 4131, 4135, 4137, 4151, 4161, 4203, 4233, 4237, 4245, 4255, 4275, 4277, 4303, 4313, 4333, 4335, 4341, 4351, 4357, 4365, 4371, 4405, 4407, 4435, 4443, 4445, 4453, 4457, 4465, 4503, 4511, 4515, 4517, 4525, 4531, 4537, 4553, 4561, 4567, 4605, 4611, 4617, 4633, 4643, 4651, 4655, 4707, 4731, 4743, 4753, 4757, 4765, 4767, 4775, 5023, 5037, 5041, 5061, 5071, 5075, 5111, 5127, 5141, 5143, 5147, 5157, 5165, 5173, 5177, 5201, 5205, 5213, 5223, 5227, 5231, 5237, 5251, 5253, 5265, 5275, 5301, 5317, 5331, 5345, 5347, 5355, 5361, 5363, 5403, 5421, 5425, 5433, 5443, 5451, 5455, 5477, 5507, 5521, 5527, 5535, 5545, 5557, 5573, 5611, 5615, 5623, 5631, 5633, 5667, 5671, 5703, 5713, 5717, 5735, 5741, 5751, 5765, 5773, 6007, 6013, 6021, 6045, 6057, 6061, 6101, 6133, 6137, 6141, 6155, 6163, 6167, 6203, 6211, 6221, 6225, 6235, 6263, 6265, 6271, 6273, 6307, 6343, 6345, 6353, 6361, 6367, 6373, 6401, 6403, 6417, 6423, 6437, 6441, 6453, 6455, 6475, 6477, 6517, 6525, 6551, 6571, 6601, 6605, 6607, 6613, 6615, 6643, 6653, 6667, 6675, 6707, 6711, 6715, 6723, 6725, 6733, 6745, 6747, 6763, 6775, 6777, 7011, 7027, 7035, 7041, 7047, 7057, 7065, 7073, 7113, 7127, 7131, 7135, 7153, 7161, 7165, 7175, 7207, 7217, 7225, 7233, 7261, 7267, 7271, 7303, 7321, 7325, 7333, 7355, 7357, 7371, 7407, 7413, 7415, 7427, 7445, 7451, 7461, 7503, 7507, 7515, 7517, 7523, 7531, 7533, 7547, 7553, 7577, 7625, 7641, 7643, 7647, 7655, 7663, 7665, 7673, 7721, 7723, 7731, 7751, 7757, 7773, 7775, 10003, 10017, 10037, 10041, 10045, 10053, 10071, 10075, 10077, 10121, 10151, 10163, 10171, 10173, 10205, 10207, 10221, 10223, 10235, 10243, 10245, 10257, 10261, 10273, 10301, 10311, 10347, 10361, 10363, 10375, 10405, 10413, 10425, 10447, 10455, 10471, 10505, 10507, 10531, 10537, 10543, 10551, 10557, 10601, 10603, 10615, 10633, 10641, 10645, 10647, 10653, 10703, 10705, 10721, 10727, 10747, 10757, 10765, 10773, 11015, 11035, 11037, 11043, 11051, 11053, 11061, 11067, 11101, 11107, 11123, 11137, 11161, 11163, 11171, 11175, 11217, 11227, 11257, 11263, 11265, 11271, 11277, 11301, 11315, 11321, 11337, 11375, 11407, 11415, 11431, 11447, 11455, 11467, 11503, 11505, 11511, 11517, 11527, 11535, 11547, 11551, 11555, 11573, 11601, 11607, 11613, 11621, 11623, 11635, 11637, 11657, 11673, 11703, 11725, 11731, 11737, 11753, 11755, 11763, 11771, 11777, 12033, 12041, 12057, 12063, 12073, 12105, 12115, 12131, 12153, 12157, 12161, 12165, 12215, 12231, 12237, 12241, 12261, 12267, 12275, 12313, 12325, 12343, 12347, 12405, 12413, 12421, 12427, 12437, 12445, 12451, 12453, 12467, 12475, 12501, 12503, 12511, 12537, 12545, 12547, 12553, 12575, 12577, 12603, 12617, 12621, 12627, 12633, 12665, 12673, 12701, 12705, 12715, 12727, 12767, 13007, 13011, 13017, 13023, 13025, 13031, 13033, 13045, 13063, 13071, 13075, 13105, 13117, 13125, 13151, 13155, 13157, 13165, 13223, 13227, 13237, 13251, 13257, 13265, 13275, 13303, 13317, 13323, 13331, 13333, 13341, 13345, 13353, 13355, 13367, 13371, 13411, 13417, 13443, 13447, 13463, 13501, 13535, 13543, 13567, 13573, 13615, 13625, 13633, 13637, 13645, 13663, 13671, 13677, 13711, 13713, 13725, 13741, 13751, 13763, 13765, 13777, 14007, 14023, 14035, 14065, 14067, 14073, 14103, 14111, 14115, 14125, 14147, 14161, 14167, 14175, 14177, 14205, 14217, 14233, 14235, 14247, 14255, 14263, 14271, 14301, 14307, 14321, 14327, 14331, 14337, 14345, 14353, 14365, 14375, 14425, 14433, 14461, 14463, 14505, 14511, 14521, 14533, 14571, 14601, 14623, 14627, 14631, 14643, 14651, 14653, 14661, 14665, 14707, 14717, 14733, 14755, 14775, 15003, 15005, 15021, 15027, 15041, 15043, 15055, 15057, 15065, 15077, 15115, 15121, 15151, 15153, 15173, 15175, 15207, 15211, 15223, 15247, 15253, 15255, 15261, 15271, 15311, 15317, 15325, 15327, 15343, 15363, 15373, 15377, 15405, 15443, 15445, 15457, 15461, 15467, 15473, 15501, 15507, 15517, 15525, 15531, 15545, 15553, 15563, 15577, 15603, 15621, 15635, 15647, 15677, 15705, 15721, 15727, 15731, 15757, 15767, 16011, 16023, 16031, 16047, 16053, 16055, 16063, 16075, 16105, 16113, 16117, 16125, 16163, 16201, 16213, 16215, 16231, 16243, 16245, 16265, 16267, 16311, 16341, 16363, 16371, 16411, 16433, 16441, 16443, 16465, 16471, 16477, 16501, 16513, 16523, 16535, 16543, 16551, 16561, 16565, 16573, 16575, 16607, 16611, 16625, 16631, 16637, 16645, 16647, 16663, 16667, 16705, 16727, 16733, 16741, 16765, 16771, 17001, 17007, 17013, 17023, 17027, 17045, 17053, 17057, 17075, 17111, 17115, 17117, 17155, 17161, 17211, 17217, 17225, 17241, 17255, 17273, 17301, 17305, 17307, 17313, 17335, 17343, 17357, 17367, 17375, 17401, 17415, ...
9	12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 102, 108, 117, 122, 124, 128, 131, 135, 151, 155, 162, 164, 175, 177, 184, 201, 205, 212, 218, 221, 232, 234, 238, 241, 254, 267, 272, 274, 278, 285, 287, 308, 315, 322, 328, 331, 337, 342, 344, 355, 371, 375, 377, 382, 407, 414, 425, 427, 432, 438, 447, 454, 461, 465, 472, 481, 485, 504, 515, 517, 528, 531, 537, 542, 548, 557, 562, 564, 568, 582, 601, 605, 614, 618, 625, 638, 641, 661, 667, 678, 685, 702, 704, 711, 722, 728, 735, 737, 744, 751, 755, 757, 771, 782, 784, 788, 805, 812, 814, 827, 832, 838, 847, 858, 867, 878, 887, 1004, 1011, 1015, 1024, 1031, 1035, 1044, 1048, 1064, 1075, 1088, 1101, 1112, 1114, 1118, 1121, 1132, 1147, 1152, 1154, 1158, 1174, 1178, 1181, 1185, 1217, 1222, 1231, 1242, 1251, 1255, 1262, 1268, 1284, 1288, 1305, 1312, 1321, 1327, 1341, 1345, 1352, 1354, 1365, 1367, 1374, 1385, 1387, 1408, 1411, 1417, 1437, 1442, 1444, 1448, 1455, 1462, 1471, 1477, 1484, 1518, 1521, 1532, 1541, 1552, 1558, 1565, 1574, 1587, 1602, 1608, 1615, 1617, 1624, 1637, 1648, 1668, 1671, 1675, 1682, 1684, 1701, 1705, 1707, 1712, 1725, 1727, 1734, 1772, 1778, 1785, 1804, 1824, 1835, 1851, 1855, 1857, 1862, 1868, 1877, 1882, 1884, 2001, 2014, 2025, 2027, 2032, 2034, 2038, 2045, 2058, 2072, 2081, 2104, 2111, 2115, 2122, 2131, 2135, 2144, 2148, 2164, 2168, 2175, 2177, 2182, 2188, 2201, 2207, 2218, 2241, 2247, 2252, 2254, 2281, 2285, 2287, 2308, 2322, 2324, 2335, 2344, 2351, 2357, 2364, 2384, 2401, 2405, 2407, 2421, 2432, 2445, 2454, 2472, 2487, 2504, 2508, 2511, 2515, 2517, 2528, 2542, 2548, 2555, 2575, 2577, 2605, 2607, 2632, 2638, 2647, 2654, 2658, 2661, 2665, 2674, 2681, 2702, 2704, 2715, 2731, 2742, 2748, 2762, 2764, 2768, 2771, 2782, 2805, 2807, 2825, 2827, 2834, 2838, 2841, 2852, 2861, 2881, 3017, 3022, 3028, 3037, 3055, 3057, 3062, 3071, 3088, 3101, 3105, 3114, 3121, 3127, 3132, 3145, 3147, 3172, 3178, 3181, 3187, 3202, 3208, 3224, 3231, 3235, 3237, 3244, 3248, 3255, 3268, 3275, 3282, 3307, 3312, 3318, 3332, 3341, 3347, 3352, 3381, 3411, 3422, 3431, 3435, 3442, 3444, 3451, 3475, 3488, 3501, 3518, 3527, 3532, 3545, 3561, 3572, 3574, 3578, 3587, 3604, 3611, 3615, 3617, 3622, 3628, 3637, 3642, 3644, 3651, 3662, 3664, 3675, 3684, 3688, 3714, 3725, 3738, 3741, 3747, 3752, 3754, 3772, 3787, 3802, 3808, 3817, 3824, 3828, 3848, 3857, 3868, 3875, 3882, 4001, 4012, 4025, 4041, 4045, 4052, 4058, 4061, 4102, 4104, 4115, 4124, 4128, 4144, 4148, 4157, 4171, 4177, 4201, 4205, 4212, 4234, 4245, 4247, 4265, 4304, 4308, 4311, 4324, 4331, 4335, 4348, 4355, 4364, 4368, 4377, 4412, 4414, 4418, 4421, 4434, 4465, 4467, 4474, 4481, 4487, 4502, 4508, 4511, 4524, 4528, 4542, 4544, 4555, 4557, 4575, 4577, 4605, 4612, 4634, 4652, 4661, 4665, 4667, 4672, 4674, 4708, 4717, 4731, 4737, 4748, 4751, 4755, 4762, 4764, 4771, 4782, 4784, 4807, 4818, 4821, 4832, 4847, 4854, 4858, 4865, 4874, 4881, 4887, 5015, 5028, 5031, 5035, 5051, 5057, 5062, 5071, 5082, 5101, 5107, 5114, 5138, 5145, 5147, 5158, 5174, 5178, 5185, 5215, 5217, 5228, 5244, 5248, 5251, 5262, 5277, 5282, 5301, 5321, 5325, 5332, 5334, 5338, 5345, 5347, 5361, 5365, 5387, 5422, 5435, 5437, 5442, 5448, 5455, 5457, 5464, 5488, 5501, 5507, 5525, 5532, 5545, 5547, 5554, 5567, 5585, 5587, 5602, 5608, 5624, 5628, 5631, 5651, 5677, 5688, 5705, 5707, 5718, 5721, 5732, 5734, 5745, 5752, 5754, 5765, 5767, 5778, 5785, 5804, 5837, 5848, 5851, 5862, 5871, 5877, 5888, 6018, 6025, 6038, 6052, 6054, 6074, 6081, 6085, 6102, 6108, 6128, 6131, 6142, 6157, 6164, 6168, 6171, 6175, 6212, 6214, 6227, 6234, 6252, 6261, 6267, 6274, 6304, 6322, 6324, 6328, 6335, 6337, 6344, 6351, 6362, 6368, 6382, 6405, 6425, 6427, 6434, 6438, 6458, 6467, 6504, 6508, 6511, 6515, 6522, 6524, 6537, 6542, 6557, 6601, 6612, 6618, 6632, 6647, 6654, 6665, 6678, 6681, 6685, 6702, 6711, 6717, 6728, 6731, 6735, 6751, 6757, 6764, 6768, 6775, 6777, 6788, 6801, 6818, 6832, 6841, 6861, 6865, 6872, 6885, 6887, 7004, 7011, 7017, 7048, 7055, 7071, 7075, 7084, 7105, 7114, 7127, 7147, 7152, 7154, 7158, 7185, 7208, 7215, 7217, 7235, 7242, 7248, 7264, 7275, 7301, 7305, 7338, 7345, 7352, 7358, 7367, 7374, 7378, 7381, 7404, 7411, 7415, 7417, 7424, 7448, 7455, 7457, 7462, 7482, 7484, 7488, 7512, 7514, 7521, 7525, 7554, 7561, 7567, 7572, 7581, 7602, 7637, 7655, 7657, 7664, 7668, 7671, 7675, 7677, 7688, 7714, 7721, 7725, 7734, 7745, 7752, 7774, 7778, 7781, 7787, 7831, 7835, 7844, 7855, 7862, 7868, 7877, 7884, 8007, 8012, 8018, 8021, 8027, 8032, 8038, 8041, 8052, 8054, 8072, 8078, 8111, 8115, 8128, 8144, 8175, 8182, 8214, 8218, 8238, 8247, 8254, 8258, 8265, 8281, 8287, 8304, 8315, 8317, 8328, 8342, 8351, 8362, 8364, 8375, 8384, 8407, 8418, 8445, 8447, 8452, 8461, 8467, 8472, 8481, 8511, 8522, 8528, 8535, 8537, 8544, 8555, 8568, 8571, 8582, 8588, 8605, 8612, 8621, 8627, 8638, 8645, 8647, 8654, 8661, 8667, 8678, 8687, 8724, 8731, 8755, 8757, 8777, 8782, 8801, 8812, 8845, 8854, 8874, 8878, 8881, 10002, 10008, 10011, 10017, 10022, 10042, 10051, 10064, 10084, 10112, 10118, 10121, 10134, 10141, 10152, 10154, 10165, 10167, 10174, 10185, 10211, 10215, 10242, 10244, 10262, 10264, 10275, 10277, 10288, 10321, 10325, 10327, 10332, 10341, 10358, 10365, 10372, 10374, 10387, 10415, 10424, 10428, 10435, 10468, 10471, 10482, 10484, 10501, 10505, 10512, 10518, 10527, 10534, 10538, 10552, 10558, 10567, 10581, 10585, 10611, 10624, 10635, 10662, 10668, 10682, 10688, 10701, 10725, 10734, 10754, 10765, 10772, 10787, 10802, 10804, 10811, 10822, 10831, 10837, 10842, 10848, 10882, 11007, 11018, 11021, 11034, 11045, 11047, 11065, 11067, 11087, 11124, 11144, 11151, 11168, 11188, 11205, 11207, 11227, 11232, 11238, 11241, 11252, 11261, 11272, 11278, 11285, 11304, 11308, 11315, 11317, 11328, 11331, 11344, 11348, 11355, 11362, 11364, 11377, 11382, 11407, 11427, 11432, 11438, 11461, 11465, 11474, 11481, 11485, 11504, 11508, 11524, 11531, 11535, 11551, 11564, 11568, 11571, 11614, 11618, 11645, 11652, 11658, 11672, 11685, 11711, 11717, 11722, 11724, 11728, 11748, 11755, 11768, 11777, 11784, 11788, 11812, ...
10	11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, ...
11	12, 16, 18, 21, 27, 29, 34, 38, 3A, 43, 49, 54, 56, 61, 65, 67, 72, 76, 81, 89, 92, 94, 98, 9A, A3, 106, 10A, 115, 117, 126, 128, 133, 139, 142, 148, 153, 155, 164, 166, 16A, 171, 182, 193, 197, 199, 1A2, 1A8, 1AA, 209, 214, 21A, 225, 227, 232, 236, 238, 247, 25A, 263, 265, 269, 281, 287, 296, 298, 2A1, 2A7, 304, 30A, 315, 319, 324, 331, 335, 342, 351, 353, 362, 364, 36A, 373, 379, 386, 38A, 391, 395, 3A6, 403, 407, 414, 418, 423, 434, 436, 452, 458, 467, 472, 478, 47A, 485, 494, 49A, 4A5, 4A7, 502, 508, 511, 513, 524, 533, 535, 539, 544, 54A, 551, 562, 566, 571, 579, 588, 595, 5A4, 601, 607, 612, 616, 623, 629, 632, 63A, 643, 656, 665, 676, 678, 687, 689, 692, 694, 6A3, 706, 70A, 711, 715, 728, 731, 733, 737, 755, 759, 766, 775, 782, 786, 791, 797, 7AA, 803, 809, 814, 821, 827, 838, 841, 847, 849, 858, 85A, 865, 874, 876, 885, 887, 892, 8A9, 902, 904, 908, 913, 919, 926, 931, 937, 957, 959, 968, 975, 984, 98A, 995, 9A2, A03, A07, A12, A18, A1A, A25, A36, A45, A61, A63, A67, A72, A74, A7A, A83, A85, A89, A9A, AA1, AA7, 1028, 1033, 1039, 1046, 1062, 1071, 1084, 1088, 108A, 1093, 1099, 10A6, 10AA, 1101, 1107, 1118, 1127, 1129, 1132, 1134, 1138, 1143, 1154, 1165, 1172, 1183, 1189, 1192, 1198, 11A5, 11A9, 1206, 120A, 1222, 1226, 1231, 1233, 1237, 1242, 1244, 124A, 1259, 1277, 1282, 1286, 1288, 12AA, 1303, 1305, 1314, 1325, 1327, 1336, 1343, 1349, 1354, 135A, 1376, 1381, 1385, 1387, 1398, 13A7, 1408, 1415, 142A, 1442, 1448, 1451, 1453, 1457, 1459, 1468, 1479, 1484, 148A, 14A6, 14A8, 1512, 1514, 1534, 153A, 1547, 1552, 1556, 1558, 1561, 1569, 1574, 1583, 1585, 1594, 15A7, 1606, 1611, 1622, 1624, 1628, 162A, 1639, 164A, 1651, 1666, 1668, 1673, 1677, 1679, 1688, 1695, 1701, 1723, 1727, 1732, 173A, 1754, 1756, 175A, 1767, 1781, 1783, 1787, 1794, 179A, 17A5, 17A9, 180A, 1811, 1831, 1837, 1839, 1844, 1848, 1853, 1866, 1871, 1875, 1877, 1882, 1886, 1891, 18A2, 18A8, 1903, 1916, 191A, 1925, 1936, 1943, 1949, 1952, 1976, 1992, 19A1, 19A9, 1A02, 1A08, 1A0A, 1A15, 1A35, 1A46, 1A48, 1A62, 1A6A, 1A73, 1A84, 1A97, 1AA6, 1AA8, 2001, 2009, 2014, 201A, 2023, 2025, 2029, 2034, 2041, 2045, 2047, 2052, 2061, 2063, 2072, 207A, 2083, 2096, 20A5, 2106, 2108, 2113, 2117, 2119, 2133, 2146, 214A, 2155, 2162, 2168, 2171, 2188, 2195, 21A4, 21AA, 2205, 2212, 2221, 2232, 2245, 2249, 2254, 225A, 2261, 2287, 2289, 2298, 22A5, 22A9, 2311, 2315, 2322, 2333, 2339, 234A, 2353, 2359, 2377, 2386, 2388, 23A2, 2416, 241A, 2421, 2432, 2438, 2441, 2452, 2458, 2465, 2469, 2476, 2496, 2498, 24A1, 24A3, 2504, 252A, 2531, 2537, 2542, 2548, 2551, 2557, 2559, 256A, 2573, 2584, 2586, 2595, 2597, 2601, 2603, 2618, 2623, 2641, 2656, 2663, 2667, 2669, 2672, 2674, 2694, 26A1, 2702, 2708, 2717, 2719, 2722, 2728, 272A, 2735, 2744, 2746, 2757, 2766, 2768, 2777, 278A, 2795, 2799, 27A4, 2801, 2807, 2812, 2827, 2838, 283A, 2843, 2856, 2861, 2865, 2872, 2881, 2889, 2894, 289A, 290A, 2915, 2917, 2926, 2939, 2942, 2948, 2964, 2966, 2975, 2988, 2991, 2993, 29A2, 2A05, 2A09, 2A16, 2A32, 2A36, 2A41, 2A43, 2A47, 2A52, 2A54, 2A65, 2A69, 2A87, 2AA7, 3008, 300A, 3013, 3019, 3024, 3026, 3031, 3051, 3053, 3059, 3073, 3079, 308A, 3091, 3097, 30A8, 3112, 3114, 3118, 3123, 3136, 313A, 3141, 3158, 317A, 3189, 3194, 3196, 31A5, 31A7, 3206, 3208, 3217, 3222, 3224, 3233, 3235, 3244, 324A, 3257, 3284, 3293, 3295, 32A4, 3301, 3307, 3316, 3332, 3338, 3349, 335A, 3361, 3378, 3383, 3387, 3392, 3398, 3404, 3406, 3415, 3428, 3433, 3437, 3439, 3442, 3464, 3466, 3477, 3482, 3497, 34A4, 34AA, 3505, 3521, 3536, 3538, 3541, 3547, 3549, 3554, 355A, 3569, 3574, 3585, 3596, 3602, 3604, 360A, 3613, 362A, 3637, 3659, 3662, 3664, 3668, 3673, 3675, 3686, 368A, 36A2, 371A, 3729, 3734, 3745, 3758, 3763, 3772, 3783, 3785, 3789, 3794, 37A1, 37A7, 3806, 3808, 3811, 3824, 382A, 3835, 3839, 3844, 3846, 3855, 3857, 3871, 3882, 388A, 38A6, 38AA, 3905, 3916, 3918, 3923, 3929, 3934, 395A, 3965, 3978, 3981, 3989, 3998, 39A5, 3A06, 3A22, 3A26, 3A28, 3A31, 3A53, 3A64, 3A6A, 3A71, 3A86, 3A91, 3A97, 3AAA, 4009, 4021, 4025, 4052, 4058, 4063, 4069, 4076, 4081, 4085, 4087, 4098, 40A3, 40A7, 40A9, 4104, 4124, 412A, 4131, 4135, 4151, 4153, 4157, 4168, 416A, 4175, 4179, 41A2, 41A8, 4203, 4207, 4214, 4223, 4252, 4267, 4269, 4274, 4278, 427A, 4283, 4285, 4294, 42A7, 4302, 4306, 4313, 4322, 4328, 4346, 434A, 4351, 4357, 4384, 4388, 4395, 43A4, 43AA, 4405, 4412, 4418, 4429, 4432, 4438, 443A, 4445, 4449, 4454, 4456, 4465, 4467, 4481, 4487, 44A5, 44A9, 450A, 4522, 4548, 4553, 4571, 4575, 4591, 4599, 45A4, 45A8, 4603, 4616, 4621, 4627, 4636, 4638, 4647, 4658, 4665, 4674, 4676, 4685, 4692, 46A3, 4702, 4724, 4726, 472A, 4737, 4742, 4746, 4753, 476A, 4779, 4784, 478A, 4791, 4797, 47A6, 4807, 4809, 4818, 4823, 4829, 4834, 4841, 4847, 4856, 4861, 4863, 4869, 4874, 487A, 4889, 4896, 4908, 4913, 4933, 4935, 4951, 4955, 4962, 4971, 4999, 49A6, 4A12, 4A16, 4A18, 4A27, 4A32, 4A34, 4A3A, 4A43, 4A5A, 4A67, 4A78, 4A94, 4AA9, 5004, 5006, 5017, 5022, 5031, 5033, 5042, 5044, 504A, 5059, 5071, 5075, 5097, 5099, 5103, 5105, 5114, 5116, 5125, 5143, 5147, 5149, 5152, 515A, 5174, 517A, 5185, 5187, 5198, 5202, 520A, 5213, 5219, 5246, 5248, 5257, 5259, 5264, 5268, 5273, 5279, 5286, 5291, 5295, 52A6, 5301, 5309, 531A, 5323, 5336, 5347, 5356, 5378, 5383, 5394, 539A, 53A1, 5411, 5419, 5435, 5444, 544A, 5462, 5466, 5468, 5473, 5482, 548A, 5495, 5499, 54A4, 5521, 5534, 5543, 5545, 5556, 5565, 5567, 5581, 5583, 559A, 5611, 5628, 5633, 5648, 5664, 566A, 5671, 5688, 5691, 5697, 5699, 56A8, 5705, 5714, 571A, 5725, 5732, 5736, 5741, 5743, 5752, 5754, 5765, 5769, 5774, 577A, 5781, 5792, 5796, 57A9, 5815, 5819, 5824, 5842, 5846, 5853, 5859, 5862, 586A, 5873, 5886, 5891, 5895, 58A8, 5909, 5912, 5914, 5941, 5945, 5967, 5972, 5978, 5989, 599A, 5A02, 5A08, 5A11, 5A13, 5A17, 5A33, 5A39, 5A4A, 5A57, 5A62, 5A66, 5A77, 5A79, ...
12	11, 15, 17, 1B, 25, 27, 31, 35, 37, 3B, 45, 4B, 51, 57, 5B, 61, 67, 6B, 75, 81, 85, 87, 8B, 91, 95, A7, AB, B5, B7, 105, 107, 111, 117, 11B, 125, 12B, 131, 13B, 141, 145, 147, 157, 167, 16B, 171, 175, 17B, 181, 18B, 195, 19B, 1A5, 1A7, 1B1, 1B5, 1B7, 205, 217, 21B, 221, 225, 237, 241, 24B, 251, 255, 25B, 267, 271, 277, 27B, 285, 291, 295, 2A1, 2AB, 2B1, 2BB, 301, 307, 30B, 315, 321, 325, 327, 32B, 33B, 347, 34B, 357, 35B, 365, 375, 377, 391, 397, 3A5, 3AB, 3B5, 3B7, 401, 40B, 415, 41B, 421, 427, 431, 435, 437, 447, 455, 457, 45B, 465, 46B, 471, 481, 485, 48B, 497, 4A5, 4B1, 4BB, 507, 511, 517, 51B, 527, 531, 535, 541, 545, 557, 565, 575, 577, 585, 587, 58B, 591, 59B, 5B1, 5B5, 5B7, 5BB, 611, 615, 617, 61B, 637, 63B, 647, 655, 661, 665, 66B, 675, 687, 68B, 695, 69B, 6A7, 6B1, 701, 705, 70B, 711, 71B, 721, 727, 735, 737, 745, 747, 751, 767, 76B, 771, 775, 77B, 785, 791, 797, 7A1, 7BB, 801, 80B, 817, 825, 82B, 835, 841, 851, 855, 85B, 865, 867, 871, 881, 88B, 8A5, 8A7, 8AB, 8B5, 8B7, 901, 905, 907, 90B, 91B, 921, 927, 955, 95B, 965, 971, 987, 995, 9A7, 9AB, 9B1, 9B5, 9BB, A07, A0B, A11, A17, A27, A35, A37, A3B, A41, A45, A4B, A5B, A6B, A77, A87, A91, A95, A9B, AA7, AAB, AB7, ABB, B11, B15, B1B, B21, B25, B2B, B31, B37, B45, B61, B67, B6B, B71, B91, B95, B97, BA5, BB5, BB7, 1005, 1011, 1017, 1021, 1027, 1041, 1047, 104B, 1051, 1061, 106B, 107B, 1087, 109B, 10B1, 10B7, 10BB, 1101, 1105, 1107, 1115, 1125, 112B, 1135, 114B, 1151, 1165, 1167, 1185, 118B, 1197, 11A1, 11A5, 11A7, 11AB, 11B7, 1201, 120B, 1211, 121B, 1231, 123B, 1245, 1255, 1257, 125B, 1261, 126B, 127B, 1281, 1295, 1297, 12A1, 12A5, 12A7, 12B5, 1301, 1317, 1337, 133B, 1345, 1351, 1365, 1367, 136B, 1377, 138B, 1391, 1395, 13A1, 13A7, 13B1, 13B5, 1405, 1407, 1425, 142B, 1431, 1437, 143B, 1445, 1457, 1461, 1465, 1467, 1471, 1475, 147B, 148B, 1495, 149B, 14B1, 14B5, 14BB, 150B, 1517, 1521, 1525, 1547, 1561, 156B, 1577, 157B, 1585, 1587, 1591, 15AB, 15BB, 1601, 1615, 1621, 1625, 1635, 1647, 1655, 1657, 165B, 1667, 1671, 1677, 167B, 1681, 1685, 168B, 1697, 169B, 16A1, 16A7, 16B5, 16B7, 1705, 1711, 1715, 1727, 1735, 1745, 1747, 1751, 1755, 1757, 176B, 1781, 1785, 178B, 1797, 17A1, 17A5, 17BB, 1807, 1815, 181B, 1825, 1831, 183B, 184B, 1861, 1865, 186B, 1875, 1877, 189B, 18A1, 18AB, 18B7, 18BB, 1911, 1915, 1921, 1931, 1937, 1947, 194B, 1955, 1971, 197B, 1981, 1995, 19B7, 19BB, 1A01, 1A11, 1A17, 1A1B, 1A2B, 1A35, 1A41, 1A45, 1A51, 1A6B, 1A71, 1A75, 1A77, 1A87, 1AAB, 1AB1, 1AB7, 1B01, 1B07, 1B0B, 1B15, 1B17, 1B27, 1B2B, 1B3B, 1B41, 1B4B, 1B51, 1B65, 1B67, 1B7B, 1B85, 1BA1, 1BB5, 2001, 2005, 2007, 200B, 2011, 202B, 2037, 2047, 2051, 205B, 2061, 2065, 206B, 2071, 2077, 2085, 2087, 2097, 20A5, 20A7, 20B5, 2107, 2111, 2115, 211B, 2127, 2131, 2137, 214B, 215B, 2161, 2165, 2177, 2181, 2185, 2191, 219B, 21A7, 21B1, 21B7, 2215, 221B, 2221, 222B, 2241, 2245, 224B, 2265, 2267, 2275, 2287, 228B, 2291, 229B, 22B1, 22B5, 2301, 2317, 231B, 2325, 2327, 232B, 2335, 2337, 2347, 234B, 2367, 2385, 2395, 2397, 239B, 23A5, 23AB, 23B1, 23B7, 2415, 2417, 2421, 2435, 243B, 244B, 2451, 2457, 2467, 247B, 2481, 2485, 248B, 24A1, 24A5, 24A7, 2501, 2521, 252B, 2535, 2537, 2545, 2547, 2555, 2557, 2565, 256B, 2571, 257B, 2581, 258B, 2595, 25A1, 2607, 2615, 2617, 2625, 2631, 2637, 2645, 265B, 2665, 2675, 2685, 2687, 26A1, 26A7, 26AB, 26B5, 26BB, 2715, 2717, 2725, 2737, 2741, 2745, 2747, 274B, 276B, 2771, 2781, 2787, 279B, 27A7, 27B1, 27B7, 2811, 2825, 2827, 282B, 2835, 2837, 2841, 2847, 2855, 285B, 286B, 287B, 2895, 2897, 28A1, 28A5, 28BB, 2907, 2927, 292B, 2931, 2935, 293B, 2941, 2951, 2955, 2967, 2991, 299B, 29A5, 29B5, 2A07, 2A11, 2A1B, 2A2B, 2A31, 2A35, 2A3B, 2A47, 2A51, 2A5B, 2A61, 2A65, 2A77, 2A81, 2A87, 2A8B, 2A95, 2A97, 2AA5, 2AA7, 2ABB, 2B0B, 2B17, 2B31, 2B35, 2B3B, 2B4B, 2B51, 2B57, 2B61, 2B67, 2B8B, 2B95, 2BA7, 2BAB, 2BB7, 3005, 3011, 3021, 3037, 303B, 3041, 3045, 3065, 3075, 307B, 3081, 3095, 309B, 30A5, 30B7, 3105, 3117, 311B, 3145, 314B, 3155, 315B, 3167, 3171, 3175, 3177, 3187, 3191, 3195, 3197, 31A1, 31BB, 3205, 3207, 320B, 3225, 3227, 322B, 323B, 3241, 3247, 324B, 3271, 3277, 3281, 3285, 3291, 329B, 3307, 331B, 3321, 3327, 332B, 3331, 3335, 3337, 3345, 3357, 3361, 3365, 3371, 337B, 3385, 33A1, 33A5, 33A7, 33B1, 3417, 341B, 3427, 3435, 343B, 3445, 3451, 3457, 3467, 346B, 3475, 3477, 3481, 3485, 348B, 3491, 349B, 34A1, 34B5, 34BB, 3517, 351B, 352B, 3541, 3565, 356B, 3587, 358B, 35A5, 35B1, 35B7, 35BB, 3605, 3617, 3621, 3627, 3635, 3637, 3645, 3655, 3661, 366B, 3671, 367B, 3687, 3697, 36A5, 3705, 3707, 370B, 3717, 3721, 3725, 3731, 3747, 3755, 375B, 3765, 3767, 3771, 377B, 378B, 3791, 379B, 37A5, 37AB, 37B5, 3801, 3807, 3815, 381B, 3821, 3827, 3831, 3837, 3845, 3851, 3871, 3877, 3895, 3897, 38B1, 38B5, 3901, 390B, 3935, 3941, 3957, 395B, 3961, 396B, 3975, 3977, 3981, 3985, 399B, 39A7, 39B7, 3A11, 3A25, 3A2B, 3A31, 3A41, 3A47, 3A55, 3A57, 3A65, 3A67, 3A71, 3A7B, 3A91, 3A95, 3AB5, 3AB7, 3B0B, 3B11, 3B1B, 3B21, 3B2B, 3B47, 3B4B, 3B51, 3B55, 3B61, 3B75, 3B7B, 3B85, 3B87, 3B97, 3BAB, 3BB7, 3BBB, 4005, 402B, 4031, 403B, 4041, 4047, 404B, 4055, 405B, 4067, 4071, 4075, 4085, 408B, 4097, 40A7, 40AB, 4101, 4111, 411B, 413B, 4145, 4155, 415B, 4161, 417B, 4187, 41A1, 41AB, 41B5, 4207, 420B, 4211, 4217, 4225, 4231, 4237, 423B, 4245, 426B, 4281, 428B, 4291, 42A1, 42AB, 42B1, 4305, 4307, 4321, 4341, 4357, 4361, 4375, 438B, 4395, 4397, 43B1, 43B5, 43BB, 4401, 440B, 4417, 4425, 442B, 4435, 4441, 4445, 444B, 4451, 445B, 4461, 4471, 4475, 447B, 4485, 4487, 4497, 449B, 44B1, 4507, 450B, 4515, 4531, 4535, 4541, 4547, 454B, 4557, 455B, 4571, 4577, 457B, 4591, 45A1, 45A5, 45A7, 4611, 4615, 4635, 463B, 4645, 4655, 4665, 4677, 4681, 4685, 4687, 468B, 46A5, 46AB, 46BB, 4707, 4711, 4715, 4725, 4727, ...
13	14, 16, 1A, 23, 25, 2B, 32, 34, 38, 41, 47, 49, 52, 56, 58, 61, 65, 6B, 76, 7A, 7C, 83, 85, 89, 9A, A1, A7, A9, B6, B8, C1, C7, CB, 104, 10A, 10C, 119, 11B, 122, 124, 133, 142, 146, 148, 14C, 155, 157, 164, 16A, 173, 179, 17B, 184, 188, 18A, 197, 1A8, 1AC, 1B1, 1B5, 1C6, 1CC, 209, 20B, 212, 218, 223, 229, 232, 236, 23C, 247, 24B, 256, 263, 265, 272, 274, 27A, 281, 287, 292, 296, 298, 29C, 2AB, 2B6, 2BA, 2C5, 2C9, 302, 311, 313, 328, 331, 33B, 344, 34A, 34C, 355, 362, 368, 371, 373, 379, 382, 386, 388, 397, 3A4, 3A6, 3AA, 3B3, 3B9, 3BB, 3CA, 401, 407, 412, 41C, 427, 434, 43C, 445, 44B, 452, 45A, 463, 467, 472, 476, 487, 494, 4A3, 4A5, 4B2, 4B4, 4B8, 4BA, 4C7, 508, 50C, 511, 515, 526, 52A, 52C, 533, 54A, 551, 559, 566, 571, 575, 57B, 584, 595, 599, 5A2, 5A8, 5B3, 5B9, 5C8, 5CC, 605, 607, 614, 616, 61C, 629, 62B, 638, 63A, 643, 658, 65C, 661, 665, 66B, 674, 67C, 685, 68B, 6A7, 6A9, 6B6, 6C1, 6CB, 704, 70A, 715, 724, 728, 731, 737, 739, 742, 751, 75B, 773, 775, 779, 782, 784, 78A, 791, 793, 797, 7A6, 7A8, 7B1, 809, 812, 818, 823, 838, 845, 856, 85A, 85C, 863, 869, 874, 878, 87A, 883, 892, 89C, 8A1, 8A5, 8A7, 8AB, 8B4, 8C3, 902, 90A, 919, 922, 926, 92C, 937, 93B, 946, 94A, 95B, 962, 968, 96A, 971, 977, 979, 982, 98C, 9A6, 9AC, 9B3, 9B5, A03, A07, A09, A16, A25, A27, A34, A3C, A45, A4B, A54, A69, A72, A76, A78, A87, A94, AA3, AAB, AC1, B02, B08, B0C, B11, B15, B17, B24, B33, B39, B42, B57, B59, B6C, B71, B8A, B93, B9B, BA4, BA8, BAA, BB1, BB9, BC2, BCC, C01, C0B, C1C, C29, C32, C41, C43, C47, C49, C56, C65, C67, C7A, C7C, C85, C89, C8B, C98, CA3, CB8, 1006, 100A, 1013, 101B, 1031, 1033, 1037, 1042, 1055, 1057, 105B, 1066, 106C, 1075, 1079, 1088, 108A, 10A6, 10AC, 10B1, 10B7, 10BB, 10C4, 1105, 110B, 1112, 1114, 111A, 1121, 1127, 1136, 113C, 1145, 1156, 115A, 1163, 1172, 117A, 1183, 1187, 11A7, 11BC, 11C9, 1204, 1208, 1211, 1213, 1219, 1235, 1244, 1246, 1259, 1264, 1268, 1277, 1288, 1295, 1297, 129B, 12A6, 12AC, 12B5, 12B9, 12BB, 12C2, 12C8, 1303, 1307, 1309, 1312, 131C, 1321, 132B, 1336, 133A, 134B, 1358, 1367, 1369, 1372, 1376, 1378, 138B, 139C, 13A3, 13A9, 13B4, 13BA, 13C1, 1406, 1411, 141B, 1424, 142A, 1435, 1442, 1451, 1462, 1466, 146C, 1475, 1477, 1499, 149B, 14A8, 14B3, 14B7, 14C8, 14CC, 1507, 1516, 151C, 152B, 1532, 1538, 1552, 155C, 1561, 1574, 1594, 1598, 159A, 15A9, 15B2, 15B6, 15C5, 15CB, 1606, 160A, 1615, 1631, 1633, 1637, 1639, 1648, 166A, 166C, 1675, 167B, 1684, 1688, 1691, 1693, 16A2, 16A6, 16B5, 16B7, 16C4, 16C6, 1709, 170B, 1721, 1727, 1741, 1754, 175C, 1763, 1765, 1769, 176B, 1787, 1792, 17A1, 17A7, 17B4, 17B6, 17BA, 17C3, 17C5, 17CB, 1808, 180A, 1819, 1826, 1828, 1835, 1846, 184C, 1853, 1859, 1864, 186A, 1873, 1886, 1895, 1897, 189B, 18AC, 18B5, 18B9, 18C4, 1901, 1909, 1912, 1918, 1934, 193A, 193C, 1949, 195A, 1961, 1967, 197C, 1981, 198B, 199C, 19A3, 19A5, 19B2, 19C3, 19C7, 1A02, 1A17, 1A1B, 1A24, 1A26, 1A2A, 1A33, 1A35, 1A44, 1A48, 1A62, 1A7B, 1A8A, 1A8C, 1A93, 1A99, 1AA2, 1AA4, 1AAA, 1AC6, 1AC8, 1B01, 1B14, 1B1A, 1B29, 1B2B, 1B34, 1B43, 1B56, 1B58, 1B5C, 1B65, 1B76, 1B7A, 1B7C, 1B94, 1BB2, 1BBC, 1BC5, 1BC7, 1C04, 1C06, 1C13, 1C15, 1C22, 1C28, 1C2A, 1C37, 1C39, 1C46, 1C4C, 1C57, 1C7B, 1C88, 1C8A, 1C97, 1CA2, 1CA8, 1CB5, 1CCA, 2003, 2012, 2021, 2023, 2038, 2041, 2045, 204B, 2054, 2069, 206B, 2078, 2089, 2092, 2096, 2098, 209C, 20BA, 20BC, 20CB, 2104, 2117, 2122, 2128, 2131, 2146, 2159, 215B, 2162, 2168, 216A, 2173, 2179, 2186, 218C, 219B, 21AA, 21C2, 21C4, 21CA, 2201, 2216, 2221, 223C, 2243, 2245, 2249, 2252, 2254, 2263, 2267, 2278, 229C, 22A9, 22B2, 22C1, 2302, 2308, 2315, 2324, 2326, 232A, 2333, 233B, 2344, 2351, 2353, 2357, 2368, 2371, 2377, 237B, 2384, 2386, 2393, 2395, 23A8, 23B7, 23C2, 2407, 240B, 2414, 2423, 2425, 242B, 2434, 243A, 245C, 2465, 2476, 247A, 2485, 2492, 249A, 24A9, 24C1, 24C5, 24C7, 24CB, 2519, 2528, 2531, 2533, 2546, 254C, 2555, 2566, 2573, 2584, 2588, 25AC, 25B5, 25BB, 25C4, 25CC, 2605, 2609, 260B, 261A, 2623, 2627, 2629, 2632, 264B, 2654, 2656, 265A, 2672, 2674, 2678, 2687, 2689, 2692, 2696, 26B6, 26BC, 26C5, 26C9, 2704, 2711, 2737, 274A, 274C, 2755, 2759, 275B, 2762, 2764, 2771, 2782, 2788, 278C, 2797, 27A4, 27AA, 27C4, 27C8, 27CA, 2803, 2827, 282B, 2836, 2843, 2849, 2852, 285A, 2863, 2872, 2876, 287C, 2881, 2887, 288B, 2894, 2896, 28A3, 28A5, 28B8, 28C1, 2908, 290C, 291B, 292C, 2951, 2957, 2971, 2975, 298A, 2995, 299B, 29A2, 29A8, 29B9, 29C2, 29C8, 2A05, 2A07, 2A14, 2A23, 2A2B, 2A38, 2A3A, 2A47, 2A52, 2A61, 2A6B, 2A89, 2A8B, 2A92, 2A9A, 2AA3, 2AA7, 2AB2, 2AC7, 2B04, 2B0A, 2B13, 2B15, 2B1B, 2B28, 2B37, 2B39, 2B46, 2B4C, 2B55, 2B5B, 2B66, 2B6C, 2B79, 2B82, 2B84, 2B8A, 2B93, 2B99, 2BA6, 2BB1, 2BCC, 2C05, 2C21, 2C23, 2C38, 2C3C, 2C47, 2C54, 2C78, 2C83, 2C98, 2C9C, 2CA1, 2CAB, 2CB4, 2CB6, 2CBC, 2CC3, 3008, 3013, 3022, 3037, 304A, 3053, 3055, 3064, 306A, 3077, 3079, 3086, 3088, 3091, 309B, 30AC, 30B3, 3101, 3103, 3116, 3118, 3125, 3127, 3134, 314B, 3152, 3154, 3158, 3163, 3176, 317C, 3185, 3187, 3196, 31A9, 31B4, 31B8, 31C1, 3215, 3217, 3224, 3226, 322C, 3233, 3239, 3242, 324A, 3253, 3257, 3266, 326C, 3277, 3286, 328A, 329B, 32AA, 32B7, 3305, 330B, 331A, 3323, 3325, 3341, 3349, 3361, 336B, 3374, 3385, 3389, 338B, 3394, 33A1, 33A9, 33B2, 33B6, 33BC, 3413, 3424, 3431, 3433, 3442, 344C, 3451, 3464, 3466, 347B, 3499, 34B1, 34B7, 34CA, 3512, 3518, 351A, 3532, 3536, 353C, 3541, 354B, 3556, 3563, 3569, 3572, 357A, 3581, 3587, 3589, 3596, 3598, 35A7, 35AB, 35B4, 35BA, 35BC, 35CB, 3602, 3613, 3628, 362C, 3635, 364C, 3653, 365B, 3664, 3668, 3673, 3677, 3688, 3691, 3695, 36A6, 36B5, 36B9, 36BB, 3712, 3716, 3734, 373A, 3743, 3752, 3761, 3772, 3778, 377C, 3781, 3785, 379A, 37A3, 37B2, 37BA, 37C3, 37C7, 3806, 3808, 3817, ...
14	13, 15, 19, 21, 23, 29, 2D, 31, 35, 3B, 43, 45, 4B, 51, 53, 59, 5D, 65, 6D, 73, 75, 79, 7B, 81, 91, 95, 9B, 9D, A9, AB, B3, B9, BD, C5, CB, CD, D9, DB, 101, 103, 111, 11D, 123, 125, 129, 131, 133, 13D, 145, 14B, 153, 155, 15B, 161, 163, 16D, 17D, 183, 185, 189, 199, 1A1, 1AB, 1AD, 1B3, 1B9, 1C3, 1C9, 1D1, 1D5, 1DB, 205, 209, 213, 21D, 221, 22B, 22D, 235, 239, 241, 249, 24D, 251, 255, 263, 26B, 271, 279, 27D, 285, 293, 295, 2A9, 2B1, 2BB, 2C3, 2C9, 2CB, 2D3, 2DD, 305, 30B, 30D, 315, 31B, 321, 323, 331, 33B, 33D, 343, 349, 351, 353, 361, 365, 36B, 375, 381, 389, 395, 39D, 3A5, 3AB, 3B1, 3B9, 3C1, 3C5, 3CD, 3D3, 403, 40D, 41B, 41D, 429, 42B, 431, 433, 43D, 44D, 453, 455, 459, 469, 46D, 471, 475, 48B, 491, 499, 4A5, 4AD, 4B3, 4B9, 4C1, 4D1, 4D5, 4DB, 503, 50B, 513, 521, 525, 52B, 52D, 539, 53B, 543, 54D, 551, 55B, 55D, 565, 579, 57D, 581, 585, 58B, 593, 59B, 5A3, 5A9, 5C3, 5C5, 5D1, 5D9, 605, 60B, 613, 61B, 629, 62D, 635, 63B, 63D, 645, 653, 65D, 673, 675, 679, 681, 683, 689, 68D, 691, 695, 6A3, 6A5, 6AB, 6D3, 6D9, 701, 709, 71D, 729, 739, 73D, 741, 745, 74B, 755, 759, 75B, 763, 771, 77B, 77D, 783, 785, 789, 791, 79D, 7AB, 7B5, 7C3, 7C9, 7CD, 7D5, 7DD, 803, 80B, 811, 821, 825, 82B, 82D, 833, 839, 83B, 843, 84D, 865, 86B, 871, 873, 88D, 893, 895, 8A1, 8AD, 8B1, 8BB, 8C5, 8CB, 8D3, 8D9, 90D, 915, 919, 91B, 929, 935, 943, 94B, 95D, 96D, 975, 979, 97B, 981, 983, 98D, 99B, 9A3, 9A9, 9BD, 9C1, 9D3, 9D5, A0D, A15, A1D, A25, A29, A2B, A31, A39, A41, A4B, A4D, A59, A69, A75, A7B, A89, A8B, A91, A93, A9D, AAB, AAD, AC1, AC3, AC9, ACD, AD1, ADB, B05, B19, B35, B39, B41, B49, B5B, B5D, B63, B6B, B7D, B81, B85, B8D, B95, B9B, BA1, BAD, BB1, BC9, BD1, BD3, BD9, BDD, C05, C15, C1B, C21, C23, C29, C2D, C35, C43, C49, C51, C61, C65, C6B, C79, C83, C89, C8D, CAB, CC1, CCB, CD5, CD9, D01, D03, D09, D23, D31, D33, D45, D4D, D53, D61, D71, D7B, D7D, D83, D8B, D93, D99, D9D, DA1, DA5, DAB, DB5, DB9, DBB, DC3, DCD, DD1, DDB, 1005, 1009, 1019, 1025, 1033, 1035, 103B, 1041, 1043, 1055, 1065, 1069, 1071, 1079, 1081, 1085, 1099, 10A3, 10AD, 10B5, 10BB, 10C5, 10D1, 10DD, 110D, 1113, 1119, 1121, 1123, 1143, 1145, 1151, 1159, 115D, 116D, 1173, 117B, 1189, 1191, 119D, 11A3, 11A9, 11C1, 11CB, 11CD, 1201, 121D, 1223, 1225, 1233, 1239, 123D, 124B, 1253, 125B, 1261, 1269, 1283, 1285, 1289, 128B, 1299, 12B9, 12BB, 12C3, 12C9, 12D1, 12D5, 12DB, 12DD, 130B, 1311, 131D, 1321, 132B, 132D, 1341, 1343, 1355, 135B, 1373, 1385, 138D, 1393, 1395, 1399, 139B, 13B5, 13BD, 13CB, 13D3, 13DD, 1401, 1405, 140B, 140D, 1415, 1421, 1423, 1431, 143B, 143D, 1449, 1459, 1461, 1465, 146B, 1475, 147B, 1483, 1495, 14A3, 14A5, 14A9, 14B9, 14C1, 14C5, 14CD, 14D9, 1503, 1509, 1511, 1529, 1531, 1533, 153D, 154D, 1553, 1559, 156D, 1571, 157B, 158B, 1591, 1593, 159D, 15AD, 15B3, 15BB, 15D1, 15D5, 15DB, 15DD, 1603, 1609, 160B, 1619, 161D, 1635, 164D, 165B, 165D, 1663, 1669, 1671, 1673, 1679, 1693, 1695, 169B, 16AD, 16B5, 16C3, 16C5, 16CB, 16D9, 170B, 170D, 1713, 1719, 1729, 172D, 1731, 1745, 1761, 176B, 1773, 1775, 1781, 1783, 178D, 1791, 179B, 17A3, 17A5, 17B1, 17B3, 17BD, 17C5, 17CD, 1811, 181B, 181D, 1829, 1833, 1839, 1845, 1859, 1861, 186D, 187B, 187D, 1893, 1899, 189D, 18A5, 18AB, 18C1, 18C3, 18CD, 18DD, 1905, 1909, 190B, 1911, 192B, 192D, 193B, 1943, 1955, 195D, 1965, 196B, 1981, 1993, 1995, 1999, 19A1, 19A3, 19A9, 19B1, 19BB, 19C3, 19D1, 19DD, 1A13, 1A15, 1A1B, 1A21, 1A35, 1A3D, 1A59, 1A5D, 1A61, 1A65, 1A6B, 1A6D, 1A7B, 1A81, 1A91, 1AB3, 1ABD, 1AC5, 1AD3, 1B03, 1B09, 1B15, 1B23, 1B25, 1B29, 1B31, 1B39, 1B41, 1B4B, 1B4D, 1B53, 1B63, 1B69, 1B71, 1B75, 1B7B, 1B7D, 1B89, 1B8B, 1B9D, 1BAB, 1BB5, 1BC9, 1BCD, 1BD5, 1C03, 1C05, 1C0B, 1C13, 1C19, 1C39, 1C41, 1C51, 1C55, 1C5D, 1C69, 1C73, 1C81, 1C95, 1C99, 1C9B, 1CA1, 1CBB, 1CC9, 1CD1, 1CD3, 1D05, 1D0B, 1D13, 1D23, 1D2D, 1D3D, 1D43, 1D65, 1D6B, 1D73, 1D79, 1D83, 1D89, 1D8D, 1D91, 1D9D, 1DA5, 1DA9, 1DAB, 1DB3, 1DCB, 1DD3, 1DD5, 1DD9, 200D, 2011, 2015, 2023, 2025, 202B, 2031, 204D, 2055, 205B, 2061, 2069, 2075, 2099, 20AB, 20AD, 20B5, 20B9, 20BB, 20C1, 20C3, 20CD, 20DD, 2105, 2109, 2113, 211D, 2125, 213B, 2141, 2143, 2149, 216B, 2171, 2179, 2185, 218B, 2193, 219B, 21A3, 21B1, 21B5, 21BB, 21BD, 21C5, 21C9, 21D1, 21D3, 21DD, 2201, 2213, 2219, 2231, 2235, 2243, 2253, 2273, 2279, 2291, 2295, 22A9, 22B3, 22B9, 22BD, 22C5, 22D5, 22DB, 2303, 230D, 2311, 231B, 2329, 2333, 233D, 2341, 234B, 2355, 2363, 236D, 2389, 238B, 2391, 2399, 23A1, 23A5, 23AD, 23C3, 23CD, 23D5, 23DB, 23DD, 2405, 2411, 241D, 2421, 242B, 2433, 2439, 2441, 2449, 2451, 245B, 2463, 2465, 246B, 2473, 2479, 2485, 248D, 24A9, 24B1, 24C9, 24CB, 2501, 2505, 250D, 2519, 253B, 2545, 2559, 255D, 2561, 256B, 2573, 2575, 257B, 2581, 2595, 259D, 25AB, 25C1, 25D3, 25D9, 25DB, 2609, 2611, 261B, 261D, 2629, 262B, 2633, 263D, 264D, 2653, 266D, 2671, 2683, 2685, 2691, 2693, 269D, 26B5, 26B9, 26BB, 26C1, 26C9, 26DB, 2703, 2709, 270B, 2719, 272B, 2735, 2739, 2741, 2763, 2765, 2771, 2773, 2779, 277D, 2785, 278B, 2795, 279B, 27A1, 27AD, 27B5, 27BD, 27CB, 27D1, 2801, 280D, 2819, 2835, 283B, 2849, 2851, 2853, 286B, 2875, 2889, 2895, 289B, 28AB, 28B1, 28B3, 28B9, 28C5, 28CD, 28D5, 28D9, 2901, 2923, 2933, 293D, 2941, 294D, 2959, 295B, 296D, 2971, 2985, 29A1, 29B5, 29BB, 29CD, 2A03, 2A09, 2A0B, 2A21, 2A25, 2A2B, 2A2D, 2A39, 2A43, 2A4D, 2A55, 2A5B, 2A65, 2A69, 2A71, 2A73, 2A7D, 2A81, 2A8D, 2A93, 2A99, 2AA1, 2AA3, 2AB1, 2AB5, 2AC5, 2AD9, 2ADD, 2B05, 2B1B, 2B21, 2B29, 2B31, 2B35, 2B3D, 2B43, 2B53, 2B59, 2B5D, 2B6D, 2B7B, 2B81, 2B83, 2BA5, 2BA9, 2BC5, 2BCB, 2BD3, 2C01, 2C0D, 2C1D, 2C25, 2C29, 2C2B, 2C31, 2C45, 2C4B, 2C59, 2C63, 2C69, 2C6D, 2C7B, 2C7D, 2C8B, ...
15	12, 14, 18, 1E, 21, 27, 2B, 2D, 32, 38, 3E, 41, 47, 4B, 4D, 54, 58, 5E, 67, 6B, 6D, 72, 74, 78, 87, 8B, 92, 94, 9E, A1, A7, AD, B2, B8, BE, C1, CB, CD, D2, D4, E1, ED, 102, 104, 108, 10E, 111, 11B, 122, 128, 12E, 131, 137, 13B, 13D, 148, 157, 15B, 15D, 162, 171, 177, 182, 184, 188, 18E, 197, 19D, 1A4, 1A8, 1AE, 1B7, 1BB, 1C4, 1CE, 1D1, 1DB, 1DD, 1E4, 1E8, 1EE, 207, 20B, 20D, 212, 21E, 227, 22B, 234, 238, 23E, 24B, 24D, 261, 267, 272, 278, 27E, 281, 287, 292, 298, 29E, 2A1, 2A7, 2AD, 2B2, 2B4, 2C1, 2CB, 2CD, 2D2, 2D8, 2DE, 2E1, 2ED, 302, 308, 311, 31B, 324, 32E, 337, 33D, 344, 348, 351, 357, 35B, 364, 368, 377, 382, 38E, 391, 39B, 39D, 3A2, 3A4, 3AE, 3BD, 3C2, 3C4, 3C8, 3D7, 3DB, 3DD, 3E2, 407, 40B, 414, 41E, 427, 42B, 432, 438, 447, 44B, 452, 458, 461, 467, 474, 478, 47E, 481, 48B, 48D, 494, 49E, 4A1, 4AB, 4AD, 4B4, 4C7, 4CB, 4CD, 4D2, 4D8, 4DE, 4E7, 4ED, 504, 51B, 51D, 528, 531, 53B, 542, 548, 551, 55D, 562, 568, 56E, 571, 577, 584, 58E, 5A2, 5A4, 5A8, 5AE, 5B1, 5B7, 5BB, 5BD, 5C2, 5CE, 5D1, 5D7, 60B, 612, 618, 621, 634, 63E, 64D, 652, 654, 658, 65E, 667, 66B, 66D, 674, 681, 68B, 68D, 692, 694, 698, 69E, 6AB, 6B8, 6C1, 6CD, 6D4, 6D8, 6DE, 6E7, 6EB, 704, 708, 717, 71B, 722, 724, 728, 72E, 731, 737, 742, 757, 75D, 762, 764, 77D, 782, 784, 78E, 79B, 79D, 7A8, 7B1, 7B7, 7BD, 7C4, 7D7, 7DD, 7E2, 7E4, 801, 80B, 818, 821, 832, 841, 847, 84B, 84D, 852, 854, 85E, 86B, 872, 878, 88B, 88D, 89E, 8A1, 8B8, 8BE, 8C7, 8CD, 8D2, 8D4, 8D8, 8E1, 8E7, 902, 904, 90E, 91D, 928, 92E, 93B, 93D, 942, 944, 94E, 95B, 95D, 96E, 971, 977, 97B, 97D, 988, 991, 9A4, 9BD, 9C2, 9C8, 9D1, 9E2, 9E4, 9E8, A01, A12, A14, A18, A21, A27, A2D, A32, A3E, A41, A58, A5E, A61, A67, A6B, A72, A81, A87, A8B, A8D, A94, A98, A9E, AAB, AB2, AB8, AC7, ACB, AD2, ADE, AE7, AED, B02, B1D, B31, B3B, B44, B48, B4E, B51, B57, B6E, B7B, B7D, B8E, B97, B9B, BA8, BB7, BC2, BC4, BC8, BD1, BD7, BDD, BE2, BE4, BE8, BEE, C07, C0B, C0D, C14, C1E, C21, C2B, C34, C38, C47, C52, C5E, C61, C67, C6B, C6D, C7E, C8D, C92, C98, CA1, CA7, CAB, CBE, CC7, CD2, CD8, CDE, CE7, D02, D0E, D1D, D22, D28, D2E, D31, D4E, D51, D5B, D64, D68, D77, D7B, D84, D91, D97, DA4, DA8, DAE, DC4, DCE, DD1, DE2, E0D, E12, E14, E21, E27, E2B, E38, E3E, E47, E4B, E54, E6B, E6D, E72, E74, E81, E9E, EA1, EA7, EAD, EB4, EB8, EBE, EC1, ECD, ED2, EDE, EE1, EEB, EED, 100E, 1011, 1022, 1028, 103D, 104E, 1057, 105B, 105D, 1062, 1064, 107B, 1084, 1091, 1097, 10A2, 10A4, 10A8, 10AE, 10B1, 10B7, 10C2, 10C4, 10D1, 10DB, 10DD, 10E8, 1107, 110D, 1112, 1118, 1121, 1127, 112D, 113E, 114B, 114D, 1152, 1161, 1167, 116B, 1174, 117E, 1187, 118D, 1194, 11AB, 11B2, 11B4, 11BE, 11CD, 11D2, 11D8, 11EB, 11ED, 1208, 1217, 121B, 121D, 1228, 1237, 123B, 1244, 1257, 125B, 1262, 1264, 1268, 126E, 1271, 127D, 1282, 1297, 12AE, 12BB, 12BD, 12C2, 12C8, 12CE, 12D1, 12D7, 12EE, 1301, 1307, 1318, 131E, 132B, 132D, 1334, 1341, 1352, 1354, 1358, 135E, 136D, 1372, 1374, 1387, 13A1, 13AB, 13B2, 13B4, 13BE, 13C1, 13CB, 13CD, 13D8, 13DE, 13E1, 13EB, 13ED, 1408, 140E, 1417, 1437, 1442, 1444, 144E, 1457, 145D, 1468, 147B, 1482, 148E, 149B, 149D, 14B1, 14B7, 14BB, 14C2, 14C8, 14DB, 14DD, 14E8, 1507, 150D, 1512, 1514, 1518, 1532, 1534, 1541, 1547, 1558, 1561, 1567, 156D, 1581, 1592, 1594, 1598, 159E, 15A1, 15A7, 15AD, 15B8, 15BE, 15CB, 15D8, 15EB, 15ED, 1604, 1608, 161B, 1624, 163D, 1642, 1644, 1648, 164E, 1651, 165D, 1662, 1671, 1691, 169B, 16A2, 16AE, 16BD, 16C4, 16CE, 16DB, 16DD, 16E2, 16E8, 1701, 1707, 1712, 1714, 1718, 1727, 172D, 1734, 1738, 173E, 1741, 174B, 174D, 175E, 176B, 1774, 1787, 178B, 1792, 179E, 17A1, 17A7, 17AD, 17B4, 17D2, 17D8, 17E7, 17EB, 1804, 180E, 1817, 1824, 1837, 183B, 183D, 1842, 185B, 1868, 186E, 1871, 1882, 1888, 188E, 189D, 18A8, 18B7, 18BB, 18DB, 18E2, 18E8, 18EE, 1907, 190D, 1912, 1914, 1921, 1927, 192B, 192D, 1934, 194B, 1952, 1954, 1958, 196B, 196D, 1972, 197E, 1981, 1987, 198B, 19A7, 19AD, 19B4, 19B8, 19C1, 19CB, 19ED, 1A0E, 1A11, 1A17, 1A1B, 1A1D, 1A22, 1A24, 1A2E, 1A3D, 1A44, 1A48, 1A51, 1A5B, 1A62, 1A77, 1A7B, 1A7D, 1A84, 1AA4, 1AA8, 1AB1, 1ABB, 1AC2, 1AC8, 1AD1, 1AD7, 1AE4, 1AE8, 1AEE, 1B01, 1B07, 1B0B, 1B12, 1B14, 1B1E, 1B21, 1B32, 1B38, 1B4D, 1B52, 1B5E, 1B6D, 1B8B, 1B92, 1BA7, 1BAB, 1BBE, 1BC7, 1BCD, 1BD2, 1BD8, 1BE7, 1BED, 1C04, 1C0E, 1C11, 1C1B, 1C28, 1C31, 1C3B, 1C3D, 1C48, 1C51, 1C5D, 1C68, 1C82, 1C84, 1C88, 1C91, 1C97, 1C9B, 1CA4, 1CB7, 1CC2, 1CC8, 1CCE, 1CD1, 1CD7, 1CE2, 1CEE, 1D01, 1D0B, 1D12, 1D18, 1D1E, 1D27, 1D2D, 1D38, 1D3E, 1D41, 1D47, 1D4D, 1D54, 1D5E, 1D67, 1D81, 1D87, 1D9E, 1DA1, 1DB4, 1DB8, 1DC1, 1DCB, 1DEB, 1E04, 1E17, 1E1B, 1E1D, 1E28, 1E2E, 1E31, 1E37, 1E3B, 1E4E, 1E57, 1E64, 1E77, 1E88, 1E8E, 1E91, 1E9D, 1EA4, 1EAE, 1EB1, 1EBB, 1EBD, 1EC4, 1ECE, 1EDD, 1EE2, 200B, 200D, 201E, 2021, 202B, 202D, 2038, 204D, 2052, 2054, 2058, 2061, 2072, 2078, 207E, 2081, 208D, 209E, 20A7, 20AB, 20B2, 20D2, 20D4, 20DE, 20E1, 20E7, 20EB, 2102, 2108, 2111, 2117, 211B, 2128, 212E, 2137, 2144, 2148, 2157, 2164, 216E, 2188, 218E, 219B, 21A2, 21A4, 21BB, 21C4, 21D7, 21E2, 21E8, 2207, 220B, 220D, 2214, 221E, 2227, 222D, 2232, 2238, 2258, 2267, 2272, 2274, 2281, 228B, 228D, 229E, 22A1, 22B4, 22CD, 22E1, 22E7, 2308, 231B, 2322, 2324, 2337, 233B, 2342, 2344, 234E, 2357, 2362, 2368, 236E, 2377, 237B, 2382, 2384, 238E, 2391, 239D, 23A2, 23A8, 23AE, 23B1, 23BD, 23C2, 23D1, 23E4, 23E8, 23EE, 2414, 2418, 2421, 2427, 242B, 2434, 2438, 2447, 244D, 2452, 2461, 246D, 2472, 2474, 2494, 2498, 24B2, 24B8, 24BE, 24CB, 24D8, 24E7, 24ED, 2502, 2504, 2508, 251B, 2522, 252E, 2537, 253D, 2542, 254E, 2551, 255D, ...
16	11, 13, 17, 1D, 1F, 25, 29, 2B, 2F, 35, 3B, 3D, 43, 47, 49, 4F, 53, 59, 61, 65, 67, 6B, 6D, 71, 7F, 83, 89, 8B, 95, 97, 9D, A3, A7, AD, B3, B5, BF, C1, C5, C7, D3, DF, E3, E5, E9, EF, F1, FB, 101, 107, 10D, 10F, 115, 119, 11B, 125, 133, 137, 139, 13D, 14B, 151, 15B, 15D, 161, 167, 16F, 175, 17B, 17F, 185, 18D, 191, 199, 1A3, 1A5, 1AF, 1B1, 1B7, 1BB, 1C1, 1C9, 1CD, 1CF, 1D3, 1DF, 1E7, 1EB, 1F3, 1F7, 1FD, 209, 20B, 21D, 223, 22D, 233, 239, 23B, 241, 24B, 251, 257, 259, 25F, 265, 269, 26B, 277, 281, 283, 287, 28D, 293, 295, 2A1, 2A5, 2AB, 2B3, 2BD, 2C5, 2CF, 2D7, 2DD, 2E3, 2E7, 2EF, 2F5, 2F9, 301, 305, 313, 31D, 329, 32B, 335, 337, 33B, 33D, 347, 355, 359, 35B, 35F, 36D, 371, 373, 377, 38B, 38F, 397, 3A1, 3A9, 3AD, 3B3, 3B9, 3C7, 3CB, 3D1, 3D7, 3DF, 3E5, 3F1, 3F5, 3FB, 3FD, 407, 409, 40F, 419, 41B, 425, 427, 42D, 43F, 443, 445, 449, 44F, 455, 45D, 463, 469, 47F, 481, 48B, 493, 49D, 4A3, 4A9, 4B1, 4BD, 4C1, 4C7, 4CD, 4CF, 4D5, 4E1, 4EB, 4FD, 4FF, 503, 509, 50B, 511, 515, 517, 51B, 527, 529, 52F, 551, 557, 55D, 565, 577, 581, 58F, 593, 595, 599, 59F, 5A7, 5AB, 5AD, 5B3, 5BF, 5C9, 5CB, 5CF, 5D1, 5D5, 5DB, 5E7, 5F3, 5FB, 607, 60D, 611, 617, 61F, 623, 62B, 62F, 63D, 641, 647, 649, 64D, 653, 655, 65B, 665, 679, 67F, 683, 685, 69D, 6A1, 6A3, 6AD, 6B9, 6BB, 6C5, 6CD, 6D3, 6D9, 6DF, 6F1, 6F7, 6FB, 6FD, 709, 713, 71F, 727, 737, 745, 74B, 74F, 751, 755, 757, 761, 76D, 773, 779, 78B, 78D, 79D, 79F, 7B5, 7BB, 7C3, 7C9, 7CD, 7CF, 7D3, 7DB, 7E1, 7EB, 7ED, 7F7, 805, 80F, 815, 821, 823, 827, 829, 833, 83F, 841, 851, 853, 859, 85D, 85F, 869, 871, 883, 89B, 89F, 8A5, 8AD, 8BD, 8BF, 8C3, 8CB, 8DB, 8DD, 8E1, 8E9, 8EF, 8F5, 8F9, 905, 907, 91D, 923, 925, 92B, 92F, 935, 943, 949, 94D, 94F, 955, 959, 95F, 96B, 971, 977, 985, 989, 98F, 99B, 9A3, 9A9, 9AD, 9C7, 9D9, 9E3, 9EB, 9EF, 9F5, 9F7, 9FD, A13, A1F, A21, A31, A39, A3D, A49, A57, A61, A63, A67, A6F, A75, A7B, A7F, A81, A85, A8B, A93, A97, A99, A9F, AA9, AAB, AB5, ABD, AC1, ACF, AD9, AE5, AE7, AED, AF1, AF3, B03, B11, B15, B1B, B23, B29, B2D, B3F, B47, B51, B57, B5D, B65, B6F, B7B, B89, B8D, B93, B99, B9B, BB7, BB9, BC3, BCB, BCF, BDD, BE1, BE9, BF5, BFB, C07, C0B, C11, C25, C2F, C31, C41, C5B, C5F, C61, C6D, C73, C77, C83, C89, C91, C95, C9D, CB3, CB5, CB9, CBB, CC7, CE3, CE5, CEB, CF1, CF7, CFB, D01, D03, D0F, D13, D1F, D21, D2B, D2D, D3D, D3F, D4F, D55, D69, D79, D81, D85, D87, D8B, D8D, DA3, DAB, DB7, DBD, DC7, DC9, DCD, DD3, DD5, DDB, DE5, DE7, DF3, DFD, DFF, E09, E17, E1D, E21, E27, E2F, E35, E3B, E4B, E57, E59, E5D, E6B, E71, E75, E7D, E87, E8F, E95, E9B, EB1, EB7, EB9, EC3, ED1, ED5, EDB, EED, EEF, EF9, F07, F0B, F0D, F17, F25, F29, F31, F43, F47, F4D, F4F, F53, F59, F5B, F67, F6B, F7F, F95, FA1, FA3, FA7, FAD, FB3, FB5, FBB, FD1, FD3, FD9, FE9, FEF, FFB, FFD, 1003, 100F, 101F, 1021, 1025, 102B, 1039, 103D, 103F, 1051, 1069, 1073, 1079, 107B, 1085, 1087, 1091, 1093, 109D, 10A3, 10A5, 10AF, 10B1, 10BB, 10C1, 10C9, 10E7, 10F1, 10F3, 10FD, 1105, 110B, 1115, 1127, 112D, 1139, 1145, 1147, 1159, 115F, 1163, 1169, 116F, 1181, 1183, 118D, 119B, 11A1, 11A5, 11A7, 11AB, 11C3, 11C5, 11D1, 11D7, 11E7, 11EF, 11F5, 11FB, 120D, 121D, 121F, 1223, 1229, 122B, 1231, 1237, 1241, 1247, 1253, 125F, 1271, 1273, 1279, 127D, 128F, 1297, 12AF, 12B3, 12B5, 12B9, 12BF, 12C1, 12CD, 12D1, 12DF, 12FD, 1307, 130D, 1319, 1327, 132D, 1337, 1343, 1345, 1349, 134F, 1357, 135D, 1367, 1369, 136D, 137B, 1381, 1387, 138B, 1391, 1393, 139D, 139F, 13AF, 13BB, 13C3, 13D5, 13D9, 13DF, 13EB, 13ED, 13F3, 13F9, 13FF, 141B, 1421, 142F, 1433, 143B, 1445, 144D, 1459, 146B, 146F, 1471, 1475, 148D, 1499, 149F, 14A1, 14B1, 14B7, 14BD, 14CB, 14D5, 14E3, 14E7, 1505, 150B, 1511, 1517, 151F, 1525, 1529, 152B, 1537, 153D, 1541, 1543, 1549, 155F, 1565, 1567, 156B, 157D, 157F, 1583, 158F, 1591, 1597, 159B, 15B5, 15BB, 15C1, 15C5, 15CD, 15D7, 15F7, 1607, 1609, 160F, 1613, 1615, 1619, 161B, 1625, 1633, 1639, 163D, 1645, 164F, 1655, 1669, 166D, 166F, 1675, 1693, 1697, 169F, 16A9, 16AF, 16B5, 16BD, 16C3, 16CF, 16D3, 16D9, 16DB, 16E1, 16E5, 16EB, 16ED, 16F7, 16F9, 1709, 170F, 1723, 1727, 1733, 1741, 175D, 1763, 1777, 177B, 178D, 1795, 179B, 179F, 17A5, 17B3, 17B9, 17BF, 17C9, 17CB, 17D5, 17E1, 17E9, 17F3, 17F5, 17FF, 1807, 1813, 181D, 1835, 1837, 183B, 1843, 1849, 184D, 1855, 1867, 1871, 1877, 187D, 187F, 1885, 188F, 189B, 189D, 18A7, 18AD, 18B3, 18B9, 18C1, 18C7, 18D1, 18D7, 18D9, 18DF, 18E5, 18EB, 18F5, 18FD, 1915, 191B, 1931, 1933, 1945, 1949, 1951, 195B, 1979, 1981, 1993, 1997, 1999, 19A3, 19A9, 19AB, 19B1, 19B5, 19C7, 19CF, 19DB, 19ED, 19FD, 1A03, 1A05, 1A11, 1A17, 1A21, 1A23, 1A2D, 1A2F, 1A35, 1A3F, 1A4D, 1A51, 1A69, 1A6B, 1A7B, 1A7D, 1A87, 1A89, 1A93, 1AA7, 1AAB, 1AAD, 1AB1, 1AB9, 1AC9, 1ACF, 1AD5, 1AD7, 1AE3, 1AF3, 1AFB, 1AFF, 1B05, 1B23, 1B25, 1B2F, 1B31, 1B37, 1B3B, 1B41, 1B47, 1B4F, 1B55, 1B59, 1B65, 1B6B, 1B73, 1B7F, 1B83, 1B91, 1B9D, 1BA7, 1BBF, 1BC5, 1BD1, 1BD7, 1BD9, 1BEF, 1BF7, 1C09, 1C13, 1C19, 1C27, 1C2B, 1C2D, 1C33, 1C3D, 1C45, 1C4B, 1C4F, 1C55, 1C73, 1C81, 1C8B, 1C8D, 1C99, 1CA3, 1CA5, 1CB5, 1CB7, 1CC9, 1CE1, 1CF3, 1CF9, 1D09, 1D1B, 1D21, 1D23, 1D35, 1D39, 1D3F, 1D41, 1D4B, 1D53, 1D5D, 1D63, 1D69, 1D71, 1D75, 1D7B, 1D7D, 1D87, 1D89, 1D95, 1D99, 1D9F, 1DA5, 1DA7, 1DB3, 1DB7, 1DC5, 1DD7, 1DDB, 1DE1, 1DF5, 1DF9, 1E01, 1E07, 1E0B, 1E13, 1E17, 1E25, 1E2B, 1E2F, 1E3D, 1E49, 1E4D, 1E4F, 1E6D, 1E71, 1E89, 1E8F, 1E95, 1EA1, 1EAD, 1EBB, 1EC1, 1EC5, 1EC7, 1ECB, 1EDD, 1EE3, 1EEF, 1EF7, 1EFD, 1F01, 1F0D, 1F0F, 1F1B, ...
17	12, 16, 1C, 1E, 23, 27, 29, 2D, 32, 38, 3A, 3G, 43, 45, 4B, 4F, 54, 5C, 5G, 61, 65, 67, 6B, 78, 7C, 81, 83, 8D, 8F, 94, 9A, 9E, A3, A9, AB, B4, B6, BA, BC, C7, D2, D6, D8, DC, E1, E3, ED, F2, F8, FE, FG, G5, G9, GB, 104, 111, 115, 117, 11B, 128, 12E, 137, 139, 13D, 142, 14A, 14G, 155, 159, 15F, 166, 16A, 171, 17B, 17D, 186, 188, 18E, 191, 197, 19F, 1A2, 1A4, 1A8, 1B3, 1BB, 1BF, 1C6, 1CA, 1CG, 1DB, 1DD, 1EE, 1F3, 1FD, 1G2, 1G8, 1GA, 1GG, 209, 20F, 214, 216, 21C, 221, 225, 227, 232, 23C, 23E, 241, 247, 24D, 24F, 25A, 25E, 263, 26B, 274, 27C, 285, 28D, 292, 298, 29C, 2A3, 2A9, 2AD, 2B4, 2B8, 2C5, 2CF, 2DA, 2DC, 2E5, 2E7, 2EB, 2ED, 2F6, 2G3, 2G7, 2G9, 2GD, 30A, 30E, 30G, 313, 326, 32A, 331, 33B, 342, 346, 34C, 351, 35F, 362, 368, 36E, 375, 37B, 386, 38A, 38G, 391, 39B, 39D, 3A2, 3AC, 3AE, 3B7, 3B9, 3BF, 3CG, 3D3, 3D5, 3D9, 3DF, 3E4, 3EC, 3F1, 3F7, 3GC, 3GE, 407, 40F, 418, 41E, 423, 42B, 436, 43A, 43G, 445, 447, 44D, 458, 461, 472, 474, 478, 47E, 47G, 485, 489, 48B, 48F, 49A, 49C, 4A1, 4C1, 4C7, 4CD, 4D4, 4E5, 4EF, 4FC, 4FG, 4G1, 4G5, 4GB, 502, 506, 508, 50E, 519, 522, 524, 528, 52A, 52E, 533, 53F, 54A, 551, 55D, 562, 566, 56C, 573, 577, 57F, 582, 58G, 593, 599, 59B, 59F, 5A4, 5A6, 5AC, 5B5, 5C8, 5CE, 5D1, 5D3, 5EA, 5EE, 5EG, 5F9, 5G4, 5G6, 5GG, 607, 60D, 612, 618, 629, 62F, 632, 634, 63G, 649, 654, 65C, 66B, 678, 67E, 681, 683, 687, 689, 692, 69E, 6A3, 6A9, 6BA, 6BC, 6CB, 6CD, 6E1, 6E7, 6EF, 6F4, 6F8, 6FA, 6FE, 6G5, 6GB, 704, 706, 70G, 71D, 726, 72C, 737, 739, 73D, 73F, 748, 753, 755, 764, 766, 76C, 76G, 771, 77B, 782, 793, 7AA, 7AE, 7B3, 7BB, 7CA, 7CC, 7CG, 7D7, 7E6, 7E8, 7EC, 7F3, 7F9, 7FF, 7G2, 7GE, 7GG, 814, 81A, 81C, 821, 825, 82B, 838, 83E, 841, 843, 849, 84D, 852, 85E, 863, 869, 876, 87A, 87G, 88B, 892, 898, 89C, 8B4, 8C5, 8CF, 8D6, 8DA, 8DG, 8E1, 8E7, 8FC, 8G7, 8G9, 908, 90G, 913, 91F, 92C, 935, 937, 93B, 942, 948, 94E, 951, 953, 957, 95D, 964, 968, 96A, 96G, 979, 97B, 984, 98C, 98G, 99D, 9A6, 9B1, 9B3, 9B9, 9BD, 9BF, 9CE, 9DB, 9DF, 9E4, 9EC, 9F1, 9F5, 9G6, 9GE, A07, A0D, A12, A1A, A23, A2F, A3C, A3G, A45, A4B, A4D, A67, A69, A72, A7A, A7E, A8B, A8F, A96, AA1, AA7, AB2, AB6, ABC, ACF, AD8, ADA, AE9, AG1, AG5, AG7, B02, B08, B0C, B17, B1D, B24, B28, B2G, B44, B46, B4A, B4C, B57, B71, B73, B79, B7F, B84, B88, B8E, B8G, B9B, B9F, BAA, BAC, BB5, BB7, BC6, BC8, BD7, BDD, BEG, BFF, BG6, BGA, BGC, BGG, C01, C16, C1E, C29, C2F, C38, C3A, C3E, C43, C45, C4B, C54, C56, C61, C6B, C6D, C76, C83, C89, C8D, C92, C9A, C9G, CA5, CB4, CBG, CC1, CC5, CD2, CD8, CDC, CE3, CED, CF4, CFA, CFG, D04, D0A, D0C, D15, D22, D26, D2C, D3D, D3F, D48, D55, D59, D5B, D64, D71, D75, D7D, D8E, D91, D97, D99, D9D, DA2, DA4, DAG, DB3, DC6, DDB, DE6, DE8, DEC, DF1, DF7, DF9, DFF, E03, E05, E0B, E1A, E1G, E2B, E2D, E32, E3E, E4D, E4F, E52, E58, E65, E69, E6B, E7C, E92, E9C, EA1, EA3, EAD, EAF, EB8, EBA, EC3, EC9, ECB, ED4, ED6, EDG, EE5, EED, EG9, F02, F04, F0E, F15, F1B, F24, F35, F3B, F46, F51, F53, F64, F6A, F6E, F73, F79, F8A, F8C, F95, FA2, FA8, FAC, FAE, FB1, FC8, FCA, FD5, FDB, FEA, FF1, FF7, FFD, FGE, G0D, G0F, G12, G18, G1A, G1G, G25, G2F, G34, G3G, G4B, G5C, G5E, G63, G67, G78, G7G, G96, G9A, G9C, G9G, GA5, GA7, GB2, GB6, GC3, GDG, GE9, GEF, GFA, GG7, GGD, 1006, 1011, 1013, 1017, 101D, 1024, 102A, 1033, 1035, 1039, 1046, 104C, 1051, 1055, 105B, 105D, 1066, 1068, 1077, 1082, 108A, 109B, 109F, 10A4, 10AG, 10B1, 10B7, 10BD, 10C2, 10DD, 10E2, 10EG, 10F3, 10FB, 10G4, 10GC, 1107, 1118, 111C, 111E, 1121, 1138, 1143, 1149, 114B, 115A, 115G, 1165, 1172, 117C, 1189, 118D, 11A9, 11AF, 11B4, 11BA, 11C1, 11C7, 11CB, 11CD, 11D8, 11DE, 11E1, 11E3, 11E9, 11FE, 11G3, 11G5, 11G9, 120A, 120C, 120G, 121B, 121D, 1222, 1226, 123F, 1244, 124A, 124E, 1255, 125F, 127D, 128C, 128E, 1293, 1297, 1299, 129D, 129F, 12A8, 12B5, 12BB, 12BF, 12C6, 12CG, 12D5, 12E8, 12EC, 12EE, 12F3, 12GG, 1303, 130B, 1314, 131A, 131G, 1327, 132D, 1338, 133C, 1341, 1343, 1349, 134D, 1352, 1354, 135E, 135G, 136F, 1374, 1387, 138B, 1396, 13A3, 13BE, 13C3, 13D6, 13DA, 13EB, 13F2, 13F8, 13FC, 13G1, 13GF, 1404, 140A, 1413, 1415, 141F, 142A, 1431, 143B, 143D, 1446, 144E, 1459, 1462, 1479, 147B, 147F, 1486, 148C, 148G, 1497, 14A8, 14B1, 14B7, 14BD, 14BF, 14C4, 14CE, 14D9, 14DB, 14E4, 14EA, 14EG, 14F5, 14FD, 14G2, 14GC, 1501, 1503, 1509, 150F, 1514, 151E, 1525, 153C, 1541, 1556, 1558, 1569, 156D, 1574, 157E, 159A, 15A1, 15B2, 15B6, 15B8, 15C1, 15C7, 15C9, 15CF, 15D2, 15E3, 15EB, 15F6, 15G7, 1606, 160C, 160E, 1619, 161F, 1628, 162A, 1633, 1635, 163B, 1644, 1651, 1655, 166C, 166E, 167D, 167F, 1688, 168A, 1693, 16A6, 16AA, 16AC, 16AG, 16B7, 16C6, 16CC, 16D1, 16D3, 16DF, 16EE, 16F5, 16F9, 16FF, 170B, 170D, 1716, 1718, 171E, 1721, 1727, 172D, 1734, 173A, 173E, 1749, 174F, 1756, 1761, 1765, 1772, 177E, 1787, 179E, 17A3, 17AF, 17B4, 17B6, 17CB, 17D2, 17E3, 17ED, 17F2, 17FG, 17G3, 17G5, 17GB, 1804, 180C, 1811, 1815, 181B, 1837, 1844, 184E, 184G, 185B, 1864, 1866, 1875, 1877, 1888, 189F, 18AG, 18B5, 18C4, 18D5, 18DB, 18DD, 18EE, 18F1, 18F7, 18F9, 18G2, 18GA, 1903, 1909, 190F, 1916, 191A, 191G, 1921, 192B, 192D, 1938, 193C, 1941, 1947, 1949, 1954, 1958, 1965, 1976, 197A, 197G, 1992, 1996, 199E, 19A3, 19A7, 19AF, 19B2, 19BG, 19C5, 19C9, 19D6, 19E1, 19E5, 19E7, 19G3, 19G7, 1A0E, 1A13, 1A19, 1A24, 1A2G, 1A3D, 1A42, 1A46, 1A48, 1A4C, 1A5D, 1A62, 1A6E, 1A75, 1A7B, 1A7F, 1A8A, 1A8C, 1A97, 1AB3, ...
18	11, 15, 1B, 1D, 21, 25, 27, 2B, 2H, 35, 37, 3D, 3H, 41, 47, 4B, 4H, 57, 5B, 5D, 5H, 61, 65, 71, 75, 7B, 7D, 85, 87, 8D, 91, 95, 9B, 9H, A1, AB, AD, AH, B1, BD, C7, CB, CD, CH, D5, D7, DH, E5, EB, EH, F1, F7, FB, FD, G5, H1, H5, H7, HB, 107, 10D, 115, 117, 11B, 11H, 127, 12D, 131, 135, 13B, 141, 145, 14D, 155, 157, 15H, 161, 167, 16B, 16H, 177, 17B, 17D, 17H, 18B, 191, 195, 19D, 19H, 1A5, 1AH, 1B1, 1C1, 1C7, 1CH, 1D5, 1DB, 1DD, 1E1, 1EB, 1EH, 1F5, 1F7, 1FD, 1G1, 1G5, 1G7, 1H1, 1HB, 1HD, 1HH, 205, 20B, 20D, 217, 21B, 21H, 227, 22H, 237, 23H, 247, 24D, 251, 255, 25D, 261, 265, 26D, 26H, 27D, 285, 28H, 291, 29B, 29D, 29H, 2A1, 2AB, 2B7, 2BB, 2BD, 2BH, 2CD, 2CH, 2D1, 2D5, 2E7, 2EB, 2F1, 2FB, 2G1, 2G5, 2GB, 2GH, 2HD, 2HH, 305, 30B, 311, 317, 321, 325, 32B, 32D, 335, 337, 33D, 345, 347, 34H, 351, 357, 367, 36B, 36D, 36H, 375, 37B, 381, 387, 38D, 39H, 3A1, 3AB, 3B1, 3BB, 3BH, 3C5, 3CD, 3D7, 3DB, 3DH, 3E5, 3E7, 3ED, 3F7, 3FH, 3GH, 3H1, 3H5, 3HB, 3HD, 401, 405, 407, 40B, 415, 417, 41D, 43B, 43H, 445, 44D, 45D, 465, 471, 475, 477, 47B, 47H, 487, 48B, 48D, 491, 49D, 4A5, 4A7, 4AB, 4AD, 4AH, 4B5, 4BH, 4CB, 4D1, 4DD, 4E1, 4E5, 4EB, 4F1, 4F5, 4FD, 4FH, 4GD, 4GH, 4H5, 4H7, 4HB, 4HH, 501, 507, 50H, 521, 527, 52B, 52D, 541, 545, 547, 54H, 55B, 55D, 565, 56D, 571, 577, 57D, 58D, 591, 595, 597, 5A1, 5AB, 5B5, 5BD, 5CB, 5D7, 5DD, 5DH, 5E1, 5E5, 5E7, 5EH, 5FB, 5FH, 5G5, 5H5, 5H7, 605, 607, 61B, 61H, 627, 62D, 62H, 631, 635, 63D, 641, 64B, 64D, 655, 661, 66B, 66H, 67B, 67D, 67H, 681, 68B, 695, 697, 6A5, 6A7, 6AD, 6AH, 6B1, 6BB, 6C1, 6D1, 6E7, 6EB, 6EH, 6F7, 6G5, 6G7, 6GB, 6H1, 6HH, 701, 705, 70D, 711, 717, 71B, 725, 727, 73B, 73H, 741, 747, 74B, 74H, 75D, 761, 765, 767, 76D, 76H, 775, 77H, 785, 78B, 797, 79B, 79H, 7AB, 7B1, 7B7, 7BB, 7D1, 7E1, 7EB, 7F1, 7F5, 7FB, 7FD, 7G1, 7H5, 7HH, 801, 80H, 817, 81B, 825, 831, 83B, 83D, 83H, 847, 84D, 851, 855, 857, 85B, 85H, 867, 86B, 86D, 871, 87B, 87D, 885, 88D, 88H, 89D, 8A5, 8AH, 8B1, 8B7, 8BB, 8BD, 8CB, 8D7, 8DB, 8DH, 8E7, 8ED, 8EH, 8FH, 8G7, 8GH, 8H5, 8HB, 901, 90B, 915, 921, 925, 92B, 92H, 931, 94B, 94D, 955, 95D, 95H, 96D, 96H, 977, 981, 987, 991, 995, 99B, 9AD, 9B5, 9B7, 9C5, 9DD, 9DH, 9E1, 9ED, 9F1, 9F5, 9FH, 9G5, 9GD, 9GH, 9H7, A0B, A0D, A0H, A11, A1D, A35, A37, A3D, A41, A47, A4B, A4H, A51, A5D, A5H, A6B, A6D, A75, A77, A85, A87, A95, A9B, AAD, ABB, AC1, AC5, AC7, ACB, ACD, ADH, AE7, AF1, AF7, AFH, AG1, AG5, AGB, AGD, AH1, AHB, AHD, B07, B0H, B11, B1B, B27, B2D, B2H, B35, B3D, B41, B47, B55, B5H, B61, B65, B71, B77, B7B, B81, B8B, B91, B97, B9D, BAH, BB5, BB7, BBH, BCD, BCH, BD5, BE5, BE7, BEH, BFD, BFH, BG1, BGB, BH7, BHB, C01, C11, C15, C1B, C1D, C1H, C25, C27, C31, C35, C47, C5B, C65, C67, C6B, C6H, C75, C77, C7D, C8H, C91, C97, CA5, CAB, CB5, CB7, CBD, CC7, CD5, CD7, CDB, CDH, CED, CEH, CF1, CG1, CH7, CHH, D05, D07, D0H, D11, D1B, D1D, D25, D2B, D2D, D35, D37, D3H, D45, D4D, D67, D6H, D71, D7B, D81, D87, D8H, D9H, DA5, DAH, DBB, DBD, DCD, DD1, DD5, DDB, DDH, DEH, DF1, DFB, DG7, DGD, DGH, DH1, DH5, E0B, E0D, E17, E1D, E2B, E31, E37, E3D, E4D, E5B, E5D, E5H, E65, E67, E6D, E71, E7B, E7H, E8B, E95, EA5, EA7, EAD, EAH, EBH, EC7, EDD, EDH, EE1, EE5, EEB, EED, EF7, EFB, EG7, F01, F0B, F0H, F1B, F27, F2D, F35, F3H, F41, F45, F4B, F51, F57, F5H, F61, F65, F71, F77, F7D, F7H, F85, F87, F8H, F91, F9H, FAB, FB1, FC1, FC5, FCB, FD5, FD7, FDD, FE1, FE7, FFH, FG5, FH1, FH5, FHD, G05, G0D, G17, G27, G2B, G2D, G2H, G45, G4H, G55, G57, G65, G6B, G6H, G7D, G85, G91, G95, GAH, GB5, GBB, GBH, GC7, GCD, GCH, GD1, GDD, GE1, GE5, GE7, GED, GFH, GG5, GG7, GGB, GHB, GHD, GHH, H0B, H0D, H11, H15, H2D, H31, H37, H3B, H41, H4B, H67, H75, H77, H7D, H7H, H81, H85, H87, H8H, H9D, HA1, HA5, HAD, HB5, HBB, HCD, HCH, HD1, HD7, HF1, HF5, HFD, HG5, HGB, HGH, HH7, HHD, 1007, 100B, 100H, 1011, 1017, 101B, 101H, 1021, 102B, 102D, 103B, 103H, 1051, 1055, 105H, 106D, 1085, 108B, 109D, 109H, 10AH, 10B7, 10BD, 10BH, 10C5, 10D1, 10D7, 10DD, 10E5, 10E7, 10EH, 10FB, 10G1, 10GB, 10GD, 10H5, 10HD, 1107, 110H, 1125, 1127, 112B, 1131, 1137, 113B, 1141, 1151, 115B, 115H, 1165, 1167, 116D, 1175, 117H, 1181, 118B, 118H, 1195, 119B, 11A1, 11A7, 11AH, 11B5, 11B7, 11BD, 11C1, 11C7, 11CH, 11D7, 11ED, 11F1, 11G5, 11G7, 11H7, 11HB, 1201, 120B, 1225, 122D, 123D, 123H, 1241, 124B, 124H, 1251, 1257, 125B, 126B, 1271, 127D, 128D, 129B, 129H, 12A1, 12AD, 12B1, 12BB, 12BD, 12C5, 12C7, 12CD, 12D5, 12E1, 12E5, 12FB, 12FD, 12GB, 12GD, 12H5, 12H7, 12HH, 1311, 1315, 1317, 131B, 1321, 132H, 1335, 133B, 133D, 1347, 1355, 135D, 135H, 1365, 137H, 1381, 138B, 138D, 1391, 1395, 139B, 139H, 13A7, 13AD, 13AH, 13BB, 13BH, 13C7, 13D1, 13D5, 13E1, 13ED, 13F5, 13GB, 13GH, 13HB, 13HH, 1401, 1415, 141D, 142D, 1435, 143B, 1447, 144B, 144D, 1451, 145B, 1461, 1467, 146B, 146H, 148B, 1497, 149H, 14A1, 14AD, 14B5, 14B7, 14C5, 14C7, 14D7, 14ED, 14FD, 14G1, 14GH, 14HH, 1505, 1507, 1517, 151B, 151H, 1521, 152B, 1531, 153B, 153H, 1545, 154D, 154H, 1555, 1557, 155H, 1561, 156D, 156H, 1575, 157B, 157D, 1587, 158B, 1597, 15A7, 15AB, 15AH, 15C1, 15C5, 15CD, 15D1, 15D5, 15DD, 15DH, 15ED, 15F1, 15F5, 15G1, 15GD, 15GH, 15H1, 160D, 160H, 1625, 162B, 162H, 163B, 1645, 1651, 1657, 165B, 165D, 165H, 166H, 1675, 167H, 1687, 168D, 168H, 169B, 169D, 16A7, 16C1, ...
19	14, 1A, 1C, 1I, 23, 25, 29, 2F, 32, 34, 3A, 3E, 3G, 43, 47, 4D, 52, 56, 58, 5C, 5E, 5I, 6D, 6H, 74, 76, 7G, 7I, 85, 8B, 8F, 92, 98, 9A, A1, A3, A7, A9, B2, BE, BI, C1, C5, CB, CD, D4, DA, DG, E3, E5, EB, EF, EH, F8, G3, G7, G9, GD, H8, HE, I5, I7, IB, IH, 106, 10C, 10I, 113, 119, 11H, 122, 12A, 131, 133, 13D, 13F, 142, 146, 14C, 151, 155, 157, 15B, 164, 16C, 16G, 175, 179, 17F, 188, 18A, 199, 19F, 1A6, 1AC, 1AI, 1B1, 1B7, 1BH, 1C4, 1CA, 1CC, 1CI, 1D5, 1D9, 1DB, 1E4, 1EE, 1EG, 1F1, 1F7, 1FD, 1FF, 1G8, 1GC, 1GI, 1H7, 1HH, 1I6, 1IG, 205, 20B, 20H, 212, 21A, 21G, 221, 229, 22D, 238, 23I, 24B, 24D, 254, 256, 25A, 25C, 263, 26H, 272, 274, 278, 283, 287, 289, 28D, 29E, 29I, 2A7, 2AH, 2B6, 2BA, 2BG, 2C3, 2CH, 2D2, 2D8, 2DE, 2E3, 2E9, 2F2, 2F6, 2FC, 2FE, 2G5, 2G7, 2GD, 2H4, 2H6, 2HG, 2HI, 2I5, 304, 308, 30A, 30E, 311, 317, 31F, 322, 328, 33B, 33D, 344, 34C, 353, 359, 35F, 364, 36G, 371, 377, 37D, 37F, 382, 38E, 395, 3A4, 3A6, 3AA, 3AG, 3AI, 3B5, 3B9, 3BB, 3BF, 3C8, 3CA, 3CG, 3EC, 3EI, 3F5, 3FD, 3GC, 3H3, 3HH, 3I2, 3I4, 3I8, 3IE, 403, 407, 409, 40F, 418, 41I, 421, 425, 427, 42B, 42H, 43A, 443, 44B, 454, 45A, 45E, 461, 469, 46D, 472, 476, 481, 485, 48B, 48D, 48H, 494, 496, 49C, 4A3, 4B4, 4BA, 4BE, 4BG, 4D2, 4D6, 4D8, 4DI, 4EB, 4ED, 4F4, 4FC, 4FI, 4G5, 4GB, 4HA, 4HG, 4I1, 4I3, 4IF, 506, 50I, 517, 524, 52I, 535, 539, 53B, 53F, 53H, 548, 551, 557, 55D, 56C, 56E, 57B, 57D, 58G, 593, 59B, 59H, 5A2, 5A4, 5A8, 5AG, 5B3, 5BD, 5BF, 5C6, 5D1, 5DB, 5DH, 5EA, 5EC, 5EG, 5EI, 5F9, 5G2, 5G4, 5H1, 5H3, 5H9, 5HD, 5HF, 5I6, 5IE, 60D, 61I, 623, 629, 62H, 63E, 63G, 641, 649, 656, 658, 65C, 661, 667, 66D, 66H, 67A, 67C, 68F, 692, 694, 69A, 69E, 6A1, 6AF, 6B2, 6B6, 6B8, 6BE, 6BI, 6C5, 6CH, 6D4, 6DA, 6E5, 6E9, 6EF, 6F8, 6FG, 6G3, 6G7, 6HE, 6ID, 704, 70C, 70G, 713, 715, 71B, 72E, 737, 739, 746, 74E, 74I, 75B, 766, 76G, 76I, 773, 77B, 77H, 784, 788, 78A, 78E, 791, 799, 79D, 79F, 7A2, 7AC, 7AE, 7B5, 7BD, 7BH, 7CC, 7D3, 7DF, 7DH, 7E4, 7E8, 7EA, 7F7, 7G2, 7G6, 7GC, 7H1, 7H7, 7HB, 7IA, 7II, 809, 80F, 812, 81A, 821, 82D, 838, 83C, 83I, 845, 847, 85G, 85I, 869, 86H, 872, 87G, 881, 889, 892, 898, 8A1, 8A5, 8AB, 8BC, 8C3, 8C5, 8D2, 8E9, 8ED, 8EF, 8F8, 8FE, 8FI, 8GB, 8GH, 8H6, 8HA, 8HI, 902, 904, 908, 90A, 913, 92C, 92E, 931, 937, 93D, 93H, 944, 946, 94I, 953, 95F, 95H, 968, 96A, 977, 979, 986, 98C, 99D, 9AA, 9AI, 9B3, 9B5, 9B9, 9BB, 9CE, 9D3, 9DF, 9E2, 9EC, 9EE, 9EI, 9F5, 9F7, 9FD, 9G4, 9G6, 9GI, 9H9, 9HB, 9I2, 9IG, A03, A07, A0D, A12, A18, A1E, A2B, A34, A36, A3A, A45, A4B, A4F, A54, A5E, A63, A69, A6F, A7I, A85, A87, A8H, A9C, A9G, AA3, AB2, AB4, ABE, AC9, ACD, ACF, AD6, AE1, AE5, AED, AFC, AFG, AG3, AG5, AG9, AGF, AGH, AHA, AHE, AIF, B0I, B1B, B1D, B1H, B24, B2A, B2C, B2I, B42, B44, B4A, B57, B5D, B66, B68, B6E, B77, B84, B86, B8A, B8G, B9B, B9F, B9H, BAG, BC2, BCC, BCI, BD1, BDB, BDD, BE4, BE6, BEG, BF3, BF5, BFF, BFH, BG8, BGE, BH3, BIE, C05, C07, C0H, C16, C1C, C23, C32, C38, C41, C4D, C4F, C5E, C61, C65, C6B, C6H, C7G, C7I, C89, C94, C9A, C9E, C9G, CA1, CB6, CB8, CC1, CC7, CD4, CDC, CDI, CE5, CF4, CG1, CG3, CG7, CGD, CGF, CH2, CH8, CHI, CI5, CIH, D0A, D19, D1B, D1H, D22, D31, D39, D4E, D4I, D51, D55, D5B, D5D, D66, D6A, D75, D8G, D97, D9D, DA6, DB1, DB7, DBH, DCA, DCC, DCG, DD3, DDB, DDH, DE8, DEA, DEE, DF9, DFF, DG2, DG6, DGC, DGE, DH5, DH7, DI4, DIG, E05, E14, E18, E1E, E27, E29, E2F, E32, E38, E4H, E54, E5I, E63, E6B, E72, E7A, E83, E92, E96, E98, E9C, EAH, EBA, EBG, EBI, ECF, ED2, ED8, EE3, EED, EF8, EFC, EH4, EHA, EHG, EI3, EIB, EIH, F02, F04, F0G, F13, F17, F19, F1F, F2I, F35, F37, F3B, F4A, F4C, F4G, F59, F5B, F5H, F62, F79, F7F, F82, F86, F8E, F95, FAI, FBF, FBH, FC4, FC8, FCA, FCE, FCG, FD7, FE2, FE8, FEC, FF1, FFB, FFH, FGI, FH3, FH5, FHB, G03, G07, G0F, G16, G1C, G1I, G27, G2D, G36, G3A, G3G, G3I, G45, G49, G4F, G4H, G58, G5A, G67, G6D, G7E, G7I, G8B, G96, GAF, GB2, GC3, GC7, GD6, GDE, GE1, GE5, GEB, GF6, GFC, GFI, GG9, GGB, GH2, GHE, GI3, GID, GIF, H06, H0E, H17, H1H, H33, H35, H39, H3H, H44, H48, H4G, H5F, H66, H6C, H6I, H71, H77, H7H, H8A, H8C, H93, H99, H9F, HA2, HAA, HAG, HB7, HBD, HBF, HC2, HC8, HCE, HD5, HDD, HEI, HF5, HG8, HGA, HH9, HHD, HI2, HIC, I14, I1C, I2B, I2F, I2H, I38, I3E, I3G, I43, I47, I56, I5E, I67, I76, I83, I89, I8B, I94, I9A, IA1, IA3, IAD, IAF, IB2, IBC, IC7, ICB, IDG, IDI, IEF, IEH, IF8, IFA, IG1, IH2, IH6, IH8, IHC, II1, IIH, 1004, 100A, 100C, 1015, 1022, 102A, 102E, 1031, 104C, 104E, 1055, 1057, 105D, 105H, 1064, 106A, 106I, 1075, 1079, 1082, 1088, 108G, 1099, 109D, 10A8, 10B1, 10BB, 10CG, 10D3, 10DF, 10E2, 10E4, 10F7, 10FF, 10GE, 10H5, 10HB, 10I6, 10IA, 10IC, 10II, 1109, 110H, 1114, 1118, 111E, 1136, 1141, 114B, 114D, 1156, 115G, 115I, 116F, 116H, 117G, 1192, 11A1, 11A7, 11B4, 11C3, 11C9, 11CB, 11DA, 11DE, 11E1, 11E3, 11ED, 11F2, 11FC, 11FI, 11G5, 11GD, 11GH, 11H4, 11H6, 11HG, 11HI, 11IB, 11IF, 1202, 1208, 120A, 1213, 1217, 1222, 1231, 1235, 123B, 124C, 124G, 1255, 125B, 125F, 1264, 1268, 1273, 1279, 127D, 1288, 1291, 1295, 1297, 12AI, 12B3, 12C8, 12CE, 12D1, 12DD, 12E6, 12F1, 12F7, 12FB, 12FD, 12FH, 12GG, 12H3, 12HF, 12I4, 12IA, 12IE, 1307, 1309, 1312, 132D, 133A, ...
20	13, 19, 1B, 1H, 21, 23, 27, 2D, 2J, 31, 37, 3B, 3D, 3J, 43, 49, 4H, 51, 53, 57, 59, 5D, 67, 6B, 6H, 6J, 79, 7B, 7H, 83, 87, 8D, 8J, 91, 9B, 9D, 9H, 9J, AB, B3, B7, B9, BD, BJ, C1, CB, CH, D3, D9, DB, DH, E1, E3, ED, F7, FB, FD, FH, GB, GH, H7, H9, HD, HJ, I7, ID, IJ, J3, J9, JH, 101, 109, 10J, 111, 11B, 11D, 11J, 123, 129, 12H, 131, 133, 137, 13J, 147, 14B, 14J, 153, 159, 161, 163, 171, 177, 17H, 183, 189, 18B, 18H, 197, 19D, 19J, 1A1, 1A7, 1AD, 1AH, 1AJ, 1BB, 1C1, 1C3, 1C7, 1CD, 1CJ, 1D1, 1DD, 1DH, 1E3, 1EB, 1F1, 1F9, 1FJ, 1G7, 1GD, 1GJ, 1H3, 1HB, 1HH, 1I1, 1I9, 1ID, 1J7, 1JH, 209, 20B, 211, 213, 217, 219, 21J, 22D, 22H, 22J, 233, 23H, 241, 243, 247, 257, 25B, 25J, 269, 26H, 271, 277, 27D, 287, 28B, 28H, 293, 29B, 29H, 2A9, 2AD, 2AJ, 2B1, 2BB, 2BD, 2BJ, 2C9, 2CB, 2D1, 2D3, 2D9, 2E7, 2EB, 2ED, 2EH, 2F3, 2F9, 2FH, 2G3, 2G9, 2HB, 2HD, 2I3, 2IB, 2J1, 2J7, 2JD, 301, 30D, 30H, 313, 319, 31B, 31H, 329, 32J, 33H, 33J, 343, 349, 34B, 34H, 351, 353, 357, 35J, 361, 367, 381, 387, 38D, 391, 39J, 3A9, 3B3, 3B7, 3B9, 3BD, 3BJ, 3C7, 3CB, 3CD, 3CJ, 3DB, 3E1, 3E3, 3E7, 3E9, 3ED, 3EJ, 3FB, 3G3, 3GB, 3H3, 3H9, 3HD, 3HJ, 3I7, 3IB, 3IJ, 3J3, 3JH, 401, 407, 409, 40D, 40J, 411, 417, 41H, 42H, 433, 437, 439, 44D, 44H, 44J, 459, 461, 463, 46D, 471, 477, 47D, 47J, 48H, 493, 497, 499, 4A1, 4AB, 4B3, 4BB, 4C7, 4D1, 4D7, 4DB, 4DD, 4DH, 4DJ, 4E9, 4F1, 4F7, 4FD, 4GB, 4GD, 4H9, 4HB, 4ID, 4IJ, 4J7, 4JD, 4JH, 4JJ, 503, 50B, 50H, 517, 519, 51J, 52D, 533, 539, 541, 543, 547, 549, 54J, 55B, 55D, 569, 56B, 56H, 571, 573, 57D, 581, 58J, 5A3, 5A7, 5AD, 5B1, 5BH, 5BJ, 5C3, 5CB, 5D7, 5D9, 5DD, 5E1, 5E7, 5ED, 5EH, 5F9, 5FB, 5GD, 5GJ, 5H1, 5H7, 5HB, 5HH, 5IB, 5IH, 5J1, 5J3, 5J9, 5JD, 5JJ, 60B, 60H, 613, 61H, 621, 627, 62J, 637, 63D, 63H, 653, 661, 66B, 66J, 673, 679, 67B, 67H, 68J, 69B, 69D, 6A9, 6AH, 6B1, 6BD, 6C7, 6CH, 6CJ, 6D3, 6DB, 6DH, 6E3, 6E7, 6E9, 6ED, 6EJ, 6F7, 6FB, 6FD, 6FJ, 6G9, 6GB, 6H1, 6H9, 6HD, 6I7, 6IH, 6J9, 6JB, 6JH, 701, 703, 70J, 71D, 71H, 723, 72B, 72H, 731, 73J, 747, 74H, 753, 759, 75H, 767, 76J, 77D, 77H, 783, 789, 78B, 79J, 7A1, 7AB, 7AJ, 7B3, 7BH, 7C1, 7C9, 7D1, 7D7, 7DJ, 7E3, 7E9, 7F9, 7FJ, 7G1, 7GH, 7I3, 7I7, 7I9, 7J1, 7J7, 7JB, 803, 809, 80H, 811, 819, 82B, 82D, 82H, 82J, 83B, 84J, 851, 857, 85D, 85J, 863, 869, 86B, 873, 877, 87J, 881, 88B, 88D, 899, 89B, 8A7, 8AD, 8BD, 8C9, 8CH, 8D1, 8D3, 8D7, 8D9, 8EB, 8EJ, 8FB, 8FH, 8G7, 8G9, 8GD, 8GJ, 8H1, 8H7, 8HH, 8HJ, 8IB, 8J1, 8J3, 8JD, 907, 90D, 90H, 913, 91B, 91H, 923, 92J, 93B, 93D, 93H, 94B, 94H, 951, 959, 95J, 967, 96D, 96J, 981, 987, 989, 98J, 99D, 99H, 9A3, 9B1, 9B3, 9BD, 9C7, 9CB, 9CD, 9D3, 9DH, 9E1, 9E9, 9F7, 9FB, 9FH, 9FJ, 9G3, 9G9, 9GB, 9H3, 9H7, 9I7, 9J9, A01, A03, A07, A0D, A0J, A11, A17, A29, A2B, A2H, A3D, A3J, A4B, A4D, A4J, A5B, A67, A69, A6D, A6J, A7D, A7H, A7J, A8H, AA1, AAB, AAH, AAJ, AB9, ABB, AC1, AC3, ACD, ACJ, AD1, ADB, ADD, AE3, AE9, AEH, AG7, AGH, AGJ, AH9, AHH, AI3, AID, AJB, AJH, B09, B11, B13, B21, B27, B2B, B2H, B33, B41, B43, B4D, B57, B5D, B5H, B5J, B63, B77, B79, B81, B87, B93, B9B, B9H, BA3, BB1, BBH, BBJ, BC3, BC9, BCB, BCH, BD3, BDD, BDJ, BEB, BF3, BG1, BG3, BG9, BGD, BHB, BHJ, BJ3, BJ7, BJ9, BJD, BJJ, C01, C0D, C0H, C1B, C31, C3B, C3H, C49, C53, C59, C5J, C6B, C6D, C6H, C73, C7B, C7H, C87, C89, C8D, C97, C9D, C9J, CA3, CA9, CAB, CB1, CB3, CBJ, CCB, CCJ, CDH, CE1, CE7, CEJ, CF1, CF7, CFD, CFJ, CH7, CHD, CI7, CIB, CIJ, CJ9, CJH, D09, D17, D1B, D1D, D1H, D31, D3D, D3J, D41, D4H, D53, D59, D63, D6D, D77, D7B, D91, D97, D9D, D9J, DA7, DAD, DAH, DAJ, DBB, DBH, DC1, DC3, DC9, DDB, DDH, DDJ, DE3, DF1, DF3, DF7, DFJ, DG1, DG7, DGB, DHH, DI3, DI9, DID, DJ1, DJB, E13, E1J, E21, E27, E2B, E2D, E2H, E2J, E39, E43, E49, E4D, E51, E5B, E5H, E6H, E71, E73, E79, E8J, E93, E9B, EA1, EA7, EAD, EB1, EB7, EBJ, EC3, EC9, ECB, ECH, ED1, ED7, ED9, EDJ, EE1, EEH, EF3, EG3, EG7, EGJ, EHD, EJ1, EJ7, F07, F0B, F19, F1H, F23, F27, F2D, F37, F3D, F3J, F49, F4B, F51, F5D, F61, F6B, F6D, F73, F7B, F83, F8D, F9H, F9J, FA3, FAB, FAH, FB1, FB9, FC7, FCH, FD3, FD9, FDB, FDH, FE7, FEJ, FF1, FFB, FFH, FG3, FG9, FGH, FH3, FHD, FHJ, FI1, FI7, FID, FIJ, FJ9, FJH, G11, G17, G29, G2B, G39, G3D, G41, G4B, G61, G69, G77, G7B, G7D, G83, G89, G8B, G8H, G91, G9J, GA7, GAJ, GBH, GCD, GCJ, GD1, GDD, GDJ, GE9, GEB, GF1, GF3, GF9, GFJ, GGD, GGH, GI1, GI3, GIJ, GJ1, GJB, GJD, H03, H13, H17, H19, H1D, H21, H2H, H33, H39, H3B, H43, H4J, H57, H5B, H5H, H77, H79, H7J, H81, H87, H8B, H8H, H93, H9B, H9H, HA1, HAD, HAJ, HB7, HBJ, HC3, HCH, HD9, HDJ, HF3, HF9, HG1, HG7, HG9, HHB, HHJ, HIH, HJ7, HJD, I07, I0B, I0D, I0J, I19, I1H, I23, I27, I2D, I43, I4H, I57, I59, I61, I6B, I6D, I79, I7B, I89, I9D, IAB, IAH, IBD, ICB, ICH, ICJ, IDH, IE1, IE7, IE9, IEJ, IF7, IFH, IG3, IG9, IGH, IH1, IH7, IH9, IHJ, II1, IID, IIH, IJ3, IJ9, IJB, J03, J07, J11, J1J, J23, J29, J39, J3D, J41, J47, J4B, J4J, J53, J5H, J63, J67, J71, J7D, J7H, J7J, J99, J9D, JAH, JB3, JB9, JC1, JCD, JD7, JDD, JDH, JDJ, JE3, JF1, JF7, JFJ, JG7, JGD, JGH, JH9, JHB, JI3, JJD, 1009, ...
21	12, 18, 1A, 1G, 1K, 21, 25, 2B, 2H, 2J, 34, 38, 3A, 3G, 3K, 45, 4D, 4H, 4J, 52, 54, 58, 61, 65, 6B, 6D, 72, 74, 7A, 7G, 7K, 85, 8B, 8D, 92, 94, 98, 9A, A1, AD, AH, AJ, B2, B8, BA, BK, C5, CB, CH, CJ, D4, D8, DA, DK, ED, EH, EJ, F2, FG, G1, GB, GD, GH, H2, HA, HG, I1, I5, IB, IJ, J2, JA, JK, K1, KB, KD, KJ, 102, 108, 10G, 10K, 111, 115, 11H, 124, 128, 12G, 12K, 135, 13H, 13J, 14G, 151, 15B, 15H, 162, 164, 16A, 16K, 175, 17B, 17D, 17J, 184, 188, 18A, 191, 19B, 19D, 19H, 1A2, 1A8, 1AA, 1B1, 1B5, 1BB, 1BJ, 1C8, 1CG, 1D5, 1DD, 1DJ, 1E4, 1E8, 1EG, 1F1, 1F5, 1FD, 1FH, 1GA, 1GK, 1HB, 1HD, 1I2, 1I4, 1I8, 1IA, 1IK, 1JD, 1JH, 1JJ, 1K2, 1KG, 1KK, 201, 205, 214, 218, 21G, 225, 22D, 22H, 232, 238, 241, 245, 24B, 24H, 254, 25A, 261, 265, 26B, 26D, 272, 274, 27A, 27K, 281, 28B, 28D, 28J, 29G, 29K, 2A1, 2A5, 2AB, 2AH, 2B4, 2BA, 2BG, 2CH, 2CJ, 2D8, 2DG, 2E5, 2EB, 2EH, 2F4, 2FG, 2FK, 2G5, 2GB, 2GD, 2GJ, 2HA, 2HK, 2IH, 2IJ, 2J2, 2J8, 2JA, 2JG, 2JK, 2K1, 2K5, 2KH, 2KJ, 304, 31H, 322, 328, 32G, 33D, 342, 34G, 34K, 351, 355, 35B, 35J, 362, 364, 36A, 371, 37B, 37D, 37H, 37J, 382, 388, 38K, 39B, 39J, 3AA, 3AG, 3AK, 3B5, 3BD, 3BH, 3C4, 3C8, 3D1, 3D5, 3DB, 3DD, 3DH, 3E2, 3E4, 3EA, 3EK, 3FJ, 3G4, 3G8, 3GA, 3HD, 3HH, 3HJ, 3I8, 3IK, 3J1, 3JB, 3JJ, 3K4, 3KA, 3KG, 40D, 40J, 412, 414, 41G, 425, 42H, 434, 43K, 44D, 44J, 452, 454, 458, 45A, 45K, 46B, 46H, 472, 47K, 481, 48H, 48J, 49K, 4A5, 4AD, 4AJ, 4B2, 4B4, 4B8, 4BG, 4C1, 4CB, 4CD, 4D2, 4DG, 4E5, 4EB, 4F2, 4F4, 4F8, 4FA, 4FK, 4GB, 4GD, 4H8, 4HA, 4HG, 4HK, 4I1, 4IB, 4IJ, 4JG, 4KJ, 502, 508, 50G, 51B, 51D, 51H, 524, 52K, 531, 535, 53D, 53J, 544, 548, 54K, 551, 562, 568, 56A, 56G, 56K, 575, 57J, 584, 588, 58A, 58G, 58K, 595, 59H, 5A2, 5A8, 5B1, 5B5, 5BB, 5C2, 5CA, 5CG, 5CK, 5E4, 5F1, 5FB, 5FJ, 5G2, 5G8, 5GA, 5GG, 5HH, 5I8, 5IA, 5J5, 5JD, 5JH, 5K8, 601, 60B, 60D, 60H, 614, 61A, 61G, 61K, 621, 625, 62B, 62J, 632, 634, 63A, 63K, 641, 64B, 64J, 652, 65G, 665, 66H, 66J, 674, 678, 67A, 685, 68J, 692, 698, 69G, 6A1, 6A5, 6B2, 6BA, 6BK, 6C5, 6CB, 6CJ, 6D8, 6DK, 6ED, 6EH, 6F2, 6F8, 6FA, 6GH, 6GJ, 6H8, 6HG, 6HK, 6ID, 6IH, 6J4, 6JG, 6K1, 6KD, 6KH, 702, 711, 71B, 71D, 728, 73D, 73H, 73J, 74A, 74G, 74K, 75B, 75H, 764, 768, 76G, 77H, 77J, 782, 784, 78G, 7A2, 7A4, 7AA, 7AG, 7B1, 7B5, 7BB, 7BD, 7C4, 7C8, 7CK, 7D1, 7DB, 7DD, 7E8, 7EA, 7F5, 7FB, 7GA, 7H5, 7HD, 7HH, 7HJ, 7I2, 7I4, 7J5, 7JD, 7K4, 7KA, 7KK, 801, 805, 80B, 80D, 80J, 818, 81A, 821, 82B, 82D, 832, 83G, 841, 845, 84B, 84J, 854, 85A, 865, 86H, 86J, 872, 87G, 881, 885, 88D, 892, 89A, 89G, 8A1, 8B2, 8B8, 8BA, 8BK, 8CD, 8CH, 8D2, 8DK, 8E1, 8EB, 8F4, 8F8, 8FA, 8FK, 8GD, 8GH, 8H4, 8I1, 8I5, 8IB, 8ID, 8IH, 8J2, 8J4, 8JG, 8JK, 8KJ, 90K, 91B, 91D, 91H, 922, 928, 92A, 92G, 93H, 93J, 944, 94K, 955, 95H, 95J, 964, 96G, 97B, 97D, 97H, 982, 98G, 98K, 991, 99J, 9B1, 9BB, 9BH, 9BJ, 9C8, 9CA, 9CK, 9D1, 9DB, 9DH, 9DJ, 9E8, 9EA, 9EK, 9F5, 9FD, 9H1, 9HB, 9HD, 9I2, 9IA, 9IG, 9J5, 9K2, 9K8, 9KK, A0B, A0D, A1A, A1G, A1K, A25, A2B, A38, A3A, A3K, A4D, A4J, A52, A54, A58, A6B, A6D, A74, A7A, A85, A8D, A8J, A94, AA1, AAH, AAJ, AB2, AB8, ABA, ABG, AC1, ACB, ACH, AD8, ADK, AEH, AEJ, AF4, AF8, AG5, AGD, AHG, AHK, AI1, AI5, AIB, AID, AJ4, AJ8, AK1, B0A, B0K, B15, B1H, B2A, B2G, B35, B3H, B3J, B42, B48, B4G, B51, B5B, B5D, B5H, B6A, B6G, B71, B75, B7B, B7D, B82, B84, B8K, B9B, B9J, BAG, BAK, BB5, BBH, BBJ, BC4, BCA, BCG, BE2, BE8, BF1, BF5, BFD, BG2, BGA, BH1, BHJ, BI2, BI4, BI8, BJB, BK2, BK8, BKA, C05, C0B, C0H, C1A, C1K, C2D, C2H, C45, C4B, C4H, C52, C5A, C5G, C5K, C61, C6D, C6J, C72, C74, C7A, C8B, C8H, C8J, C92, C9K, CA1, CA5, CAH, CAJ, CB4, CB8, CCD, CCJ, CD4, CD8, CDG, CE5, CFG, CGB, CGD, CGJ, CH2, CH4, CH8, CHA, CHK, CID, CIJ, CJ2, CJA, CJK, CK5, D04, D08, D0A, D0G, D24, D28, D2G, D35, D3B, D3H, D44, D4A, D51, D55, D5B, D5D, D5J, D62, D68, D6A, D6K, D71, D7H, D82, D91, D95, D9H, DAA, DBH, DC2, DD1, DD5, DE2, DEA, DEG, DEK, DF5, DFJ, DG4, DGA, DGK, DH1, DHB, DI2, DIA, DIK, DJ1, DJB, DJJ, DKA, DKK, E12, E14, E18, E1G, E21, E25, E2D, E3A, E3K, E45, E4B, E4D, E4J, E58, E5K, E61, E6B, E6H, E72, E78, E7G, E81, E8B, E8H, E8J, E94, E9A, E9G, EA5, EAD, EBG, EC1, ED2, ED4, EE1, EE5, EED, EF2, EGB, EGJ, EHG, EHK, EI1, EIB, EIH, EIJ, EJ4, EJ8, EK5, EKD, F04, F11, F1H, F22, F24, F2G, F31, F3B, F3D, F42, F44, F4A, F4K, F5D, F5H, F6K, F71, F7H, F7J, F88, F8A, F8K, F9J, FA2, FA4, FA8, FAG, FBB, FBH, FC2, FC4, FCG, FDB, FDJ, FE2, FE8, FFH, FFJ, FG8, FGA, FGG, FGK, FH5, FHB, FHJ, FI4, FI8, FIK, FJ5, FJD, FK4, FK8, G01, G0D, G12, G25, G2B, G32, G38, G3A, G4B, G4J, G5G, G65, G6B, G74, G78, G7A, G7G, G85, G8D, G8J, G92, G98, GAH, GBA, GBK, GC1, GCD, GD2, GD4, GDK, GE1, GEJ, GG1, GGJ, GH4, GHK, GIH, GJ2, GJ4, GK1, GK5, GKB, GKD, H02, H0A, H0K, H15, H1B, H1J, H22, H28, H2A, H2K, H31, H3D, H3H, H42, H48, H4A, H51, H55, H5J, H6G, H6K, H75, H84, H88, H8G, H91, H95, H9D, H9H, HAA, HAG, HAK, HBD, HC4, HC8, HCA, HDJ, HE2, HF5, HFB, HFH, HG8, HGK, HHD, HHJ, HI2, HI4, HI8, HJ5, HJB, HK2, HKA, HKG, HKK, I0B, I0D, I14, I2D, I38, ...
22	11, 17, 19, 1F, 1J, 1L, 23, 29, 2F, 2H, 31, 35, 37, 3D, 3H, 41, 49, 4D, 4F, 4J, 4L, 53, 5H, 5L, 65, 67, 6H, 6J, 73, 79, 7D, 7J, 83, 85, 8F, 8H, 8L, 91, 9D, A3, A7, A9, AD, AJ, AL, B9, BF, BL, C5, C7, CD, CH, CJ, D7, DL, E3, E5, E9, F1, F7, FH, FJ, G1, G7, GF, GL, H5, H9, HF, I1, I5, ID, J1, J3, JD, JF, JL, K3, K9, KH, KL, L1, L5, LH, 103, 107, 10F, 10J, 113, 11F, 11H, 12D, 12J, 137, 13D, 13J, 13L, 145, 14F, 14L, 155, 157, 15D, 15J, 161, 163, 16F, 173, 175, 179, 17F, 17L, 181, 18D, 18H, 191, 199, 19J, 1A5, 1AF, 1B1, 1B7, 1BD, 1BH, 1C3, 1C9, 1CD, 1CL, 1D3, 1DH, 1E5, 1EH, 1EJ, 1F7, 1F9, 1FD, 1FF, 1G3, 1GH, 1GL, 1H1, 1H5, 1HJ, 1I1, 1I3, 1I7, 1J5, 1J9, 1JH, 1K5, 1KD, 1KH, 1L1, 1L7, 1LL, 203, 209, 20F, 211, 217, 21J, 221, 227, 229, 22J, 22L, 235, 23F, 23H, 245, 247, 24D, 259, 25D, 25F, 25J, 263, 269, 26H, 271, 277, 287, 289, 28J, 295, 29F, 29L, 2A5, 2AD, 2B3, 2B7, 2BD, 2BJ, 2BL, 2C5, 2CH, 2D5, 2E1, 2E3, 2E7, 2ED, 2EF, 2EL, 2F3, 2F5, 2F9, 2FL, 2G1, 2G7, 2HJ, 2I3, 2I9, 2IH, 2JD, 2K1, 2KF, 2KJ, 2KL, 2L3, 2L9, 2LH, 2LL, 301, 307, 30J, 317, 319, 31D, 31F, 31J, 323, 32F, 335, 33D, 343, 349, 34D, 34J, 355, 359, 35H, 35L, 36D, 36H, 371, 373, 377, 37D, 37F, 37L, 389, 397, 39D, 39H, 39J, 3AL, 3B3, 3B5, 3BF, 3C5, 3C7, 3CH, 3D3, 3D9, 3DF, 3DL, 3EH, 3F1, 3F5, 3F7, 3FJ, 3G7, 3GJ, 3H5, 3HL, 3ID, 3IJ, 3J1, 3J3, 3J7, 3J9, 3JJ, 3K9, 3KF, 3KL, 3LH, 3LJ, 40D, 40F, 41F, 41L, 427, 42D, 42H, 42J, 431, 439, 43F, 443, 445, 44F, 457, 45H, 461, 46D, 46F, 46J, 46L, 479, 47L, 481, 48H, 48J, 493, 497, 499, 49J, 4A5, 4B1, 4C3, 4C7, 4CD, 4CL, 4DF, 4DH, 4DL, 4E7, 4F1, 4F3, 4F7, 4FF, 4FL, 4G5, 4G9, 4GL, 4H1, 4I1, 4I7, 4I9, 4IF, 4IJ, 4J3, 4JH, 4K1, 4K5, 4K7, 4KD, 4KH, 4L1, 4LD, 4LJ, 503, 50H, 50L, 515, 51H, 523, 529, 52D, 53H, 54D, 551, 559, 55D, 55J, 55L, 565, 575, 57H, 57J, 58D, 58L, 593, 59F, 5A7, 5AH, 5AJ, 5B1, 5B9, 5BF, 5BL, 5C3, 5C5, 5C9, 5CF, 5D1, 5D5, 5D7, 5DD, 5E1, 5E3, 5ED, 5EL, 5F3, 5FH, 5G5, 5GH, 5GJ, 5H3, 5H7, 5H9, 5I3, 5IH, 5IL, 5J5, 5JD, 5JJ, 5K1, 5KJ, 5L5, 5LF, 5LL, 605, 60D, 611, 61D, 625, 629, 62F, 62L, 631, 647, 649, 64J, 655, 659, 661, 665, 66D, 673, 679, 67L, 683, 689, 697, 69H, 69J, 6AD, 6BH, 6BL, 6C1, 6CD, 6CJ, 6D1, 6DD, 6DJ, 6E5, 6E9, 6EH, 6FH, 6FJ, 6G1, 6G3, 6GF, 6HL, 6I1, 6I7, 6ID, 6IJ, 6J1, 6J7, 6J9, 6JL, 6K3, 6KF, 6KH, 6L5, 6L7, 701, 703, 70J, 713, 721, 72H, 733, 737, 739, 73D, 73F, 74F, 751, 75D, 75J, 767, 769, 76D, 76J, 76L, 775, 77F, 77H, 787, 78H, 78J, 797, 79L, 7A5, 7A9, 7AF, 7B1, 7B7, 7BD, 7C7, 7CJ, 7CL, 7D3, 7DH, 7E1, 7E5, 7ED, 7F1, 7F9, 7FF, 7FL, 7GL, 7H5, 7H7, 7HH, 7I9, 7ID, 7IJ, 7JF, 7JH, 7K5, 7KJ, 7L1, 7L3, 7LD, 805, 809, 80H, 81D, 81H, 821, 823, 827, 82D, 82F, 835, 839, 847, 857, 85J, 85L, 863, 869, 86F, 86H, 871, 881, 883, 889, 893, 899, 89L, 8A1, 8A7, 8AJ, 8BD, 8BF, 8BJ, 8C3, 8CH, 8CL, 8D1, 8DJ, 8EL, 8F9, 8FF, 8FH, 8G5, 8G7, 8GH, 8GJ, 8H7, 8HD, 8HF, 8I3, 8I5, 8IF, 8IL, 8J7, 8KF, 8L3, 8L5, 8LF, 901, 907, 90H, 91D, 91J, 929, 92L, 931, 93J, 943, 947, 94D, 94J, 95F, 95H, 965, 96J, 973, 977, 979, 97D, 98F, 98H, 997, 99D, 9A7, 9AF, 9AL, 9B5, 9C1, 9CH, 9CJ, 9D1, 9D7, 9D9, 9DF, 9DL, 9E9, 9EF, 9F5, 9FH, 9GD, 9GF, 9GL, 9H3, 9HL, 9I7, 9J9, 9JD, 9JF, 9JJ, 9K3, 9K5, 9KH, 9KL, 9LD, A0L, A19, A1F, A25, A2J, A33, A3D, A43, A45, A49, A4F, A51, A57, A5H, A5J, A61, A6F, A6L, A75, A79, A7F, A7H, A85, A87, A91, A9D, A9L, AAH, AAL, AB5, ABH, ABJ, AC3, AC9, ACF, ADL, AE5, AEJ, AF1, AF9, AFJ, AG5, AGH, AHD, AHH, AHJ, AI1, AJ3, AJF, AJL, AK1, AKH, AL1, AL7, ALL, B09, B11, B15, B2D, B2J, B33, B39, B3H, B41, B45, B47, B4J, B53, B57, B59, B5F, B6F, B6L, B71, B75, B81, B83, B87, B8J, B8L, B95, B99, BAD, BAJ, BB3, BB7, BBF, BC3, BDD, BE7, BE9, BEF, BEJ, BEL, BF3, BF5, BFF, BG7, BGD, BGH, BH3, BHD, BHJ, BIH, BIL, BJ1, BJ7, BKF, BKJ, BL5, BLF, BLL, C05, C0D, C0J, C19, C1D, C1J, C1L, C25, C29, C2F, C2H, C35, C37, C41, C47, C55, C59, C5L, C6D, C7J, C83, C91, C95, CA1, CA9, CAF, CAJ, CB3, CBH, CC1, CC7, CCH, CCJ, CD7, CDJ, CE5, CEF, CEH, CF5, CFD, CG3, CGD, CHF, CHH, CHL, CI7, CID, CIH, CJ3, CJL, CK9, CKF, CKL, CL1, CL7, CLH, D07, D09, D0J, D13, D19, D1F, D21, D27, D2H, D31, D33, D39, D3F, D3L, D49, D4H, D5J, D63, D73, D75, D81, D85, D8D, D91, DA9, DAH, DBD, DBH, DBJ, DC7, DCD, DCF, DCL, DD3, DDL, DE7, DEJ, DFF, DG9, DGF, DGH, DH7, DHD, DI1, DI3, DID, DIF, DIL, DJ9, DK1, DK5, DL7, DL9, E03, E05, E0F, E0H, E15, E23, E27, E29, E2D, E2L, E3F, E3L, E45, E47, E4J, E5D, E5L, E63, E69, E7H, E7J, E87, E89, E8F, E8J, E93, E99, E9H, EA1, EA5, EAH, EB1, EB9, EBL, EC3, ECH, ED7, EDH, EEJ, EF3, EFF, EFL, EG1, EH1, EH9, EI5, EIF, EIL, EJD, EJH, EJJ, EK3, EKD, EKL, EL5, EL9, ELF, F11, F1F, F23, F25, F2H, F35, F37, F41, F43, F4L, F61, F6J, F73, F7J, F8F, F8L, F91, F9J, FA1, FA7, FA9, FAJ, FB5, FBF, FBL, FC5, FCD, FCH, FD1, FD3, FDD, FDF, FE5, FE9, FEF, FEL, FF1, FFD, FFH, FG9, FH5, FH9, FHF, FID, FIH, FJ3, FJ9, FJD, FJL, FK3, FKH, FL1, FL5, FLJ, G09, G0D, G0F, G21, G25, G37, G3D, G3J, G49, G4L, G5D, G5J, G61, G63, G67, G73, G79, G7L, G87, G8D, G8H, G97, G99, G9L, GB7, GC1, ...
23	16, 18, 1E, 1I, 1K, 21, 27, 2D, 2F, 2L, 32, 34, 3A, 3E, 3K, 45, 49, 4B, 4F, 4H, 4L, 5C, 5G, 5M, 61, 6B, 6D, 6J, 72, 76, 7C, 7I, 7K, 87, 89, 8D, 8F, 94, 9G, 9K, 9M, A3, A9, AB, AL, B4, BA, BG, BI, C1, C5, C7, CH, D8, DC, DE, DI, E9, EF, F2, F4, F8, FE, FM, G5, GB, GF, GL, H6, HA, HI, I5, I7, IH, IJ, J2, J6, JC, JK, K1, K3, K7, KJ, L4, L8, LG, LK, M3, MF, MH, 10C, 10I, 115, 11B, 11H, 11J, 122, 12C, 12I, 131, 133, 139, 13F, 13J, 13L, 14A, 14K, 14M, 153, 159, 15F, 15H, 166, 16A, 16G, 171, 17B, 17J, 186, 18E, 18K, 193, 197, 19F, 19L, 1A2, 1AA, 1AE, 1B5, 1BF, 1C4, 1C6, 1CG, 1CI, 1CM, 1D1, 1DB, 1E2, 1E6, 1E8, 1EC, 1F3, 1F7, 1F9, 1FD, 1GA, 1GE, 1GM, 1H9, 1HH, 1HL, 1I4, 1IA, 1J1, 1J5, 1JB, 1JH, 1K2, 1K8, 1KK, 1L1, 1L7, 1L9, 1LJ, 1LL, 1M4, 1ME, 1MG, 203, 205, 20B, 216, 21A, 21C, 21G, 21M, 225, 22D, 22J, 232, 241, 243, 24D, 24L, 258, 25E, 25K, 265, 26H, 26L, 274, 27A, 27C, 27I, 287, 28H, 29C, 29E, 29I, 2A1, 2A3, 2A9, 2AD, 2AF, 2AJ, 2B8, 2BA, 2BG, 2D4, 2DA, 2DG, 2E1, 2EJ, 2F6, 2FK, 2G1, 2G3, 2G7, 2GD, 2GL, 2H2, 2H4, 2HA, 2HM, 2I9, 2IB, 2IF, 2IH, 2IL, 2J4, 2JG, 2K5, 2KD, 2L2, 2L8, 2LC, 2LI, 2M3, 2M7, 2MF, 2MJ, 30A, 30E, 30K, 30M, 313, 319, 31B, 31H, 324, 331, 337, 33B, 33D, 34E, 34I, 34K, 357, 35J, 35L, 368, 36G, 36M, 375, 37B, 386, 38C, 38G, 38I, 397, 39H, 3A6, 3AE, 3B7, 3BL, 3C4, 3C8, 3CA, 3CE, 3CG, 3D3, 3DF, 3DL, 3E4, 3EM, 3F1, 3FH, 3FJ, 3GI, 3H1, 3H9, 3HF, 3HJ, 3HL, 3I2, 3IA, 3IG, 3J3, 3J5, 3JF, 3K6, 3KG, 3KM, 3LB, 3LD, 3LH, 3LJ, 3M6, 3MI, 3MK, 40D, 40F, 40L, 412, 414, 41E, 41M, 42H, 43I, 43M, 445, 44D, 456, 458, 45C, 45K, 46D, 46F, 46J, 474, 47A, 47G, 47K, 489, 48B, 49A, 49G, 49I, 4A1, 4A5, 4AB, 4B2, 4B8, 4BC, 4BE, 4BK, 4C1, 4C7, 4CJ, 4D2, 4D8, 4DM, 4E3, 4E9, 4EL, 4F6, 4FC, 4FG, 4GJ, 4HE, 4I1, 4I9, 4ID, 4IJ, 4IL, 4J4, 4K3, 4KF, 4KH, 4LA, 4LI, 4LM, 4MB, 502, 50C, 50E, 50I, 513, 519, 51F, 51J, 51L, 522, 528, 52G, 52K, 52M, 535, 53F, 53H, 544, 54C, 54G, 557, 55H, 566, 568, 56E, 56I, 56K, 57D, 584, 588, 58E, 58M, 595, 599, 5A4, 5AC, 5AM, 5B5, 5BB, 5BJ, 5C6, 5CI, 5D9, 5DD, 5DJ, 5E2, 5E4, 5F9, 5FB, 5FL, 5G6, 5GA, 5H1, 5H5, 5HD, 5I2, 5I8, 5IK, 5J1, 5J7, 5K4, 5KE, 5KG, 5L9, 5MC, 5MG, 5MI, 607, 60D, 60H, 616, 61C, 61K, 621, 629, 638, 63A, 63E, 63G, 645, 65A, 65C, 65I, 661, 667, 66B, 66H, 66J, 678, 67C, 681, 683, 68D, 68F, 698, 69A, 6A3, 6A9, 6B6, 6BM, 6C7, 6CB, 6CD, 6CH, 6CJ, 6DI, 6E3, 6EF, 6EL, 6F8, 6FA, 6FE, 6FK, 6FM, 6G5, 6GF, 6GH, 6H6, 6HG, 6HI, 6I5, 6IJ, 6J2, 6J6, 6JC, 6JK, 6K3, 6K9, 6L2, 6LE, 6LG, 6LK, 6MB, 6MH, 6ML, 706, 70G, 711, 717, 71D, 72C, 72I, 72K, 737, 73L, 742, 748, 753, 755, 75F, 766, 76A, 76C, 76M, 77D, 77H, 782, 78K, 791, 797, 799, 79D, 79J, 79L, 7AA, 7AE, 7BB, 7CA, 7CM, 7D1, 7D5, 7DB, 7DH, 7DJ, 7E2, 7F1, 7F3, 7F9, 7G2, 7G8, 7GK, 7GM, 7H5, 7HH, 7IA, 7IC, 7IG, 7IM, 7JD, 7JH, 7JJ, 7KE, 7LF, 7M2, 7M8, 7MA, 7MK, 7MM, 809, 80B, 80L, 814, 816, 81G, 81I, 825, 82B, 82J, 843, 84D, 84F, 852, 85A, 85G, 863, 86L, 874, 87G, 885, 887, 892, 898, 89C, 89I, 8A1, 8AJ, 8AL, 8B8, 8BM, 8C5, 8C9, 8CB, 8CF, 8DG, 8DI, 8E7, 8ED, 8F6, 8FE, 8FK, 8G3, 8GL, 8HE, 8HG, 8HK, 8I3, 8I5, 8IB, 8IH, 8J4, 8JA, 8JM, 8KB, 8L6, 8L8, 8LE, 8LI, 8MD, 8ML, 90M, 913, 915, 919, 91F, 91H, 926, 92A, 931, 948, 94I, 951, 95D, 964, 96A, 96K, 979, 97B, 97F, 97L, 986, 98C, 98M, 991, 995, 99J, 9A2, 9A8, 9AC, 9AI, 9AK, 9B7, 9B9, 9C2, 9CE, 9CM, 9DH, 9DL, 9E4, 9EG, 9EI, 9F1, 9F7, 9FD, 9GI, 9H1, 9HF, 9HJ, 9I4, 9IE, 9IM, 9JB, 9K6, 9KA, 9KC, 9KG, 9LH, 9M6, 9MC, 9ME, A07, A0D, A0J, A1A, A1K, A2B, A2F, A3M, A45, A4B, A4H, A52, A58, A5C, A5E, A63, A69, A6D, A6F, A6L, A7K, A83, A85, A89, A94, A96, A9A, A9M, AA1, AA7, AAB, ABE, ABK, AC3, AC7, ACF, AD2, AEB, AF4, AF6, AFC, AFG, AFI, AFM, AG1, AGB, AH2, AH8, AHC, AHK, AI7, AID, AJA, AJE, AJG, AJM, AL6, ALA, ALI, AM5, AMB, AMH, B02, B08, B0K, B11, B17, B19, B1F, B1J, B22, B24, B2E, B2G, B39, B3F, B4C, B4G, B55, B5J, B71, B77, B84, B88, B93, B9B, B9H, B9L, BA4, BAI, BB1, BB7, BBH, BBJ, BC6, BCI, BD3, BDD, BDF, BE2, BEA, BEM, BF9, BGA, BGC, BGG, BH1, BH7, BHB, BHJ, BIE, BJ1, BJ7, BJD, BJF, BJL, BK8, BKK, BKM, BL9, BLF, BLL, BM4, BMC, BMI, C05, C0B, C0D, C0J, C12, C18, C1I, C23, C34, C3A, C49, C4B, C56, C5A, C5I, C65, C7C, C7K, C8F, C8J, C8L, C98, C9E, C9G, C9M, CA3, CAL, CB6, CBI, CCD, CD6, CDC, CDE, CE3, CE9, CEJ, CEL, CF8, CFA, CFG, CG3, CGH, CGL, CHM, CI1, CIH, CIJ, CJ6, CJ8, CJI, CKF, CKJ, CKL, CL2, CLA, CM3, CM9, CMF, CMH, D06, D0M, D17, D1B, D1H, D31, D33, D3D, D3F, D3L, D42, D48, D4E, D4M, D55, D59, D5L, D64, D6C, D71, D75, D7J, D88, D8I, D9J, DA2, DAE, DAK, DAM, DBL, DC6, DD1, DDB, DDH, DE8, DEC, DEE, DEK, DF7, DFF, DFL, DG2, DG8, DHF, DI6, DIG, DII, DJ7, DJH, DJJ, DKC, DKE, DL9, DMA, E05, E0B, E14, E1M, E25, E27, E32, E36, E3C, E3E, E41, E49, E4J, E52, E58, E5G, E5K, E63, E65, E6F, E6H, E76, E7A, E7G, E7M, E81, E8D, E8H, E98, EA3, EA7, EAD, EBA, EBE, EBM, EC5, EC9, ECH, ECL, EDC, EDI, EDM, EED, EF2, EF6, EF8, EGF, EGJ, EHK, EI3, EI9, EIL, EJA, EK1, EK7, EKB, EKD, EKH, ELC, ELI, EM7, EMF, EML, F02, F0E, F0G, F15, F2C, F35, F37, ...
24	15, 17, 1D, 1H, 1J, 1N, 25, 2B, 2D, 2J, 2N, 31, 37, 3B, 3H, 41, 45, 47, 4B, 4D, 4H, 57, 5B, 5H, 5J, 65, 67, 6D, 6J, 6N, 75, 7B, 7D, 7N, 81, 85, 87, 8J, 97, 9B, 9D, 9H, 9N, A1, AB, AH, AN, B5, B7, BD, BH, BJ, C5, CJ, CN, D1, D5, DJ, E1, EB, ED, EH, EN, F7, FD, FJ, FN, G5, GD, GH, H1, HB, HD, HN, I1, I7, IB, IH, J1, J5, J7, JB, JN, K7, KB, KJ, KN, L5, LH, LJ, MD, MJ, N5, NB, NH, NJ, 101, 10B, 10H, 10N, 111, 117, 11D, 11H, 11J, 127, 12H, 12J, 12N, 135, 13B, 13D, 141, 145, 14B, 14J, 155, 15D, 15N, 167, 16D, 16J, 16N, 177, 17D, 17H, 181, 185, 18J, 195, 19H, 19J, 1A5, 1A7, 1AB, 1AD, 1AN, 1BD, 1BH, 1BJ, 1BN, 1CD, 1CH, 1CJ, 1CN, 1DJ, 1DN, 1E7, 1EH, 1F1, 1F5, 1FB, 1FH, 1G7, 1GB, 1GH, 1GN, 1H7, 1HD, 1I1, 1I5, 1IB, 1ID, 1IN, 1J1, 1J7, 1JH, 1JJ, 1K5, 1K7, 1KD, 1L7, 1LB, 1LD, 1LH, 1LN, 1M5, 1MD, 1MJ, 1N1, 1NN, 201, 20B, 20J, 215, 21B, 21H, 221, 22D, 22H, 22N, 235, 237, 23D, 241, 24B, 255, 257, 25B, 25H, 25J, 261, 265, 267, 26B, 26N, 271, 277, 28H, 28N, 295, 29D, 2A7, 2AH, 2B7, 2BB, 2BD, 2BH, 2BN, 2C7, 2CB, 2CD, 2CJ, 2D7, 2DH, 2DJ, 2DN, 2E1, 2E5, 2EB, 2EN, 2FB, 2FJ, 2G7, 2GD, 2GH, 2GN, 2H7, 2HB, 2HJ, 2HN, 2ID, 2IH, 2IN, 2J1, 2J5, 2JB, 2JD, 2JJ, 2K5, 2L1, 2L7, 2LB, 2LD, 2MD, 2MH, 2MJ, 2N5, 2NH, 2NJ, 305, 30D, 30J, 311, 317, 321, 327, 32B, 32D, 331, 33B, 33N, 347, 34N, 35D, 35J, 35N, 361, 365, 367, 36H, 375, 37B, 37H, 38B, 38D, 395, 397, 3A5, 3AB, 3AJ, 3B1, 3B5, 3B7, 3BB, 3BJ, 3C1, 3CB, 3CD, 3CN, 3DD, 3DN, 3E5, 3EH, 3EJ, 3EN, 3F1, 3FB, 3FN, 3G1, 3GH, 3GJ, 3H1, 3H5, 3H7, 3HH, 3I1, 3IJ, 3JJ, 3JN, 3K5, 3KD, 3L5, 3L7, 3LB, 3LJ, 3MB, 3MD, 3MH, 3N1, 3N7, 3ND, 3NH, 405, 407, 415, 41B, 41D, 41J, 41N, 425, 42J, 431, 435, 437, 43D, 43H, 43N, 44B, 44H, 44N, 45D, 45H, 45N, 46B, 46J, 471, 475, 487, 491, 49B, 49J, 49N, 4A5, 4A7, 4AD, 4BB, 4BN, 4C1, 4CH, 4D1, 4D5, 4DH, 4E7, 4EH, 4EJ, 4EN, 4F7, 4FD, 4FJ, 4FN, 4G1, 4G5, 4GB, 4GJ, 4GN, 4H1, 4H7, 4HH, 4HJ, 4I5, 4ID, 4IH, 4J7, 4JH, 4K5, 4K7, 4KD, 4KH, 4KJ, 4LB, 4M1, 4M5, 4MB, 4MJ, 4N1, 4N5, 4NN, 507, 50H, 50N, 515, 51D, 51N, 52B, 531, 535, 53B, 53H, 53J, 54N, 551, 55B, 55J, 55N, 56D, 56H, 571, 57D, 57J, 587, 58B, 58H, 59D, 59N, 5A1, 5AH, 5BJ, 5BN, 5C1, 5CD, 5CJ, 5CN, 5DB, 5DH, 5E1, 5E5, 5ED, 5FB, 5FD, 5FH, 5FJ, 5G7, 5HB, 5HD, 5HJ, 5I1, 5I7, 5IB, 5IH, 5IJ, 5J7, 5JB, 5JN, 5K1, 5KB, 5KD, 5L5, 5L7, 5LN, 5M5, 5N1, 5NH, 601, 605, 607, 60B, 60D, 61B, 61J, 627, 62D, 62N, 631, 635, 63B, 63D, 63J, 645, 647, 64J, 655, 657, 65H, 667, 66D, 66H, 66N, 677, 67D, 67J, 68B, 68N, 691, 695, 69J, 6A1, 6A5, 6AD, 6AN, 6B7, 6BD, 6BJ, 6CH, 6CN, 6D1, 6DB, 6E1, 6E5, 6EB, 6F5, 6F7, 6FH, 6G7, 6GB, 6GD, 6GN, 6HD, 6HH, 6I1, 6IJ, 6IN, 6J5, 6J7, 6JB, 6JH, 6JJ, 6K7, 6KB, 6L7, 6M5, 6MH, 6MJ, 6MN, 6N5, 6NB, 6ND, 6NJ, 70H, 70J, 711, 71H, 71N, 72B, 72D, 72J, 737, 73N, 741, 745, 74B, 751, 755, 757, 761, 771, 77B, 77H, 77J, 785, 787, 78H, 78J, 795, 79B, 79D, 79N, 7A1, 7AB, 7AH, 7B1, 7C7, 7CH, 7CJ, 7D5, 7DD, 7DJ, 7E5, 7EN, 7F5, 7FH, 7G5, 7G7, 7H1, 7H7, 7HB, 7HH, 7HN, 7IH, 7IJ, 7J5, 7JJ, 7K1, 7K5, 7K7, 7KB, 7LB, 7LD, 7M1, 7M7, 7MN, 7N7, 7ND, 7NJ, 80D, 815, 817, 81B, 81H, 81J, 821, 827, 82H, 82N, 83B, 83N, 84H, 84J, 851, 855, 85N, 867, 877, 87B, 87D, 87H, 87N, 881, 88D, 88H, 897, 8AD, 8AN, 8B5, 8BH, 8C7, 8CD, 8CN, 8DB, 8DD, 8DH, 8DN, 8E7, 8ED, 8EN, 8F1, 8F5, 8FJ, 8G1, 8G7, 8GB, 8GH, 8GJ, 8H5, 8H7, 8HN, 8IB, 8IJ, 8JD, 8JH, 8JN, 8KB, 8KD, 8KJ, 8L1, 8L7, 8MB, 8MH, 8N7, 8NB, 8NJ, 905, 90D, 911, 91J, 91N, 921, 925, 935, 93H, 93N, 941, 94H, 94N, 955, 95J, 965, 96J, 96N, 985, 98B, 98H, 98N, 997, 99D, 99H, 99J, 9A7, 9AD, 9AH, 9AJ, 9B1, 9BN, 9C5, 9C7, 9CB, 9D5, 9D7, 9DB, 9DN, 9E1, 9E7, 9EB, 9FD, 9FJ, 9G1, 9G5, 9GD, 9GN, 9I7, 9IN, 9J1, 9J7, 9JB, 9JD, 9JH, 9JJ, 9K5, 9KJ, 9L1, 9L5, 9LD, 9LN, 9M5, 9N1, 9N5, 9N7, 9ND, A0J, A0N, A17, A1H, A1N, A25, A2D, A2J, A37, A3B, A3H, A3J, A41, A45, A4B, A4D, A4N, A51, A5H, A5N, A6J, A6N, A7B, A81, A95, A9B, AA7, AAB, AB5, ABD, ABJ, ABN, AC5, ACJ, AD1, AD7, ADH, ADJ, AE5, AEH, AF1, AFB, AFD, AFN, AG7, AGJ, AH5, AI5, AI7, AIB, AIJ, AJ1, AJ5, AJD, AK7, AKH, AKN, AL5, AL7, ALD, ALN, AMB, AMD, AMN, AN5, ANB, ANH, B01, B07, B0H, B0N, B11, B17, B1D, B1J, B25, B2D, B3D, B3J, B4H, B4J, B5D, B5H, B61, B6B, B7H, B81, B8J, B8N, B91, B9B, B9H, B9J, BA1, BA5, BAN, BB7, BBJ, BCD, BD5, BDB, BDD, BE1, BE7, BEH, BEJ, BF5, BF7, BFD, BFN, BGD, BGH, BHH, BHJ, BIB, BID, BIN, BJ1, BJB, BK7, BKB, BKD, BKH, BL1, BLH, BLN, BM5, BM7, BMJ, BNB, BNJ, BNN, C05, C1B, C1D, C1N, C21, C27, C2B, C2H, C2N, C37, C3D, C3H, C45, C4B, C4J, C57, C5B, C61, C6D, C6N, C7N, C85, C8H, C8N, C91, C9N, CA7, CB1, CBB, CBH, CC7, CCB, CCD, CCJ, CD5, CDD, CDJ, CDN, CE5, CFB, CG1, CGB, CGD, CH1, CHB, CHD, CI5, CI7, CJ1, CK1, CKJ, CL1, CLH, CMB, CMH, CMJ, CND, CNH, CNN, D01, D0B, D0J, D15, D1B, D1H, D21, D25, D2B, D2D, D2N, D31, D3D, D3H, D3N, D45, D47, D4J, D4N, D5D, D67, D6B, D6H, D7D, D7H, D81, D87, D8B, D8J, D8N, D9D, D9J, D9N, DAD, DB1, DB5, DB7, DCD, DCH, DDH, DDN, DE5, DEH, DF5, DFJ, DG1, DG5, DG7, DGB, DH5, DHB, DHN, DI7, DID, DIH, DJ5, DJ7, DJJ, DL1, DLH, DLJ, ...
25	14, 16, 1C, 1G, 1I, 1M, 23, 29, 2B, 2H, 2L, 2N, 34, 38, 3E, 3M, 41, 43, 47, 49, 4D, 52, 56, 5C, 5E, 5O, 61, 67, 6D, 6H, 6N, 74, 76, 7G, 7I, 7M, 7O, 8B, 8N, 92, 94, 98, 9E, 9G, A1, A7, AD, AJ, AL, B2, B6, B8, BI, C7, CB, CD, CH, D6, DC, DM, DO, E3, E9, EH, EN, F4, F8, FE, FM, G1, G9, GJ, GL, H6, H8, HE, HI, HO, I7, IB, ID, IH, J4, JC, JG, JO, K3, K9, KL, KN, LG, LM, M7, MD, MJ, ML, N2, NC, NI, NO, O1, O7, OD, OH, OJ, 106, 10G, 10I, 10M, 113, 119, 11B, 11N, 122, 128, 12G, 131, 139, 13J, 142, 148, 14E, 14I, 151, 157, 15B, 15J, 15N, 16C, 16M, 179, 17B, 17L, 17N, 182, 184, 18E, 193, 197, 199, 19D, 1A2, 1A6, 1A8, 1AC, 1B7, 1BB, 1BJ, 1C4, 1CC, 1CG, 1CM, 1D3, 1DH, 1DL, 1E2, 1E8, 1EG, 1EM, 1F9, 1FD, 1FJ, 1FL, 1G6, 1G8, 1GE, 1GO, 1H1, 1HB, 1HD, 1HJ, 1IC, 1IG, 1II, 1IM, 1J3, 1J9, 1JH, 1JN, 1K4, 1L1, 1L3, 1LD, 1LL, 1M6, 1MC, 1MI, 1N1, 1ND, 1NH, 1NN, 1O4, 1O6, 1OC, 1OO, 209, 212, 214, 218, 21E, 21G, 21M, 221, 223, 227, 22J, 22L, 232, 24B, 24H, 24N, 256, 25O, 269, 26N, 272, 274, 278, 27E, 27M, 281, 283, 289, 28L, 296, 298, 29C, 29E, 29I, 29O, 2AB, 2AN, 2B6, 2BI, 2BO, 2C3, 2C9, 2CH, 2CL, 2D4, 2D8, 2DM, 2E1, 2E7, 2E9, 2ED, 2EJ, 2EL, 2F2, 2FC, 2G7, 2GD, 2GH, 2GJ, 2HI, 2HM, 2HO, 2I9, 2IL, 2IN, 2J8, 2JG, 2JM, 2K3, 2K9, 2L2, 2L8, 2LC, 2LE, 2M1, 2MB, 2MN, 2N6, 2NM, 2OB, 2OH, 2OL, 2ON, 302, 304, 30E, 311, 317, 31D, 326, 328, 32O, 331, 33N, 344, 34C, 34I, 34M, 34O, 353, 35B, 35H, 362, 364, 36E, 373, 37D, 37J, 386, 388, 38C, 38E, 38O, 39B, 39D, 3A4, 3A6, 3AC, 3AG, 3AI, 3B3, 3BB, 3C4, 3D3, 3D7, 3DD, 3DL, 3EC, 3EE, 3EI, 3F1, 3FH, 3FJ, 3FN, 3G6, 3GC, 3GI, 3GM, 3H9, 3HB, 3I8, 3IE, 3IG, 3IM, 3J1, 3J7, 3JL, 3K2, 3K6, 3K8, 3KE, 3KI, 3KO, 3LB, 3LH, 3LN, 3MC, 3MG, 3MM, 3N9, 3NH, 3NN, 3O2, 403, 40L, 416, 41E, 41I, 41O, 421, 427, 434, 43G, 43I, 449, 44H, 44L, 458, 45M, 467, 469, 46D, 46L, 472, 478, 47C, 47E, 47I, 47O, 487, 48B, 48D, 48J, 494, 496, 49G, 49O, 4A3, 4AH, 4B2, 4BE, 4BG, 4BM, 4C1, 4C3, 4CJ, 4D8, 4DC, 4DI, 4E1, 4E7, 4EB, 4F4, 4FC, 4FM, 4G3, 4G9, 4GH, 4H2, 4HE, 4I3, 4I7, 4ID, 4IJ, 4IL, 4JO, 4K1, 4KB, 4KJ, 4KN, 4LC, 4LG, 4LO, 4MB, 4MH, 4N4, 4N8, 4NE, 4O9, 4OJ, 4OL, 50C, 51D, 51H, 51J, 526, 52C, 52G, 533, 539, 53H, 53L, 544, 551, 553, 557, 559, 55L, 56O, 571, 577, 57D, 57J, 57N, 584, 586, 58I, 58M, 599, 59B, 59L, 59N, 5AE, 5AG, 5B7, 5BD, 5C8, 5CO, 5D7, 5DB, 5DD, 5DH, 5DJ, 5EG, 5EO, 5FB, 5FH, 5G2, 5G4, 5G8, 5GE, 5GG, 5GM, 5H7, 5H9, 5HL, 5I6, 5I8, 5II, 5J7, 5JD, 5JH, 5JN, 5K6, 5KC, 5KI, 5L9, 5LL, 5LN, 5M2, 5MG, 5MM, 5N1, 5N9, 5NJ, 5O2, 5O8, 5OE, 60B, 60H, 60J, 614, 61I, 61M, 623, 62L, 62N, 638, 63M, 641, 643, 64D, 652, 656, 65E, 667, 66B, 66H, 66J, 66N, 674, 676, 67I, 67M, 68H, 69E, 6A1, 6A3, 6A7, 6AD, 6AJ, 6AL, 6B2, 6BO, 6C1, 6C7, 6CN, 6D4, 6DG, 6DI, 6DO, 6EB, 6F2, 6F4, 6F8, 6FE, 6G3, 6G7, 6G9, 6H2, 6I1, 6IB, 6IH, 6IJ, 6J4, 6J6, 6JG, 6JI, 6K3, 6K9, 6KB, 6KL, 6KN, 6L8, 6LE, 6LM, 6N2, 6NC, 6NE, 6NO, 6O7, 6OD, 6ON, 70G, 70M, 719, 71L, 71N, 72G, 72M, 731, 737, 73D, 746, 748, 74I, 757, 75D, 75H, 75J, 75N, 76M, 76O, 77B, 77H, 788, 78G, 78M, 793, 79L, 7AC, 7AE, 7AI, 7AO, 7B1, 7B7, 7BD, 7BN, 7C4, 7CG, 7D3, 7DL, 7DN, 7E4, 7E8, 7F1, 7F9, 7G8, 7GC, 7GE, 7GI, 7GO, 7H1, 7HD, 7HH, 7I6, 7JB, 7JL, 7K2, 7KE, 7L3, 7L9, 7LJ, 7M6, 7M8, 7MC, 7MI, 7N1, 7N7, 7NH, 7NJ, 7NN, 7OC, 7OI, 7OO, 803, 809, 80B, 80L, 80N, 81E, 821, 829, 832, 836, 83C, 83O, 841, 847, 84D, 84J, 85M, 863, 86H, 86L, 874, 87E, 87M, 889, 892, 896, 898, 89C, 8AB, 8AN, 8B4, 8B6, 8BM, 8C3, 8C9, 8CN, 8D8, 8DM, 8E1, 8F6, 8FC, 8FI, 8FO, 8G7, 8GD, 8GH, 8GJ, 8H6, 8HC, 8HG, 8HI, 8HO, 8IL, 8J2, 8J4, 8J8, 8K1, 8K3, 8K7, 8KJ, 8KL, 8L2, 8L6, 8M7, 8MD, 8MJ, 8MN, 8N6, 8NG, 8ON, 90E, 90G, 90M, 911, 913, 917, 919, 91J, 928, 92E, 92I, 931, 93B, 93H, 94C, 94G, 94I, 94O, 964, 968, 96G, 971, 977, 97D, 97L, 982, 98E, 98I, 98O, 991, 997, 99B, 99H, 99J, 9A4, 9A6, 9AM, 9B3, 9BN, 9C2, 9CE, 9D3, 9E6, 9EC, 9F7, 9FB, 9G4, 9GC, 9GI, 9GM, 9H3, 9HH, 9HN, 9I4, 9IE, 9IG, 9J1, 9JD, 9JL, 9K6, 9K8, 9KI, 9L1, 9LD, 9LN, 9MM, 9MO, 9N3, 9NB, 9NH, 9NL, 9O4, 9OM, A07, A0D, A0J, A0L, A12, A1C, A1O, A21, A2B, A2H, A2N, A34, A3C, A3I, A43, A49, A4B, A4H, A4N, A54, A5E, A5M, A6L, A72, A7O, A81, A8J, A8N, A96, A9G, AAL, AB4, ABM, AC1, AC3, ACD, ACJ, ACL, AD2, AD6, ADO, AE7, AEJ, AFC, AG3, AG9, AGB, AGN, AH4, AHE, AHG, AI1, AI3, AI9, AIJ, AJ8, AJC, AKB, AKD, AL4, AL6, ALG, ALI, AM3, AMN, AN2, AN4, AN8, ANG, AO7, AOD, AOJ, AOL, B08, B0O, B17, B1B, B1H, B2M, B2O, B39, B3B, B3H, B3L, B42, B48, B4G, B4M, B51, B5D, B5J, B62, B6E, B6I, B77, B7J, B84, B93, B99, B9L, BA2, BA4, BB1, BB9, BC2, BCC, BCI, BD7, BDB, BDD, BDJ, BE4, BEC, BEI, BEM, BF3, BG8, BGM, BH7, BH9, BHL, BI6, BI8, BIO, BJ1, BJJ, BKI, BLB, BLH, BM8, BN1, BN7, BN9, BO2, BO6, BOC, BOE, BOO, C07, C0H, C0N, C14, C1C, C1G, C1M, C1O, C29, C2B, C2N, C32, C38, C3E, C3G, C43, C47, C4L, C5E, C5I, C5O, C6J, C6N, C76, C7C, C7G, C7O, C83, C8H, C8N, C92, C9G, CA3, CA7, CA9, CBE, CBI, CCH, CCN, CD4, CDG, CE3, CEH, CEN, CF2, CF4, CF8, CG1, CG7, CGJ, CH2, CH8, CHC, CHO, CI1, CID, CJI, CK9, CKB, ...
26	13, 15, 1B, 1F, 1H, 1L, 21, 27, 29, 2F, 2J, 2L, 31, 35, 3B, 3J, 3N, 3P, 43, 45, 49, 4N, 51, 57, 59, 5J, 5L, 61, 67, 6B, 6H, 6N, 6P, 79, 7B, 7F, 7H, 83, 8F, 8J, 8L, 8P, 95, 97, 9H, 9N, A3, A9, AB, AH, AL, AN, B7, BL, BP, C1, C5, CJ, CP, D9, DB, DF, DL, E3, E9, EF, EJ, EP, F7, FB, FJ, G3, G5, GF, GH, GN, H1, H7, HF, HJ, HL, HP, IB, IJ, IN, J5, J9, JF, K1, K3, KL, L1, LB, LH, LN, LP, M5, MF, ML, N1, N3, N9, NF, NJ, NL, O7, OH, OJ, ON, P3, P9, PB, PN, 101, 107, 10F, 10P, 117, 11H, 11P, 125, 12B, 12F, 12N, 133, 137, 13F, 13J, 147, 14H, 153, 155, 15F, 15H, 15L, 15N, 167, 16L, 16P, 171, 175, 17J, 17N, 17P, 183, 18N, 191, 199, 19J, 1A1, 1A5, 1AB, 1AH, 1B5, 1B9, 1BF, 1BL, 1C3, 1C9, 1CL, 1CP, 1D5, 1D7, 1DH, 1DJ, 1DP, 1E9, 1EB, 1EL, 1EN, 1F3, 1FL, 1FP, 1G1, 1G5, 1GB, 1GH, 1GP, 1H5, 1HB, 1I7, 1I9, 1IJ, 1J1, 1JB, 1JH, 1JN, 1K5, 1KH, 1KL, 1L1, 1L7, 1L9, 1LF, 1M1, 1MB, 1N3, 1N5, 1N9, 1NF, 1NH, 1NN, 1O1, 1O3, 1O7, 1OJ, 1OL, 1P1, 209, 20F, 20L, 213, 21L, 225, 22J, 22N, 22P, 233, 239, 23H, 23L, 23N, 243, 24F, 24P, 251, 255, 257, 25B, 25H, 263, 26F, 26N, 279, 27F, 27J, 27P, 287, 28B, 28J, 28N, 29B, 29F, 29L, 29N, 2A1, 2A7, 2A9, 2AF, 2AP, 2BJ, 2BP, 2C3, 2C5, 2D3, 2D7, 2D9, 2DJ, 2E5, 2E7, 2EH, 2EP, 2F5, 2FB, 2FH, 2G9, 2GF, 2GJ, 2GL, 2H7, 2HH, 2I3, 2IB, 2J1, 2JF, 2JL, 2JP, 2K1, 2K5, 2K7, 2KH, 2L3, 2L9, 2LF, 2M7, 2M9, 2MP, 2N1, 2NN, 2O3, 2OB, 2OH, 2OL, 2ON, 2P1, 2P9, 2PF, 2PP, 301, 30B, 30P, 319, 31F, 321, 323, 327, 329, 32J, 335, 337, 33N, 33P, 345, 349, 34B, 34L, 353, 35L, 36J, 36N, 373, 37B, 381, 383, 387, 38F, 395, 397, 39B, 39J, 39P, 3A5, 3A9, 3AL, 3AN, 3BJ, 3BP, 3C1, 3C7, 3CB, 3CH, 3D5, 3DB, 3DF, 3DH, 3DN, 3E1, 3E7, 3EJ, 3EP, 3F5, 3FJ, 3FN, 3G3, 3GF, 3GN, 3H3, 3H7, 3I7, 3IP, 3J9, 3JH, 3JL, 3K1, 3K3, 3K9, 3L5, 3LH, 3LJ, 3M9, 3MH, 3ML, 3N7, 3NL, 3O5, 3O7, 3OB, 3OJ, 3OP, 3P5, 3P9, 3PB, 3PF, 3PL, 403, 407, 409, 40F, 40P, 411, 41B, 41J, 41N, 42B, 42L, 437, 439, 43F, 43J, 43L, 44B, 44P, 453, 459, 45H, 45N, 461, 46J, 471, 47B, 47H, 47N, 485, 48F, 491, 49F, 49J, 49P, 4A5, 4A7, 4B9, 4BB, 4BL, 4C3, 4C7, 4CL, 4CP, 4D7, 4DJ, 4DP, 4EB, 4EF, 4EL, 4FF, 4FP, 4G1, 4GH, 4HH, 4HL, 4HN, 4I9, 4IF, 4IJ, 4J5, 4JB, 4JJ, 4JN, 4K5, 4L1, 4L3, 4L7, 4L9, 4LL, 4MN, 4MP, 4N5, 4NB, 4NH, 4NL, 4O1, 4O3, 4OF, 4OJ, 4P5, 4P7, 4PH, 4PJ, 509, 50B, 511, 517, 521, 52H, 52P, 533, 535, 539, 53B, 547, 54F, 551, 557, 55H, 55J, 55N, 563, 565, 56B, 56L, 56N, 579, 57J, 57L, 585, 58J, 58P, 593, 599, 59H, 59N, 5A3, 5AJ, 5B5, 5B7, 5BB, 5BP, 5C5, 5C9, 5CH, 5D1, 5D9, 5DF, 5DL, 5EH, 5EN, 5EP, 5F9, 5FN, 5G1, 5G7, 5GP, 5H1, 5HB, 5HP, 5I3, 5I5, 5IF, 5J3, 5J7, 5JF, 5K7, 5KB, 5KH, 5KJ, 5KN, 5L3, 5L5, 5LH, 5LL, 5MF, 5NB, 5NN, 5NP, 5O3, 5O9, 5OF, 5OH, 5ON, 5PJ, 5PL, 601, 60H, 60N, 619, 61B, 61H, 623, 62J, 62L, 62P, 635, 63J, 63N, 63P, 64H, 65F, 65P, 665, 667, 66H, 66J, 673, 675, 67F, 67L, 67N, 687, 689, 68J, 68P, 697, 6AB, 6AL, 6AN, 6B7, 6BF, 6BL, 6C5, 6CN, 6D3, 6DF, 6E1, 6E3, 6EL, 6F1, 6F5, 6FB, 6FH, 6G9, 6GB, 6GL, 6H9, 6HF, 6HJ, 6HL, 6HP, 6IN, 6IP, 6JB, 6JH, 6K7, 6KF, 6KL, 6L1, 6LJ, 6M9, 6MB, 6MF, 6ML, 6MN, 6N3, 6N9, 6NJ, 6NP, 6OB, 6ON, 6PF, 6PH, 6PN, 701, 70J, 711, 71P, 723, 725, 729, 72F, 72H, 733, 737, 73L, 74P, 759, 75F, 761, 76F, 76L, 775, 77H, 77J, 77N, 783, 78B, 78H, 791, 793, 797, 79L, 7A1, 7A7, 7AB, 7AH, 7AJ, 7B3, 7B5, 7BL, 7C7, 7CF, 7D7, 7DB, 7DH, 7E3, 7E5, 7EB, 7EH, 7EN, 7FP, 7G5, 7GJ, 7GN, 7H5, 7HF, 7HN, 7I9, 7J1, 7J5, 7J7, 7JB, 7K9, 7KL, 7L1, 7L3, 7LJ, 7LP, 7M5, 7MJ, 7N3, 7NH, 7NL, 7OP, 7P5, 7PB, 7PH, 7PP, 805, 809, 80B, 80N, 813, 817, 819, 81F, 82B, 82H, 82J, 82N, 83F, 83H, 83L, 847, 849, 84F, 84J, 85J, 85P, 865, 869, 86H, 871, 887, 88N, 88P, 895, 899, 89B, 89F, 89H, 8A1, 8AF, 8AL, 8AP, 8B7, 8BH, 8BN, 8CH, 8CL, 8CN, 8D3, 8E7, 8EB, 8EJ, 8F3, 8F9, 8FF, 8FN, 8G3, 8GF, 8GJ, 8GP, 8H1, 8H7, 8HB, 8HH, 8HJ, 8I3, 8I5, 8IL, 8J1, 8JL, 8JP, 8KB, 8KP, 8M1, 8M7, 8N1, 8N5, 8NN, 8O5, 8OB, 8OF, 8OL, 8P9, 8PF, 8PL, 905, 907, 90H, 913, 91B, 91L, 91N, 927, 92F, 931, 93B, 949, 94B, 94F, 94N, 953, 957, 95F, 967, 96H, 96N, 973, 975, 97B, 97L, 987, 989, 98J, 98P, 995, 99B, 99J, 99P, 9A9, 9AF, 9AH, 9AN, 9B3, 9B9, 9BJ, 9C1, 9CP, 9D5, 9E1, 9E3, 9EL, 9EP, 9F7, 9FH, 9GL, 9H3, 9HL, 9HP, 9I1, 9IB, 9IH, 9IJ, 9IP, 9J3, 9JL, 9K3, 9KF, 9L7, 9LN, 9M3, 9M5, 9MH, 9MN, 9N7, 9N9, 9NJ, 9NL, 9O1, 9OB, 9OP, 9P3, A01, A03, A0J, A0L, A15, A17, A1H, A2B, A2F, A2H, A2L, A33, A3J, A3P, A45, A47, A4J, A59, A5H, A5L, A61, A75, A77, A7H, A7J, A7P, A83, A89, A8F, A8N, A93, A97, A9J, A9P, AA7, AAJ, AAN, ABB, ABN, AC7, AD5, ADB, ADN, AE3, AE5, AF1, AF9, AG1, AGB, AGH, AH5, AH9, AHB, AHH, AI1, AI9, AIF, AIJ, AIP, AK3, AKH, AL1, AL3, ALF, ALP, AM1, AMH, AMJ, ANB, AO9, AP1, AP7, APN, B0F, B0L, B0N, B1F, B1J, B1P, B21, B2B, B2J, B33, B39, B3F, B3N, B41, B47, B49, B4J, B4L, B57, B5B, B5H, B5N, B5P, B6B, B6F, B73, B7L, B7P, B85, B8P, B93, B9B, B9H, B9L, BA3, BA7, BAL, BB1, BB5, BBJ, BC5, BC9, BCB, BDF, BDJ, BEH, BEN, BF3, BFF, BG1, BGF, BGL, BGP, BH1, BH5, BHN, BI3, BIF, BIN, BJ3, BJ7, BJJ, BJL, BK7, BLB, BM1, BM3, ...
27	12, 14, 1A, 1E, 1G, 1K, 1Q, 25, 27, 2D, 2H, 2J, 2P, 32, 38, 3G, 3K, 3M, 3Q, 41, 45, 4J, 4N, 52, 54, 5E, 5G, 5M, 61, 65, 6B, 6H, 6J, 72, 74, 78, 7A, 7M, 87, 8B, 8D, 8H, 8N, 8P, 98, 9E, 9K, 9Q, A1, A7, AB, AD, AN, BA, BE, BG, BK, C7, CD, CN, CP, D2, D8, DG, DM, E1, E5, EB, EJ, EN, F4, FE, FG, FQ, G1, G7, GB, GH, GP, H2, H4, H8, HK, I1, I5, ID, IH, IN, J8, JA, K1, K7, KH, KN, L2, L4, LA, LK, LQ, M5, M7, MD, MJ, MN, MP, NA, NK, NM, NQ, O5, OB, OD, OP, P2, P8, PG, PQ, Q7, QH, QP, 104, 10A, 10E, 10M, 111, 115, 11D, 11H, 124, 12E, 12Q, 131, 13B, 13D, 13H, 13J, 142, 14G, 14K, 14M, 14Q, 15D, 15H, 15J, 15N, 16G, 16K, 171, 17B, 17J, 17N, 182, 188, 18M, 18Q, 195, 19B, 19J, 19P, 1AA, 1AE, 1AK, 1AM, 1B5, 1B7, 1BD, 1BN, 1BP, 1C8, 1CA, 1CG, 1D7, 1DB, 1DD, 1DH, 1DN, 1E2, 1EA, 1EG, 1EM, 1FH, 1FJ, 1G2, 1GA, 1GK, 1GQ, 1H5, 1HD, 1HP, 1I2, 1I8, 1IE, 1IG, 1IM, 1J7, 1JH, 1K8, 1KA, 1KE, 1KK, 1KM, 1L1, 1L5, 1L7, 1LB, 1LN, 1LP, 1M4, 1NB, 1NH, 1NN, 1O4, 1OM, 1P5, 1PJ, 1PN, 1PP, 1Q2, 1Q8, 1QG, 1QK, 1QM, 201, 20D, 20N, 20P, 212, 214, 218, 21E, 21Q, 22B, 22J, 234, 23A, 23E, 23K, 241, 245, 24D, 24H, 254, 258, 25E, 25G, 25K, 25Q, 261, 267, 26H, 27A, 27G, 27K, 27M, 28J, 28N, 28P, 298, 29K, 29M, 2A5, 2AD, 2AJ, 2AP, 2B4, 2BM, 2C1, 2C5, 2C7, 2CJ, 2D2, 2DE, 2DM, 2EB, 2EP, 2F4, 2F8, 2FA, 2FE, 2FG, 2FQ, 2GB, 2GH, 2GN, 2HE, 2HG, 2I5, 2I7, 2J2, 2J8, 2JG, 2JM, 2JQ, 2K1, 2K5, 2KD, 2KJ, 2L2, 2L4, 2LE, 2M1, 2MB, 2MH, 2N2, 2N4, 2N8, 2NA, 2NK, 2O5, 2O7, 2ON, 2OP, 2P4, 2P8, 2PA, 2PK, 2Q1, 2QJ, 30G, 30K, 30Q, 317, 31N, 31P, 322, 32A, 32Q, 331, 335, 33D, 33J, 33P, 342, 34E, 34G, 35B, 35H, 35J, 35P, 362, 368, 36M, 371, 375, 377, 37D, 37H, 37N, 388, 38E, 38K, 397, 39B, 39H, 3A2, 3AA, 3AG, 3AK, 3BJ, 3CA, 3CK, 3D1, 3D5, 3DB, 3DD, 3DJ, 3EE, 3EQ, 3F1, 3FH, 3FP, 3G2, 3GE, 3H1, 3HB, 3HD, 3HH, 3HP, 3I4, 3IA, 3IE, 3IG, 3IK, 3IQ, 3J7, 3JB, 3JD, 3JJ, 3K2, 3K4, 3KE, 3KM, 3KQ, 3LD, 3LN, 3M8, 3MA, 3MG, 3MK, 3MM, 3NB, 3NP, 3O2, 3O8, 3OG, 3OM, 3OQ, 3PH, 3PP, 3Q8, 3QE, 3QK, 401, 40B, 40N, 41A, 41E, 41K, 41Q, 421, 432, 434, 43E, 43M, 43Q, 44D, 44H, 44P, 45A, 45G, 461, 465, 46B, 474, 47E, 47G, 485, 494, 498, 49A, 49M, 4A1, 4A5, 4AH, 4AN, 4B4, 4B8, 4BG, 4CB, 4CD, 4CH, 4CJ, 4D4, 4E5, 4E7, 4ED, 4EJ, 4EP, 4F2, 4F8, 4FA, 4FM, 4FQ, 4GB, 4GD, 4GN, 4GP, 4HE, 4HG, 4I5, 4IB, 4J4, 4JK, 4K1, 4K5, 4K7, 4KB, 4KD, 4L8, 4LG, 4M1, 4M7, 4MH, 4MJ, 4MN, 4N2, 4N4, 4NA, 4NK, 4NM, 4O7, 4OH, 4OJ, 4P2, 4PG, 4PM, 4PQ, 4Q5, 4QD, 4QJ, 4QP, 50E, 50Q, 511, 515, 51J, 51P, 522, 52A, 52K, 531, 537, 53D, 548, 54E, 54G, 54Q, 55D, 55H, 55N, 56E, 56G, 56Q, 57D, 57H, 57J, 582, 58G, 58K, 591, 59J, 59N, 5A2, 5A4, 5A8, 5AE, 5AG, 5B1, 5B5, 5BP, 5CK, 5D5, 5D7, 5DB, 5DH, 5DN, 5DP, 5E4, 5EQ, 5F1, 5F7, 5FN, 5G2, 5GE, 5GG, 5GM, 5H7, 5HN, 5HP, 5I2, 5I8, 5IM, 5IQ, 5J1, 5JJ, 5KG, 5KQ, 5L5, 5L7, 5LH, 5LJ, 5M2, 5M4, 5ME, 5MK, 5MM, 5N5, 5N7, 5NH, 5NN, 5O4, 5P7, 5PH, 5PJ, 5Q2, 5QA, 5QG, 5QQ, 60H, 60N, 618, 61K, 61M, 62D, 62J, 62N, 632, 638, 63Q, 641, 64B, 64P, 654, 658, 65A, 65E, 66B, 66D, 66P, 674, 67K, 681, 687, 68D, 694, 69K, 69M, 69Q, 6A5, 6A7, 6AD, 6AJ, 6B2, 6B8, 6BK, 6C5, 6CN, 6CP, 6D4, 6D8, 6DQ, 6E7, 6F4, 6F8, 6FA, 6FE, 6FK, 6FM, 6G7, 6GB, 6GP, 6I1, 6IB, 6IH, 6J2, 6JG, 6JM, 6K5, 6KH, 6KJ, 6KN, 6L2, 6LA, 6LG, 6LQ, 6M1, 6M5, 6MJ, 6MP, 6N4, 6N8, 6NE, 6NG, 6NQ, 6O1, 6OH, 6P2, 6PA, 6Q1, 6Q5, 6QB, 6QN, 6QP, 704, 70A, 70G, 71H, 71N, 72A, 72E, 72M, 735, 73D, 73P, 74G, 74K, 74M, 74Q, 75N, 768, 76E, 76G, 775, 77B, 77H, 784, 78E, 791, 795, 7A8, 7AE, 7AK, 7AQ, 7B7, 7BD, 7BH, 7BJ, 7C4, 7CA, 7CE, 7CG, 7CM, 7DH, 7DN, 7DP, 7E2, 7EK, 7EM, 7EQ, 7FB, 7FD, 7FJ, 7FN, 7GM, 7H1, 7H7, 7HB, 7HJ, 7I2, 7J7, 7JN, 7JP, 7K4, 7K8, 7KA, 7KE, 7KG, 7KQ, 7LD, 7LJ, 7LN, 7M4, 7ME, 7MK, 7ND, 7NH, 7NJ, 7NP, 7P1, 7P5, 7PD, 7PN, 7Q2, 7Q8, 7QG, 7QM, 807, 80B, 80H, 80J, 80P, 812, 818, 81A, 81K, 81M, 82B, 82H, 83A, 83E, 83Q, 84D, 85E, 85K, 86D, 86H, 878, 87G, 87M, 87Q, 885, 88J, 88P, 894, 89E, 89G, 89Q, 8AB, 8AJ, 8B2, 8B4, 8BE, 8BM, 8C7, 8CH, 8DE, 8DG, 8DK, 8E1, 8E7, 8EB, 8EJ, 8FA, 8FK, 8FQ, 8G5, 8G7, 8GD, 8GN, 8H8, 8HA, 8HK, 8HQ, 8I5, 8IB, 8IJ, 8IP, 8J8, 8JE, 8JG, 8JM, 8K1, 8K7, 8KH, 8KP, 8LM, 8M1, 8MN, 8MP, 8NG, 8NK, 8O1, 8OB, 8PE, 8PM, 8QD, 8QH, 8QJ, 902, 908, 90A, 90G, 90K, 91B, 91J, 924, 92M, 93B, 93H, 93J, 944, 94A, 94K, 94M, 955, 957, 95D, 95N, 96A, 96E, 97B, 97D, 982, 984, 98E, 98G, 98Q, 99J, 99N, 99P, 9A2, 9AA, 9AQ, 9B5, 9BB, 9BD, 9BP, 9CE, 9CM, 9CQ, 9D5, 9E8, 9EA, 9EK, 9EM, 9F1, 9F5, 9FB, 9FH, 9FP, 9G4, 9G8, 9GK, 9GQ, 9H7, 9HJ, 9HN, 9IA, 9IM, 9J5, 9K2, 9K8, 9KK, 9KQ, 9L1, 9LN, 9M4, 9MM, 9N5, 9NB, 9NP, 9O2, 9O4, 9OA, 9OK, 9P1, 9P7, 9PB, 9PH, 9QK, A07, A0H, A0J, A14, A1E, A1G, A25, A27, A2P, A3M, A4D, A4J, A58, A5Q, A65, A67, A6P, A72, A78, A7A, A7K, A81, A8B, A8H, A8N, A94, A98, A9E, A9G, A9Q, AA1, AAD, AAH, AAN, AB2, AB4, ABG, ABK, AC7, ACP, AD2, AD8, AE1, AE5, AED, AEJ, AEN, AF4, AF8, AFM, AG1, AG5, AGJ, AH4, AH8, AHA, AID, AIH, AJE, AJK, AJQ, AKB, AKN, ALA, ALG, ALK, ALM, ALQ, AMH, AMN, AN8, ANG, ANM, ANQ, AOB, AOD, AOP, AQ1, AQH, AQJ, ...
28	11, 13, 19, 1D, 1F, 1J, 1P, 23, 25, 2B, 2F, 2H, 2N, 2R, 35, 3D, 3H, 3J, 3N, 3P, 41, 4F, 4J, 4P, 4R, 59, 5B, 5H, 5N, 5R, 65, 6B, 6D, 6N, 6P, 71, 73, 7F, 7R, 83, 85, 89, 8F, 8H, 8R, 95, 9B, 9H, 9J, 9P, A1, A3, AD, AR, B3, B5, B9, BN, C1, CB, CD, CH, CN, D3, D9, DF, DJ, DP, E5, E9, EH, ER, F1, FB, FD, FJ, FN, G1, G9, GD, GF, GJ, H3, HB, HF, HN, HR, I5, IH, IJ, J9, JF, JP, K3, K9, KB, KH, KR, L5, LB, LD, LJ, LP, M1, M3, MF, MP, MR, N3, N9, NF, NH, O1, O5, OB, OJ, P1, P9, PJ, PR, Q5, QB, QF, QN, R1, R5, RD, RH, 103, 10D, 10P, 10R, 119, 11B, 11F, 11H, 11R, 12D, 12H, 12J, 12N, 139, 13D, 13F, 13J, 14B, 14F, 14N, 155, 15D, 15H, 15N, 161, 16F, 16J, 16P, 173, 17B, 17H, 181, 185, 18B, 18D, 18N, 18P, 193, 19D, 19F, 19P, 19R, 1A5, 1AN, 1AR, 1B1, 1B5, 1BB, 1BH, 1BP, 1C3, 1C9, 1D3, 1D5, 1DF, 1DN, 1E5, 1EB, 1EH, 1EP, 1F9, 1FD, 1FJ, 1FP, 1FR, 1G5, 1GH, 1GR, 1HH, 1HJ, 1HN, 1I1, 1I3, 1I9, 1ID, 1IF, 1IJ, 1J3, 1J5, 1JB, 1KH, 1KN, 1L1, 1L9, 1LR, 1M9, 1MN, 1MR, 1N1, 1N5, 1NB, 1NJ, 1NN, 1NP, 1O3, 1OF, 1OP, 1OR, 1P3, 1P5, 1P9, 1PF, 1PR, 1QB, 1QJ, 1R3, 1R9, 1RD, 1RJ, 1RR, 203, 20B, 20F, 211, 215, 21B, 21D, 21H, 21N, 21P, 223, 22D, 235, 23B, 23F, 23H, 24D, 24H, 24J, 251, 25D, 25F, 25P, 265, 26B, 26H, 26N, 27D, 27J, 27N, 27P, 289, 28J, 293, 29B, 29R, 2AD, 2AJ, 2AN, 2AP, 2B1, 2B3, 2BD, 2BP, 2C3, 2C9, 2CR, 2D1, 2DH, 2DJ, 2ED, 2EJ, 2ER, 2F5, 2F9, 2FB, 2FF, 2FN, 2G1, 2GB, 2GD, 2GN, 2H9, 2HJ, 2HP, 2I9, 2IB, 2IF, 2IH, 2IR, 2JB, 2JD, 2K1, 2K3, 2K9, 2KD, 2KF, 2KP, 2L5, 2LN, 2MJ, 2MN, 2N1, 2N9, 2NP, 2NR, 2O3, 2OB, 2OR, 2P1, 2P5, 2PD, 2PJ, 2PP, 2Q1, 2QD, 2QF, 2R9, 2RF, 2RH, 2RN, 2RR, 305, 30J, 30P, 311, 313, 319, 31D, 31J, 323, 329, 32F, 331, 335, 33B, 33N, 343, 349, 34D, 35B, 361, 36B, 36J, 36N, 371, 373, 379, 383, 38F, 38H, 395, 39D, 39H, 3A1, 3AF, 3AP, 3AR, 3B3, 3BB, 3BH, 3BN, 3BR, 3C1, 3C5, 3CB, 3CJ, 3CN, 3CP, 3D3, 3DD, 3DF, 3DP, 3E5, 3E9, 3EN, 3F5, 3FH, 3FJ, 3FP, 3G1, 3G3, 3GJ, 3H5, 3H9, 3HF, 3HN, 3I1, 3I5, 3IN, 3J3, 3JD, 3JJ, 3JP, 3K5, 3KF, 3KR, 3LD, 3LH, 3LN, 3M1, 3M3, 3N3, 3N5, 3NF, 3NN, 3NR, 3OD, 3OH, 3OP, 3P9, 3PF, 3PR, 3Q3, 3Q9, 3R1, 3RB, 3RD, 401, 40R, 413, 415, 41H, 41N, 41R, 42B, 42H, 42P, 431, 439, 443, 445, 449, 44B, 44N, 45N, 45P, 463, 469, 46F, 46J, 46P, 46R, 47B, 47F, 47R, 481, 48B, 48D, 491, 493, 49J, 49P, 4AH, 4B5, 4BD, 4BH, 4BJ, 4BN, 4BP, 4CJ, 4CR, 4DB, 4DH, 4DR, 4E1, 4E5, 4EB, 4ED, 4EJ, 4F1, 4F3, 4FF, 4FP, 4FR, 4G9, 4GN, 4H1, 4H5, 4HB, 4HJ, 4HP, 4I3, 4IJ, 4J3, 4J5, 4J9, 4JN, 4K1, 4K5, 4KD, 4KN, 4L3, 4L9, 4LF, 4M9, 4MF, 4MH, 4MR, 4ND, 4NH, 4NN, 4OD, 4OF, 4OP, 4PB, 4PF, 4PH, 4PR, 4QD, 4QH, 4QP, 4RF, 4RJ, 4RP, 4RR, 503, 509, 50B, 50N, 50R, 51J, 52D, 52P, 52R, 533, 539, 53F, 53H, 53N, 54H, 54J, 54P, 55D, 55J, 563, 565, 56B, 56N, 57B, 57D, 57H, 57N, 589, 58D, 58F, 595, 5A1, 5AB, 5AH, 5AJ, 5B1, 5B3, 5BD, 5BF, 5BP, 5C3, 5C5, 5CF, 5CH, 5CR, 5D5, 5DD, 5EF, 5EP, 5ER, 5F9, 5FH, 5FN, 5G5, 5GN, 5H1, 5HD, 5HP, 5HR, 5IH, 5IN, 5IR, 5J5, 5JB, 5K1, 5K3, 5KD, 5KR, 5L5, 5L9, 5LB, 5LF, 5MB, 5MD, 5MP, 5N3, 5NJ, 5NR, 5O5, 5OB, 5P1, 5PH, 5PJ, 5PN, 5Q1, 5Q3, 5Q9, 5QF, 5QP, 5R3, 5RF, 5RR, 60H, 60J, 60P, 611, 61J, 61R, 62N, 62R, 631, 635, 63B, 63D, 63P, 641, 64F, 65H, 65R, 665, 66H, 673, 679, 67J, 683, 685, 689, 68F, 68N, 691, 69B, 69D, 69H, 6A3, 6A9, 6AF, 6AJ, 6AP, 6AR, 6B9, 6BB, 6BR, 6CB, 6CJ, 6D9, 6DD, 6DJ, 6E3, 6E5, 6EB, 6EH, 6EN, 6FN, 6G1, 6GF, 6GJ, 6GR, 6H9, 6HH, 6I1, 6IJ, 6IN, 6IP, 6J1, 6JP, 6K9, 6KF, 6KH, 6L5, 6LB, 6LH, 6M3, 6MD, 6MR, 6N3, 6O5, 6OB, 6OH, 6ON, 6P3, 6P9, 6PD, 6PF, 6PR, 6Q5, 6Q9, 6QB, 6QH, 6RB, 6RH, 6RJ, 6RN, 70D, 70F, 70J, 713, 715, 71B, 71F, 72D, 72J, 72P, 731, 739, 73J, 74N, 75B, 75D, 75J, 75N, 75P, 761, 763, 76D, 76R, 775, 779, 77H, 77R, 785, 78P, 791, 793, 799, 7AB, 7AF, 7AN, 7B5, 7BB, 7BH, 7BP, 7C3, 7CF, 7CJ, 7CP, 7CR, 7D5, 7D9, 7DF, 7DH, 7DR, 7E1, 7EH, 7EN, 7FF, 7FJ, 7G3, 7GH, 7HH, 7HN, 7IF, 7IJ, 7J9, 7JH, 7JN, 7JR, 7K5, 7KJ, 7KP, 7L3, 7LD, 7LF, 7LP, 7M9, 7MH, 7MR, 7N1, 7NB, 7NJ, 7O3, 7OD, 7P9, 7PB, 7PF, 7PN, 7Q1, 7Q5, 7QD, 7R3, 7RD, 7RJ, 7RP, 7RR, 805, 80F, 80R, 811, 81B, 81H, 81N, 821, 829, 82F, 82P, 833, 835, 83B, 83H, 83N, 845, 84D, 859, 85F, 869, 86B, 871, 875, 87D, 87N, 88P, 895, 89N, 89R, 8A1, 8AB, 8AH, 8AJ, 8AP, 8B1, 8BJ, 8BR, 8CB, 8D1, 8DH, 8DN, 8DP, 8E9, 8EF, 8EP, 8ER, 8F9, 8FB, 8FH, 8FR, 8GD, 8GH, 8HD, 8HF, 8I3, 8I5, 8IF, 8IH, 8IR, 8JJ, 8JN, 8JP, 8K1, 8K9, 8KP, 8L3, 8L9, 8LB, 8LN, 8MB, 8MJ, 8MN, 8N1, 8O3, 8O5, 8OF, 8OH, 8ON, 8OR, 8P5, 8PB, 8PJ, 8PP, 8Q1, 8QD, 8QJ, 8QR, 8RB, 8RF, 901, 90D, 90N, 91J, 91P, 929, 92F, 92H, 93B, 93J, 949, 94J, 94P, 95B, 95F, 95H, 95N, 965, 96D, 96J, 96N, 971, 983, 98H, 98R, 991, 99D, 99N, 99P, 9AD, 9AF, 9B5, 9C1, 9CJ, 9CP, 9DD, 9E3, 9E9, 9EB, 9F1, 9F5, 9FB, 9FD, 9FN, 9G3, 9GD, 9GJ, 9GP, 9H5, 9H9, 9HF, 9HH, 9HR, 9I1, 9ID, 9IH, 9IN, 9J1, 9J3, 9JF, 9JJ, 9K5, 9KN, 9KR, 9L5, 9LP, 9M1, 9M9, 9MF, 9MJ, 9MR, 9N3, 9NH, 9NN, 9NR, 9OD, 9OP, 9P1, 9P3, 9Q5, 9Q9, 9R5, 9RB, 9RH, A01, A0D, A0R, A15, A19, A1B, A1F, A25, A2B, A2N, A33, A39, A3D, A3P, A3R, A4B, A5D, A61, A63, ...
29	12, 18, 1C, 1E, 1I, 1O, 21, 23, 29, 2D, 2F, 2L, 2P, 32, 3A, 3E, 3G, 3K, 3M, 3Q, 4B, 4F, 4L, 4N, 54, 56, 5C, 5I, 5M, 5S, 65, 67, 6H, 6J, 6N, 6P, 78, 7K, 7O, 7Q, 81, 87, 89, 8J, 8P, 92, 98, 9A, 9G, 9K, 9M, A3, AH, AL, AN, AR, BC, BI, BS, C1, C5, CB, CJ, CP, D2, D6, DC, DK, DO, E3, ED, EF, EP, ER, F4, F8, FE, FM, FQ, FS, G3, GF, GN, GR, H6, HA, HG, HS, I1, IJ, IP, J6, JC, JI, JK, JQ, K7, KD, KJ, KL, KR, L4, L8, LA, LM, M3, M5, M9, MF, ML, MN, N6, NA, NG, NO, O5, OD, ON, P2, P8, PE, PI, PQ, Q3, Q7, QF, QJ, R4, RE, RQ, RS, S9, SB, SF, SH, SR, 10C, 10G, 10I, 10M, 117, 11B, 11D, 11H, 128, 12C, 12K, 131, 139, 13D, 13J, 13P, 14A, 14E, 14K, 14Q, 155, 15B, 15N, 15R, 164, 166, 16G, 16I, 16O, 175, 177, 17H, 17J, 17P, 18E, 18I, 18K, 18O, 191, 197, 19F, 19L, 19R, 1AK, 1AM, 1B3, 1BB, 1BL, 1BR, 1C4, 1CC, 1CO, 1CS, 1D5, 1DB, 1DD, 1DJ, 1E2, 1EC, 1F1, 1F3, 1F7, 1FD, 1FF, 1FL, 1FP, 1FR, 1G2, 1GE, 1GG, 1GM, 1HR, 1I4, 1IA, 1II, 1J7, 1JH, 1K2, 1K6, 1K8, 1KC, 1KI, 1KQ, 1L1, 1L3, 1L9, 1LL, 1M2, 1M4, 1M8, 1MA, 1ME, 1MK, 1N3, 1NF, 1NN, 1O6, 1OC, 1OG, 1OM, 1P1, 1P5, 1PD, 1PH, 1Q2, 1Q6, 1QC, 1QE, 1QI, 1QO, 1QQ, 1R3, 1RD, 1S4, 1SA, 1SE, 1SG, 20B, 20F, 20H, 20R, 21A, 21C, 21M, 221, 227, 22D, 22J, 238, 23E, 23I, 23K, 243, 24D, 24P, 254, 25K, 265, 26B, 26F, 26H, 26L, 26N, 274, 27G, 27M, 27S, 28H, 28J, 296, 298, 2A1, 2A7, 2AF, 2AL, 2AP, 2AR, 2B2, 2BA, 2BG, 2BQ, 2BS, 2C9, 2CN, 2D4, 2DA, 2DM, 2DO, 2DS, 2E1, 2EB, 2EN, 2EP, 2FC, 2FE, 2FK, 2FO, 2FQ, 2G7, 2GF, 2H4, 2HS, 2I3, 2I9, 2IH, 2J4, 2J6, 2JA, 2JI, 2K5, 2K7, 2KB, 2KJ, 2KP, 2L2, 2L6, 2LI, 2LK, 2MD, 2MJ, 2ML, 2MR, 2N2, 2N8, 2NM, 2NS, 2O3, 2O5, 2OB, 2OF, 2OL, 2P4, 2PA, 2PG, 2Q1, 2Q5, 2QB, 2QN, 2R2, 2R8, 2RC, 2S9, 2SR, 308, 30G, 30K, 30Q, 30S, 315, 31R, 32A, 32C, 32S, 337, 33B, 33N, 348, 34I, 34K, 34O, 353, 359, 35F, 35J, 35L, 35P, 362, 36A, 36E, 36G, 36M, 373, 375, 37F, 37N, 37R, 38C, 38M, 395, 397, 39D, 39H, 39J, 3A6, 3AK, 3AO, 3B1, 3B9, 3BF, 3BJ, 3C8, 3CG, 3CQ, 3D3, 3D9, 3DH, 3DR, 3EA, 3EO, 3ES, 3F5, 3FB, 3FD, 3GC, 3GE, 3GO, 3H3, 3H7, 3HL, 3HP, 3I4, 3IG, 3IM, 3J5, 3J9, 3JF, 3K6, 3KG, 3KI, 3L5, 3M2, 3M6, 3M8, 3MK, 3MQ, 3N1, 3ND, 3NJ, 3NR, 3O2, 3OA, 3P3, 3P5, 3P9, 3PB, 3PN, 3QM, 3QO, 3R1, 3R7, 3RD, 3RH, 3RN, 3RP, 3S8, 3SC, 3SO, 3SQ, 407, 409, 40P, 40R, 41E, 41K, 42B, 42R, 436, 43A, 43C, 43G, 43I, 44B, 44J, 452, 458, 45I, 45K, 45O, 461, 463, 469, 46J, 46L, 474, 47E, 47G, 47Q, 48B, 48H, 48L, 48R, 496, 49C, 49I, 4A5, 4AH, 4AJ, 4AN, 4B8, 4BE, 4BI, 4BQ, 4C7, 4CF, 4CL, 4CR, 4DK, 4DQ, 4DS, 4E9, 4EN, 4ER, 4F4, 4FM, 4FO, 4G5, 4GJ, 4GN, 4GP, 4H6, 4HK, 4HO, 4I3, 4IL, 4IP, 4J2, 4J4, 4J8, 4JE, 4JG, 4JS, 4K3, 4KN, 4LG, 4LS, 4M1, 4M5, 4MB, 4MH, 4MJ, 4MP, 4NI, 4NK, 4NQ, 4OD, 4OJ, 4P2, 4P4, 4PA, 4PM, 4Q9, 4QB, 4QF, 4QL, 4R6, 4RA, 4RC, 4S1, 4SP, 506, 50C, 50E, 50O, 50Q, 517, 519, 51J, 51P, 51R, 528, 52A, 52K, 52Q, 535, 546, 54G, 54I, 54S, 557, 55D, 55N, 56C, 56I, 571, 57D, 57F, 584, 58A, 58E, 58K, 58Q, 59F, 59H, 59R, 5AC, 5AI, 5AM, 5AO, 5AS, 5BN, 5BP, 5C8, 5CE, 5D1, 5D9, 5DF, 5DL, 5EA, 5EQ, 5ES, 5F3, 5F9, 5FB, 5FH, 5FN, 5G4, 5GA, 5GM, 5H5, 5HN, 5HP, 5I2, 5I6, 5IO, 5J3, 5JR, 5K2, 5K4, 5K8, 5KE, 5KG, 5KS, 5L3, 5LH, 5MI, 5MS, 5N5, 5NH, 5O2, 5O8, 5OI, 5P1, 5P3, 5P7, 5PD, 5PL, 5PR, 5Q8, 5QA, 5QE, 5QS, 5R5, 5RB, 5RF, 5RL, 5RN, 5S4, 5S6, 5SM, 605, 60D, 612, 616, 61C, 61O, 61Q, 623, 629, 62F, 63E, 63K, 645, 649, 64H, 64R, 656, 65I, 667, 66B, 66D, 66H, 67C, 67O, 681, 683, 68J, 68P, 692, 69G, 69Q, 6AB, 6AF, 6BG, 6BM, 6BS, 6C5, 6CD, 6CJ, 6CN, 6CP, 6D8, 6DE, 6DI, 6DK, 6DQ, 6EJ, 6EP, 6ER, 6F2, 6FK, 6FM, 6FQ, 6G9, 6GB, 6GH, 6GL, 6HI, 6HO, 6I1, 6I5, 6ID, 6IN, 6JQ, 6KD, 6KF, 6KL, 6KP, 6KR, 6L2, 6L4, 6LE, 6LS, 6M5, 6M9, 6MH, 6MR, 6N4, 6NO, 6NS, 6O1, 6O7, 6P8, 6PC, 6PK, 6Q1, 6Q7, 6QD, 6QL, 6QR, 6RA, 6RE, 6RK, 6RM, 6RS, 6S3, 6S9, 6SB, 6SL, 6SN, 70A, 70G, 717, 71B, 71N, 728, 737, 73D, 744, 748, 74Q, 755, 75B, 75F, 75L, 766, 76C, 76I, 76S, 771, 77B, 77N, 782, 78C, 78E, 78O, 793, 79F, 79P, 7AK, 7AM, 7AQ, 7B5, 7BB, 7BF, 7BN, 7CC, 7CM, 7CS, 7D5, 7D7, 7DD, 7DN, 7E6, 7E8, 7EI, 7EO, 7F1, 7F7, 7FF, 7FL, 7G2, 7G8, 7GA, 7GG, 7GM, 7GS, 7H9, 7HH, 7IC, 7II, 7JB, 7JD, 7K2, 7K6, 7KE, 7KO, 7LP, 7M4, 7MM, 7MQ, 7MS, 7N9, 7NF, 7NH, 7NN, 7NR, 7OG, 7OO, 7P7, 7PP, 7QC, 7QI, 7QK, 7R3, 7R9, 7RJ, 7RL, 7S2, 7S4, 7SA, 7SK, 805, 809, 814, 816, 81M, 81O, 825, 827, 82H, 838, 83C, 83E, 83I, 83Q, 84D, 84J, 84P, 84R, 85A, 85Q, 865, 869, 86F, 87G, 87I, 87S, 881, 887, 88B, 88H, 88N, 892, 898, 89C, 89O, 8A1, 8A9, 8AL, 8AP, 8BA, 8BM, 8C3, 8CR, 8D4, 8DG, 8DM, 8DO, 8EH, 8EP, 8FE, 8FO, 8G1, 8GF, 8GJ, 8GL, 8GR, 8H8, 8HG, 8HM, 8HQ, 8I3, 8J4, 8JI, 8JS, 8K1, 8KD, 8KN, 8KP, 8LC, 8LE, 8M3, 8MR, 8NG, 8NM, 8O9, 8OR, 8P4, 8P6, 8PO, 8PS, 8Q5, 8Q7, 8QH, 8QP, 8R6, 8RC, 8RI, 8RQ, 8S1, 8S7, 8S9, 8SJ, 8SL, 904, 908, 90E, 90K, 90M, 915, 919, 91N, 92C, 92G, 92M, 93D, 93H, 93P, 942, 946, 94E, 94I, 953, 959, 95D, 95R, 96A, 96E, 96G, 97H, 97L, 98G, 98M, 98S, 99B, 99N, 9A8, 9AE, 9AI, 9AK, 9AO, 9BD, 9BJ, 9C2, 9CA, 9CG, 9CK, 9D3, 9D5, 9DH, 9EI, 9F5, 9F7, 9FD, ...
30	11, 17, 1B, 1D, 1H, 1N, 1T, 21, 27, 2B, 2D, 2J, 2N, 2T, 37, 3B, 3D, 3H, 3J, 3N, 47, 4B, 4H, 4J, 4T, 51, 57, 5D, 5H, 5N, 5T, 61, 6B, 6D, 6H, 6J, 71, 7D, 7H, 7J, 7N, 7T, 81, 8B, 8H, 8N, 8T, 91, 97, 9B, 9D, 9N, A7, AB, AD, AH, B1, B7, BH, BJ, BN, BT, C7, CD, CJ, CN, CT, D7, DB, DJ, DT, E1, EB, ED, EJ, EN, ET, F7, FB, FD, FH, FT, G7, GB, GJ, GN, GT, HB, HD, I1, I7, IH, IN, IT, J1, J7, JH, JN, JT, K1, K7, KD, KH, KJ, L1, LB, LD, LH, LN, LT, M1, MD, MH, MN, N1, NB, NJ, NT, O7, OD, OJ, ON, P1, P7, PB, PJ, PN, Q7, QH, QT, R1, RB, RD, RH, RJ, RT, SD, SH, SJ, SN, T7, TB, TD, TH, 107, 10B, 10J, 10T, 117, 11B, 11H, 11N, 127, 12B, 12H, 12N, 131, 137, 13J, 13N, 13T, 141, 14B, 14D, 14J, 14T, 151, 15B, 15D, 15J, 167, 16B, 16D, 16H, 16N, 16T, 177, 17D, 17J, 18B, 18D, 18N, 191, 19B, 19H, 19N, 1A1, 1AD, 1AH, 1AN, 1AT, 1B1, 1B7, 1BJ, 1BT, 1CH, 1CJ, 1CN, 1CT, 1D1, 1D7, 1DB, 1DD, 1DH, 1DT, 1E1, 1E7, 1FB, 1FH, 1FN, 1G1, 1GJ, 1GT, 1HD, 1HH, 1HJ, 1HN, 1HT, 1I7, 1IB, 1ID, 1IJ, 1J1, 1JB, 1JD, 1JH, 1JJ, 1JN, 1JT, 1KB, 1KN, 1L1, 1LD, 1LJ, 1LN, 1LT, 1M7, 1MB, 1MJ, 1MN, 1N7, 1NB, 1NH, 1NJ, 1NN, 1NT, 1O1, 1O7, 1OH, 1P7, 1PD, 1PH, 1PJ, 1QD, 1QH, 1QJ, 1QT, 1RB, 1RD, 1RN, 1S1, 1S7, 1SD, 1SJ, 1T7, 1TD, 1TH, 1TJ, 201, 20B, 20N, 211, 21H, 221, 227, 22B, 22D, 22H, 22J, 22T, 23B, 23H, 23N, 24B, 24D, 24T, 251, 25N, 25T, 267, 26D, 26H, 26J, 26N, 271, 277, 27H, 27J, 27T, 28D, 28N, 28T, 29B, 29D, 29H, 29J, 29T, 2AB, 2AD, 2AT, 2B1, 2B7, 2BB, 2BD, 2BN, 2C1, 2CJ, 2DD, 2DH, 2DN, 2E1, 2EH, 2EJ, 2EN, 2F1, 2FH, 2FJ, 2FN, 2G1, 2G7, 2GD, 2GH, 2GT, 2H1, 2HN, 2HT, 2I1, 2I7, 2IB, 2IH, 2J1, 2J7, 2JB, 2JD, 2JJ, 2JN, 2JT, 2KB, 2KH, 2KN, 2L7, 2LB, 2LH, 2LT, 2M7, 2MD, 2MH, 2ND, 2O1, 2OB, 2OJ, 2ON, 2OT, 2P1, 2P7, 2PT, 2QB, 2QD, 2QT, 2R7, 2RB, 2RN, 2S7, 2SH, 2SJ, 2SN, 2T1, 2T7, 2TD, 2TH, 2TJ, 2TN, 2TT, 307, 30B, 30D, 30J, 30T, 311, 31B, 31J, 31N, 327, 32H, 32T, 331, 337, 33B, 33D, 33T, 34D, 34H, 34N, 351, 357, 35B, 35T, 367, 36H, 36N, 36T, 377, 37H, 37T, 38D, 38H, 38N, 38T, 391, 39T, 3A1, 3AB, 3AJ, 3AN, 3B7, 3BB, 3BJ, 3C1, 3C7, 3CJ, 3CN, 3CT, 3DJ, 3DT, 3E1, 3EH, 3FD, 3FH, 3FJ, 3G1, 3G7, 3GB, 3GN, 3GT, 3H7, 3HB, 3HJ, 3IB, 3ID, 3IH, 3IJ, 3J1, 3JT, 3K1, 3K7, 3KD, 3KJ, 3KN, 3KT, 3L1, 3LD, 3LH, 3LT, 3M1, 3MB, 3MD, 3MT, 3N1, 3NH, 3NN, 3OD, 3OT, 3P7, 3PB, 3PD, 3PH, 3PJ, 3QB, 3QJ, 3R1, 3R7, 3RH, 3RJ, 3RN, 3RT, 3S1, 3S7, 3SH, 3SJ, 3T1, 3TB, 3TD, 3TN, 407, 40D, 40H, 40N, 411, 417, 41D, 41T, 42B, 42D, 42H, 431, 437, 43B, 43J, 43T, 447, 44D, 44J, 45B, 45H, 45J, 45T, 46D, 46H, 46N, 47B, 47D, 47N, 487, 48B, 48D, 48N, 497, 49B, 49J, 4A7, 4AB, 4AH, 4AJ, 4AN, 4AT, 4B1, 4BD, 4BH, 4C7, 4CT, 4DB, 4DD, 4DH, 4DN, 4DT, 4E1, 4E7, 4ET, 4F1, 4F7, 4FN, 4FT, 4GB, 4GD, 4GJ, 4H1, 4HH, 4HJ, 4HN, 4HT, 4ID, 4IH, 4IJ, 4J7, 4K1, 4KB, 4KH, 4KJ, 4KT, 4L1, 4LB, 4LD, 4LN, 4LT, 4M1, 4MB, 4MD, 4MN, 4MT, 4N7, 4O7, 4OH, 4OJ, 4OT, 4P7, 4PD, 4PN, 4QB, 4QH, 4QT, 4RB, 4RD, 4S1, 4S7, 4SB, 4SH, 4SN, 4TB, 4TD, 4TN, 507, 50D, 50H, 50J, 50N, 51H, 51J, 521, 527, 52N, 531, 537, 53D, 541, 54H, 54J, 54N, 54T, 551, 557, 55D, 55N, 55T, 56B, 56N, 57B, 57D, 57J, 57N, 58B, 58J, 59D, 59H, 59J, 59N, 59T, 5A1, 5AD, 5AH, 5B1, 5C1, 5CB, 5CH, 5CT, 5DD, 5DJ, 5DT, 5EB, 5ED, 5EH, 5EN, 5F1, 5F7, 5FH, 5FJ, 5FN, 5G7, 5GD, 5GJ, 5GN, 5GT, 5H1, 5HB, 5HD, 5HT, 5IB, 5IJ, 5J7, 5JB, 5JH, 5JT, 5K1, 5K7, 5KD, 5KJ, 5LH, 5LN, 5M7, 5MB, 5MJ, 5MT, 5N7, 5NJ, 5O7, 5OB, 5OD, 5OH, 5PB, 5PN, 5PT, 5Q1, 5QH, 5QN, 5QT, 5RD, 5RN, 5S7, 5SB, 5TB, 5TH, 5TN, 5TT, 607, 60D, 60H, 60J, 611, 617, 61B, 61D, 61J, 62B, 62H, 62J, 62N, 63B, 63D, 63H, 63T, 641, 647, 64B, 657, 65D, 65J, 65N, 661, 66B, 67D, 67T, 681, 687, 68B, 68D, 68H, 68J, 68T, 69D, 69J, 69N, 6A1, 6AB, 6AH, 6B7, 6BB, 6BD, 6BJ, 6CJ, 6CN, 6D1, 6DB, 6DH, 6DN, 6E1, 6E7, 6EJ, 6EN, 6ET, 6F1, 6F7, 6FB, 6FH, 6FJ, 6FT, 6G1, 6GH, 6GN, 6HD, 6HH, 6HT, 6ID, 6JB, 6JH, 6K7, 6KB, 6KT, 6L7, 6LD, 6LH, 6LN, 6M7, 6MD, 6MJ, 6MT, 6N1, 6NB, 6NN, 6O1, 6OB, 6OD, 6ON, 6P1, 6PD, 6PN, 6QH, 6QJ, 6QN, 6R1, 6R7, 6RB, 6RJ, 6S7, 6SH, 6SN, 6ST, 6T1, 6T7, 6TH, 6TT, 701, 70B, 70H, 70N, 70T, 717, 71D, 71N, 71T, 721, 727, 72D, 72J, 72T, 737, 741, 747, 74T, 751, 75J, 75N, 761, 76B, 77B, 77J, 787, 78B, 78D, 78N, 78T, 791, 797, 79B, 79T, 7A7, 7AJ, 7B7, 7BN, 7BT, 7C1, 7CD, 7CJ, 7CT, 7D1, 7DB, 7DD, 7DJ, 7DT, 7ED, 7EH, 7FB, 7FD, 7FT, 7G1, 7GB, 7GD, 7GN, 7HD, 7HH, 7HJ, 7HN, 7I1, 7IH, 7IN, 7IT, 7J1, 7JD, 7JT, 7K7, 7KB, 7KH, 7LH, 7LJ, 7LT, 7M1, 7M7, 7MB, 7MH, 7MN, 7N1, 7N7, 7NB, 7NN, 7NT, 7O7, 7OJ, 7ON, 7P7, 7PJ, 7PT, 7QN, 7QT, 7RB, 7RH, 7RJ, 7SB, 7SJ, 7T7, 7TH, 7TN, 807, 80B, 80D, 80J, 80T, 817, 81D, 81H, 81N, 82N, 837, 83H, 83J, 841, 84B, 84D, 84T, 851, 85J, 86D, 871, 877, 87N, 88B, 88H, 88J, 897, 89B, 89H, 89J, 89T, 8A7, 8AH, 8AN, 8AT, 8B7, 8BB, 8BH, 8BJ, 8BT, 8C1, 8CD, 8CH, 8CN, 8CT, 8D1, 8DD, 8DH, 8E1, 8EJ, 8EN, 8ET, 8FJ, 8FN, 8G1, 8G7, 8GB, 8GJ, 8GN, 8H7, 8HD, 8HH, 8I1, 8ID, 8IH, 8IJ, 8JJ, 8JN, 8KH, 8KN, 8KT, 8LB, 8LN, 8M7, 8MD, 8MH, 8MJ, 8MN, 8NB, 8NH, 8NT, 8O7, 8OD, 8OH, 8OT, 8P1, 8PD, 8QD, 8QT, 8R1, 8R7, ...
31	16, 1A, 1C, 1G, 1M, 1S, 1U, 25, 29, 2B, 2H, 2L, 2R, 34, 38, 3A, 3E, 3G, 3K, 43, 47, 4D, 4F, 4P, 4R, 52, 58, 5C, 5I, 5O, 5Q, 65, 67, 6B, 6D, 6P, 76, 7A, 7C, 7G, 7M, 7O, 83, 89, 8F, 8L, 8N, 8T, 92, 94, 9E, 9S, A1, A3, A7, AL, AR, B6, B8, BC, BI, BQ, C1, C7, CB, CH, CP, CT, D6, DG, DI, DS, DU, E5, E9, EF, EN, ER, ET, F2, FE, FM, FQ, G3, G7, GD, GP, GR, HE, HK, HU, I5, IB, ID, IJ, IT, J4, JA, JC, JI, JO, JS, JU, KB, KL, KN, KR, L2, L8, LA, LM, LQ, M1, M9, MJ, MR, N6, NE, NK, NQ, NU, O7, OD, OH, OP, OT, PC, PM, Q3, Q5, QF, QH, QL, QN, R2, RG, RK, RM, RQ, S9, SD, SF, SJ, T8, TC, TK, TU, U7, UB, UH, UN, 106, 10A, 10G, 10M, 10U, 115, 11H, 11L, 11R, 11T, 128, 12A, 12G, 12Q, 12S, 137, 139, 13F, 142, 146, 148, 14C, 14I, 14O, 151, 157, 15D, 164, 166, 16G, 16O, 173, 179, 17F, 17N, 184, 188, 18E, 18K, 18M, 18S, 199, 19J, 1A6, 1A8, 1AC, 1AI, 1AK, 1AQ, 1AU, 1B1, 1B5, 1BH, 1BJ, 1BP, 1CS, 1D3, 1D9, 1DH, 1E4, 1EE, 1ES, 1F1, 1F3, 1F7, 1FD, 1FL, 1FP, 1FR, 1G2, 1GE, 1GO, 1GQ, 1GU, 1H1, 1H5, 1HB, 1HN, 1I4, 1IC, 1IO, 1IU, 1J3, 1J9, 1JH, 1JL, 1JT, 1K2, 1KG, 1KK, 1KQ, 1KS, 1L1, 1L7, 1L9, 1LF, 1LP, 1ME, 1MK, 1MO, 1MQ, 1NJ, 1NN, 1NP, 1O4, 1OG, 1OI, 1OS, 1P5, 1PB, 1PH, 1PN, 1QA, 1QG, 1QK, 1QM, 1R3, 1RD, 1RP, 1S2, 1SI, 1T1, 1T7, 1TB, 1TD, 1TH, 1TJ, 1TT, 1UA, 1UG, 1UM, 209, 20B, 20R, 20T, 21K, 21Q, 223, 229, 22D, 22F, 22J, 22R, 232, 23C, 23E, 23O, 247, 24H, 24N, 254, 256, 25A, 25C, 25M, 263, 265, 26L, 26N, 26T, 272, 274, 27E, 27M, 289, 292, 296, 29C, 29K, 2A5, 2A7, 2AB, 2AJ, 2B4, 2B6, 2BA, 2BI, 2BO, 2BU, 2C3, 2CF, 2CH, 2D8, 2DE, 2DG, 2DM, 2DQ, 2E1, 2EF, 2EL, 2EP, 2ER, 2F2, 2F6, 2FC, 2FO, 2FU, 2G5, 2GJ, 2GN, 2GT, 2HA, 2HI, 2HO, 2HS, 2IN, 2JA, 2JK, 2JS, 2K1, 2K7, 2K9, 2KF, 2L6, 2LI, 2LK, 2M5, 2MD, 2MH, 2MT, 2NC, 2NM, 2NO, 2NS, 2O5, 2OB, 2OH, 2OL, 2ON, 2OR, 2P2, 2PA, 2PE, 2PG, 2PM, 2Q1, 2Q3, 2QD, 2QL, 2QP, 2R8, 2RI, 2RU, 2S1, 2S7, 2SB, 2SD, 2ST, 2TC, 2TG, 2TM, 2TU, 2U5, 2U9, 2UR, 304, 30E, 30K, 30Q, 313, 31D, 31P, 328, 32C, 32I, 32O, 32Q, 33N, 33P, 344, 34C, 34G, 34U, 353, 35B, 35N, 35T, 36A, 36E, 36K, 379, 37J, 37L, 386, 391, 395, 397, 39J, 39P, 39T, 3AA, 3AG, 3AO, 3AS, 3B5, 3BR, 3BT, 3C2, 3C4, 3CG, 3DD, 3DF, 3DL, 3DR, 3E2, 3E6, 3EC, 3EE, 3EQ, 3EU, 3FB, 3FD, 3FN, 3FP, 3GA, 3GC, 3GS, 3H3, 3HN, 3I8, 3IG, 3IK, 3IM, 3IQ, 3IS, 3JJ, 3JR, 3K8, 3KE, 3KO, 3KQ, 3KU, 3L5, 3L7, 3LD, 3LN, 3LP, 3M6, 3MG, 3MI, 3MS, 3NB, 3NH, 3NL, 3NR, 3O4, 3OA, 3OG, 3P1, 3PD, 3PF, 3PJ, 3Q2, 3Q8, 3QC, 3QK, 3QU, 3R7, 3RD, 3RJ, 3SA, 3SG, 3SI, 3SS, 3TB, 3TF, 3TL, 3U8, 3UA, 3UK, 403, 407, 409, 40J, 412, 416, 41E, 421, 425, 42B, 42D, 42H, 42N, 42P, 436, 43A, 43U, 44L, 452, 454, 458, 45E, 45K, 45M, 45S, 46J, 46L, 46R, 47C, 47I, 47U, 481, 487, 48J, 494, 496, 49A, 49G, 49U, 4A3, 4A5, 4AN, 4BG, 4BQ, 4C1, 4C3, 4CD, 4CF, 4CP, 4CR, 4D6, 4DC, 4DE, 4DO, 4DQ, 4E5, 4EB, 4EJ, 4FI, 4FS, 4FU, 4G9, 4GH, 4GN, 4H2, 4HK, 4HQ, 4I7, 4IJ, 4IL, 4J8, 4JE, 4JI, 4JO, 4JU, 4KH, 4KJ, 4KT, 4LC, 4LI, 4LM, 4LO, 4LS, 4ML, 4MN, 4N4, 4NA, 4NQ, 4O3, 4O9, 4OF, 4P2, 4PI, 4PK, 4PO, 4PU, 4Q1, 4Q7, 4QD, 4QN, 4QT, 4RA, 4RM, 4S9, 4SB, 4SH, 4SL, 4T8, 4TG, 4U9, 4UD, 4UF, 4UJ, 4UP, 4UR, 508, 50C, 50Q, 51P, 524, 52A, 52M, 535, 53B, 53L, 542, 544, 548, 54E, 54M, 54S, 557, 559, 55D, 55R, 562, 568, 56C, 56I, 56K, 56U, 571, 57H, 57T, 586, 58O, 58S, 593, 59F, 59H, 59N, 59T, 5A4, 5B1, 5B7, 5BL, 5BP, 5C2, 5CC, 5CK, 5D1, 5DJ, 5DN, 5DP, 5DT, 5EM, 5F3, 5F9, 5FB, 5FR, 5G2, 5G8, 5GM, 5H1, 5HF, 5HJ, 5II, 5IO, 5IU, 5J5, 5JD, 5JJ, 5JN, 5JP, 5K6, 5KC, 5KG, 5KI, 5KO, 5LF, 5LL, 5LN, 5LR, 5ME, 5MG, 5MK, 5N1, 5N3, 5N9, 5ND, 5O8, 5OE, 5OK, 5OO, 5P1, 5PB, 5QC, 5QS, 5QU, 5R5, 5R9, 5RB, 5RF, 5RH, 5RR, 5SA, 5SG, 5SK, 5SS, 5T7, 5TD, 5U2, 5U6, 5U8, 5UE, 60D, 60H, 60P, 614, 61A, 61G, 61O, 61U, 62B, 62F, 62L, 62N, 62T, 632, 638, 63A, 63K, 63M, 647, 64D, 652, 656, 65I, 661, 66T, 674, 67O, 67S, 68F, 68N, 68T, 692, 698, 69M, 69S, 6A3, 6AD, 6AF, 6AP, 6B6, 6BE, 6BO, 6BQ, 6C5, 6CD, 6CP, 6D4, 6DS, 6DU, 6E3, 6EB, 6EH, 6EL, 6ET, 6FG, 6FQ, 6G1, 6G7, 6G9, 6GF, 6GP, 6H6, 6H8, 6HI, 6HO, 6HU, 6I5, 6ID, 6IJ, 6IT, 6J4, 6J6, 6JC, 6JI, 6JO, 6K3, 6KB, 6L4, 6LA, 6M1, 6M3, 6ML, 6MP, 6N2, 6NC, 6OB, 6OJ, 6P6, 6PA, 6PC, 6PM, 6PS, 6PU, 6Q5, 6Q9, 6QR, 6R4, 6RG, 6S3, 6SJ, 6SP, 6SR, 6T8, 6TE, 6TO, 6TQ, 6U5, 6U7, 6UD, 6UN, 706, 70A, 713, 715, 71L, 71N, 722, 724, 72E, 733, 737, 739, 73D, 73L, 746, 74C, 74I, 74K, 751, 75H, 75P, 75T, 764, 773, 775, 77F, 77H, 77N, 77R, 782, 788, 78G, 78M, 78Q, 797, 79D, 79L, 7A2, 7A6, 7AK, 7B1, 7BB, 7C4, 7CA, 7CM, 7CS, 7CU, 7DL, 7DT, 7EG, 7EQ, 7F1, 7FF, 7FJ, 7FL, 7FR, 7G6, 7GE, 7GK, 7GO, 7GU, 7HT, 7IC, 7IM, 7IO, 7J5, 7JF, 7JH, 7K2, 7K4, 7KM, 7LF, 7M2, 7M8, 7MO, 7NB, 7NH, 7NJ, 7O6, 7OA, 7OG, 7OI, 7OS, 7P5, 7PF, 7PL, 7PR, 7Q4, 7Q8, 7QE, 7QG, 7QQ, 7QS, 7R9, 7RD, 7RJ, 7RP, 7RR, 7S8, 7SC, 7SQ, 7TD, 7TH, 7TN, 7UC, 7UG, 7UO, 7UU, 803, 80B, 80F, 80T, 814, 818, 81M, 823, 827, 829, 838, 83C, 845, 84B, 84H, 84T, 85A, 85O, 85U, 863, 865, 869, 86R, 872, 87E, 87M, 87S, 881, 88D, 88F, 88R, 89Q, 8AB, 8AD, 8AJ, 8BA, ...
32	15, 19, 1B, 1F, 1L, 1R, 1T, 23, 27, 29, 2F, 2J, 2P, 31, 35, 37, 3B, 3D, 3H, 3V, 43, 49, 4B, 4L, 4N, 4T, 53, 57, 5D, 5J, 5L, 5V, 61, 65, 67, 6J, 6V, 73, 75, 79, 7F, 7H, 7R, 81, 87, 8D, 8F, 8L, 8P, 8R, 95, 9J, 9N, 9P, 9T, AB, AH, AR, AT, B1, B7, BF, BL, BR, BV, C5, CD, CH, CP, D3, D5, DF, DH, DN, DR, E1, E9, ED, EF, EJ, EV, F7, FB, FJ, FN, FT, G9, GB, GT, H3, HD, HJ, HP, HR, I1, IB, IH, IN, IP, IV, J5, J9, JB, JN, K1, K3, K7, KD, KJ, KL, L1, L5, LB, LJ, LT, M5, MF, MN, MT, N3, N7, NF, NL, NP, O1, O5, OJ, OT, P9, PB, PL, PN, PR, PT, Q7, QL, QP, QR, QV, RD, RH, RJ, RN, SB, SF, SN, T1, T9, TD, TJ, TP, U7, UB, UH, UN, UV, V5, VH, VL, VR, VT, 107, 109, 10F, 10P, 10R, 115, 117, 11D, 11V, 123, 125, 129, 12F, 12L, 12T, 133, 139, 13V, 141, 14B, 14J, 14T, 153, 159, 15H, 15T, 161, 167, 16D, 16F, 16L, 171, 17B, 17T, 17V, 183, 189, 18B, 18H, 18L, 18N, 18R, 197, 199, 19F, 1AH, 1AN, 1AT, 1B5, 1BN, 1C1, 1CF, 1CJ, 1CL, 1CP, 1CV, 1D7, 1DB, 1DD, 1DJ, 1DV, 1E9, 1EB, 1EF, 1EH, 1EL, 1ER, 1F7, 1FJ, 1FR, 1G7, 1GD, 1GH, 1GN, 1GV, 1H3, 1HB, 1HF, 1HT, 1I1, 1I7, 1I9, 1ID, 1IJ, 1IL, 1IR, 1J5, 1JP, 1JV, 1K3, 1K5, 1KT, 1L1, 1L3, 1LD, 1LP, 1LR, 1M5, 1MD, 1MJ, 1MP, 1MV, 1NH, 1NN, 1NR, 1NT, 1O9, 1OJ, 1OV, 1P7, 1PN, 1Q5, 1QB, 1QF, 1QH, 1QL, 1QN, 1R1, 1RD, 1RJ, 1RP, 1SB, 1SD, 1ST, 1SV, 1TL, 1TR, 1U3, 1U9, 1UD, 1UF, 1UJ, 1UR, 1V1, 1VB, 1VD, 1VN, 205, 20F, 20L, 211, 213, 217, 219, 21J, 21V, 221, 22H, 22J, 22P, 22T, 22V, 239, 23H, 243, 24R, 24V, 255, 25D, 25T, 25V, 263, 26B, 26R, 26T, 271, 279, 27F, 27L, 27P, 285, 287, 28T, 293, 295, 29B, 29F, 29L, 2A3, 2A9, 2AD, 2AF, 2AL, 2AP, 2AV, 2BB, 2BH, 2BN, 2C5, 2C9, 2CF, 2CR, 2D3, 2D9, 2DD, 2E7, 2EP, 2F3, 2FB, 2FF, 2FL, 2FN, 2FT, 2GJ, 2GV, 2H1, 2HH, 2HP, 2HT, 2I9, 2IN, 2J1, 2J3, 2J7, 2JF, 2JL, 2JR, 2JV, 2K1, 2K5, 2KB, 2KJ, 2KN, 2KP, 2KV, 2L9, 2LB, 2LL, 2LT, 2M1, 2MF, 2MP, 2N5, 2N7, 2ND, 2NH, 2NJ, 2O3, 2OH, 2OL, 2OR, 2P3, 2P9, 2PD, 2PV, 2Q7, 2QH, 2QN, 2QT, 2R5, 2RF, 2RR, 2S9, 2SD, 2SJ, 2SP, 2SR, 2TN, 2TP, 2U3, 2UB, 2UF, 2UT, 2V1, 2V9, 2VL, 2VR, 307, 30B, 30H, 315, 31F, 31H, 321, 32R, 32V, 331, 33D, 33J, 33N, 343, 349, 34H, 34L, 34T, 35J, 35L, 35P, 35R, 367, 373, 375, 37B, 37H, 37N, 37R, 381, 383, 38F, 38J, 38V, 391, 39B, 39D, 39T, 39V, 3AF, 3AL, 3B9, 3BP, 3C1, 3C5, 3C7, 3CB, 3CD, 3D3, 3DB, 3DN, 3DT, 3E7, 3E9, 3ED, 3EJ, 3EL, 3ER, 3F5, 3F7, 3FJ, 3FT, 3FV, 3G9, 3GN, 3GT, 3H1, 3H7, 3HF, 3HL, 3HR, 3IB, 3IN, 3IP, 3IT, 3JB, 3JH, 3JL, 3JT, 3K7, 3KF, 3KL, 3KR, 3LH, 3LN, 3LP, 3M3, 3MH, 3ML, 3MR, 3ND, 3NF, 3NP, 3O7, 3OB, 3OD, 3ON, 3P5, 3P9, 3PH, 3Q3, 3Q7, 3QD, 3QF, 3QJ, 3QP, 3QR, 3R7, 3RB, 3RV, 3SL, 3T1, 3T3, 3T7, 3TD, 3TJ, 3TL, 3TR, 3UH, 3UJ, 3UP, 3V9, 3VF, 3VR, 3VT, 403, 40F, 40V, 411, 415, 41B, 41P, 41T, 41V, 42H, 439, 43J, 43P, 43R, 445, 447, 44H, 44J, 44T, 453, 455, 45F, 45H, 45R, 461, 469, 477, 47H, 47J, 47T, 485, 48B, 48L, 497, 49D, 49P, 4A5, 4A7, 4AP, 4AV, 4B3, 4B9, 4BF, 4C1, 4C3, 4CD, 4CR, 4D1, 4D5, 4D7, 4DB, 4E3, 4E5, 4EH, 4EN, 4F7, 4FF, 4FL, 4FR, 4GD, 4GT, 4GV, 4H3, 4H9, 4HB, 4HH, 4HN, 4I1, 4I7, 4IJ, 4IV, 4JH, 4JJ, 4JP, 4JT, 4KF, 4KN, 4LF, 4LJ, 4LL, 4LP, 4LV, 4M1, 4MD, 4MH, 4MV, 4NT, 4O7, 4OD, 4OP, 4P7, 4PD, 4PN, 4Q3, 4Q5, 4Q9, 4QF, 4QN, 4QT, 4R7, 4R9, 4RD, 4RR, 4S1, 4S7, 4SB, 4SH, 4SJ, 4ST, 4SV, 4TF, 4TR, 4U3, 4UL, 4UP, 4UV, 4VB, 4VD, 4VJ, 4VP, 4VV, 50R, 511, 51F, 51J, 51R, 525, 52D, 52P, 53B, 53F, 53H, 53L, 54D, 54P, 54V, 551, 55H, 55N, 55T, 56B, 56L, 573, 577, 585, 58B, 58H, 58N, 58V, 595, 599, 59B, 59N, 59T, 5A1, 5A3, 5A9, 5AV, 5B5, 5B7, 5BB, 5BT, 5BV, 5C3, 5CF, 5CH, 5CN, 5CR, 5DL, 5DR, 5E1, 5E5, 5ED, 5EN, 5FN, 5G7, 5G9, 5GF, 5GJ, 5GL, 5GP, 5GR, 5H5, 5HJ, 5HP, 5HT, 5I5, 5IF, 5IL, 5J9, 5JD, 5JF, 5JL, 5KJ, 5KN, 5KV, 5L9, 5LF, 5LL, 5LT, 5M3, 5MF, 5MJ, 5MP, 5MR, 5N1, 5N5, 5NB, 5ND, 5NN, 5NP, 5O9, 5OF, 5P3, 5P7, 5PJ, 5Q1, 5QT, 5R3, 5RN, 5RR, 5SD, 5SL, 5SR, 5SV, 5T5, 5TJ, 5TP, 5TV, 5U9, 5UB, 5UL, 5V1, 5V9, 5VJ, 5VL, 5VV, 607, 60J, 60T, 61L, 61N, 61R, 623, 629, 62D, 62L, 637, 63H, 63N, 63T, 63V, 645, 64F, 64R, 64T, 657, 65D, 65J, 65P, 661, 667, 66H, 66N, 66P, 66V, 675, 67B, 67L, 67T, 68L, 68R, 69H, 69J, 6A5, 6A9, 6AH, 6AR, 6BP, 6C1, 6CJ, 6CN, 6CP, 6D3, 6D9, 6DB, 6DH, 6DL, 6E7, 6EF, 6ER, 6FD, 6FT, 6G3, 6G5, 6GH, 6GN, 6H1, 6H3, 6HD, 6HF, 6HL, 6HV, 6ID, 6IH, 6J9, 6JB, 6JR, 6JT, 6K7, 6K9, 6KJ, 6L7, 6LB, 6LD, 6LH, 6LP, 6M9, 6MF, 6ML, 6MN, 6N3, 6NJ, 6NR, 6NV, 6O5, 6P3, 6P5, 6PF, 6PH, 6PN, 6PR, 6Q1, 6Q7, 6QF, 6QL, 6QP, 6R5, 6RB, 6RJ, 6RV, 6S3, 6SH, 6ST, 6T7, 6TV, 6U5, 6UH, 6UN, 6UP, 6VF, 6VN, 709, 70J, 70P, 717, 71B, 71D, 71J, 71T, 725, 72B, 72F, 72L, 73J, 741, 74B, 74D, 74P, 753, 755, 75L, 75N, 769, 771, 77J, 77P, 789, 78R, 791, 793, 79L, 79P, 79V, 7A1, 7AB, 7AJ, 7AT, 7B3, 7B9, 7BH, 7BL, 7BR, 7BT, 7C7, 7C9, 7CL, 7CP, 7CV, 7D5, 7D7, 7DJ, 7DN, 7E5, 7EN, 7ER, 7F1, 7FL, 7FP, 7G1, 7G7, 7GB, 7GJ, 7GN, 7H5, 7HB, 7HF, 7HT, 7I9, 7ID, 7IF, 7JD, 7JH, 7K9, 7KF, 7KL, 7L1, 7LD, 7LR, 7M1, 7M5, 7M7, 7MB, 7MT, 7N3, 7NF, 7NN, 7NT, 7O1, 7OD, 7OF, 7OR, 7PP, 7Q9, 7QB, 7QH, 7R7, ...
33	14, 18, 1A, 1E, 1K, 1Q, 1S, 21, 25, 27, 2D, 2H, 2N, 2V, 32, 34, 38, 3A, 3E, 3S, 3W, 45, 47, 4H, 4J, 4P, 4V, 52, 58, 5E, 5G, 5Q, 5S, 5W, 61, 6D, 6P, 6T, 6V, 72, 78, 7A, 7K, 7Q, 7W, 85, 87, 8D, 8H, 8J, 8T, 9A, 9E, 9G, 9K, A1, A7, AH, AJ, AN, AT, B4, BA, BG, BK, BQ, C1, C5, CD, CN, CP, D2, D4, DA, DE, DK, DS, DW, E1, E5, EH, EP, ET, F4, F8, FE, FQ, FS, GD, GJ, GT, H2, H8, HA, HG, HQ, HW, I5, I7, ID, IJ, IN, IP, J4, JE, JG, JK, JQ, JW, K1, KD, KH, KN, KV, L8, LG, LQ, M1, M7, MD, MH, MP, MV, N2, NA, NE, NS, O5, OH, OJ, OT, OV, P2, P4, PE, PS, PW, Q1, Q5, QJ, QN, QP, QT, RG, RK, RS, S5, SD, SH, SN, ST, TA, TE, TK, TQ, U1, U7, UJ, UN, UT, UV, V8, VA, VG, VQ, VS, W5, W7, WD, WV, 102, 104, 108, 10E, 10K, 10S, 111, 117, 11T, 11V, 128, 12G, 12Q, 12W, 135, 13D, 13P, 13T, 142, 148, 14A, 14G, 14S, 155, 15N, 15P, 15T, 162, 164, 16A, 16E, 16G, 16K, 16W, 171, 177, 188, 18E, 18K, 18S, 19D, 19N, 1A4, 1A8, 1AA, 1AE, 1AK, 1AS, 1AW, 1B1, 1B7, 1BJ, 1BT, 1BV, 1C2, 1C4, 1C8, 1CE, 1CQ, 1D5, 1DD, 1DP, 1DV, 1E2, 1E8, 1EG, 1EK, 1ES, 1EW, 1FD, 1FH, 1FN, 1FP, 1FT, 1G2, 1G4, 1GA, 1GK, 1H7, 1HD, 1HH, 1HJ, 1IA, 1IE, 1IG, 1IQ, 1J5, 1J7, 1JH, 1JP, 1JV, 1K4, 1KA, 1KS, 1L1, 1L5, 1L7, 1LJ, 1LT, 1M8, 1MG, 1MW, 1ND, 1NJ, 1NN, 1NP, 1NT, 1NV, 1O8, 1OK, 1OQ, 1OW, 1PH, 1PJ, 1Q2, 1Q4, 1QQ, 1QW, 1R7, 1RD, 1RH, 1RJ, 1RN, 1RV, 1S4, 1SE, 1SG, 1SQ, 1T7, 1TH, 1TN, 1U2, 1U4, 1U8, 1UA, 1UK, 1UW, 1V1, 1VH, 1VJ, 1VP, 1VT, 1VV, 1W8, 1WG, 201, 20P, 20T, 212, 21A, 21Q, 21S, 21W, 227, 22N, 22P, 22T, 234, 23A, 23G, 23K, 23W, 241, 24N, 24T, 24V, 254, 258, 25E, 25S, 261, 265, 267, 26D, 26H, 26N, 272, 278, 27E, 27S, 27W, 285, 28H, 28P, 28V, 292, 29S, 2AD, 2AN, 2AV, 2B2, 2B8, 2BA, 2BG, 2C5, 2CH, 2CJ, 2D2, 2DA, 2DE, 2DQ, 2E7, 2EH, 2EJ, 2EN, 2EV, 2F4, 2FA, 2FE, 2FG, 2FK, 2FQ, 2G1, 2G5, 2G7, 2GD, 2GN, 2GP, 2H2, 2HA, 2HE, 2HS, 2I5, 2IH, 2IJ, 2IP, 2IT, 2IV, 2JE, 2JS, 2JW, 2K5, 2KD, 2KJ, 2KN, 2L8, 2LG, 2LQ, 2LW, 2M5, 2MD, 2MN, 2N2, 2NG, 2NK, 2NQ, 2NW, 2O1, 2OT, 2OV, 2P8, 2PG, 2PK, 2Q1, 2Q5, 2QD, 2QP, 2QV, 2RA, 2RE, 2RK, 2S7, 2SH, 2SJ, 2T2, 2TS, 2TW, 2U1, 2UD, 2UJ, 2UN, 2V2, 2V8, 2VG, 2VK, 2VS, 2WH, 2WJ, 2WN, 2WP, 304, 30W, 311, 317, 31D, 31J, 31N, 31T, 31V, 32A, 32E, 32Q, 32S, 335, 337, 33N, 33P, 348, 34E, 351, 35H, 35P, 35T, 35V, 362, 364, 36Q, 371, 37D, 37J, 37T, 37V, 382, 388, 38A, 38G, 38Q, 38S, 397, 39H, 39J, 39T, 3AA, 3AG, 3AK, 3AQ, 3B1, 3B7, 3BD, 3BT, 3C8, 3CA, 3CE, 3CS, 3D1, 3D5, 3DD, 3DN, 3DV, 3E4, 3EA, 3EW, 3F5, 3F7, 3FH, 3FV, 3G2, 3G8, 3GQ, 3GS, 3H5, 3HJ, 3HN, 3HP, 3I2, 3IG, 3IK, 3IS, 3JD, 3JH, 3JN, 3JP, 3JT, 3K2, 3K4, 3KG, 3KK, 3L7, 3LT, 3M8, 3MA, 3ME, 3MK, 3MQ, 3MS, 3N1, 3NN, 3NP, 3NV, 3OE, 3OK, 3OW, 3P1, 3P7, 3PJ, 3Q2, 3Q4, 3Q8, 3QE, 3QS, 3QW, 3R1, 3RJ, 3SA, 3SK, 3SQ, 3SS, 3T5, 3T7, 3TH, 3TJ, 3TT, 3U2, 3U4, 3UE, 3UG, 3UQ, 3UW, 3V7, 3W4, 3WE, 3WG, 3WQ, 401, 407, 40H, 412, 418, 41K, 41W, 421, 42J, 42P, 42T, 432, 438, 43Q, 43S, 445, 44J, 44P, 44T, 44V, 452, 45Q, 45S, 467, 46D, 46T, 474, 47A, 47G, 481, 48H, 48J, 48N, 48T, 48V, 494, 49A, 49K, 49Q, 4A5, 4AH, 4B2, 4B4, 4BA, 4BE, 4BW, 4C7, 4CV, 4D2, 4D4, 4D8, 4DE, 4DG, 4DS, 4DW, 4ED, 4FA, 4FK, 4FQ, 4G5, 4GJ, 4GP, 4H2, 4HE, 4HG, 4HK, 4HQ, 4I1, 4I7, 4IH, 4IJ, 4IN, 4J4, 4JA, 4JG, 4JK, 4JQ, 4JS, 4K5, 4K7, 4KN, 4L2, 4LA, 4LS, 4LW, 4M5, 4MH, 4MJ, 4MP, 4MV, 4N4, 4NW, 4O5, 4OJ, 4ON, 4OV, 4P8, 4PG, 4PS, 4QD, 4QH, 4QJ, 4QN, 4RE, 4RQ, 4RW, 4S1, 4SH, 4SN, 4ST, 4TA, 4TK, 4U1, 4U5, 4V2, 4V8, 4VE, 4VK, 4VS, 4W1, 4W5, 4W7, 4WJ, 4WP, 4WT, 4WV, 504, 50Q, 50W, 511, 515, 51N, 51P, 51T, 528, 52A, 52G, 52K, 53D, 53J, 53P, 53T, 544, 54E, 55D, 55T, 55V, 564, 568, 56A, 56E, 56G, 56Q, 577, 57D, 57H, 57P, 582, 588, 58S, 58W, 591, 597, 5A4, 5A8, 5AG, 5AQ, 5AW, 5B5, 5BD, 5BJ, 5BV, 5C2, 5C8, 5CA, 5CG, 5CK, 5CQ, 5CS, 5D5, 5D7, 5DN, 5DT, 5EG, 5EK, 5EW, 5FD, 5G8, 5GE, 5H1, 5H5, 5HN, 5HV, 5I4, 5I8, 5IE, 5IS, 5J1, 5J7, 5JH, 5JJ, 5JT, 5K8, 5KG, 5KQ, 5KS, 5L5, 5LD, 5LP, 5M2, 5MQ, 5MS, 5MW, 5N7, 5ND, 5NH, 5NP, 5OA, 5OK, 5OQ, 5OW, 5P1, 5P7, 5PH, 5PT, 5PV, 5Q8, 5QE, 5QK, 5QQ, 5R1, 5R7, 5RH, 5RN, 5RP, 5RV, 5S4, 5SA, 5SK, 5SS, 5TJ, 5TP, 5UE, 5UG, 5V1, 5V5, 5VD, 5VN, 5WK, 5WS, 60D, 60H, 60J, 60T, 612, 614, 61A, 61E, 61W, 627, 62J, 634, 63K, 63Q, 63S, 647, 64D, 64N, 64P, 652, 654, 65A, 65K, 661, 665, 66T, 66V, 67E, 67G, 67Q, 67S, 685, 68P, 68T, 68V, 692, 69A, 69Q, 69W, 6A5, 6A7, 6AJ, 6B2, 6BA, 6BE, 6BK, 6CH, 6CJ, 6CT, 6CV, 6D4, 6D8, 6DE, 6DK, 6DS, 6E1, 6E5, 6EH, 6EN, 6EV, 6FA, 6FE, 6FS, 6G7, 6GH, 6H8, 6HE, 6HQ, 6HW, 6I1, 6IN, 6IV, 6JG, 6JQ, 6JW, 6KD, 6KH, 6KJ, 6KP, 6L2, 6LA, 6LG, 6LK, 6LQ, 6MN, 6N4, 6NE, 6NG, 6NS, 6O5, 6O7, 6ON, 6OP, 6PA, 6Q1, 6QJ, 6QP, 6R8, 6RQ, 6RW, 6S1, 6SJ, 6SN, 6ST, 6SV, 6T8, 6TG, 6TQ, 6TW, 6U5, 6UD, 6UH, 6UN, 6UP, 6V2, 6V4, 6VG, 6VK, 6VQ, 6VW, 6W1, 6WD, 6WH, 6WV, 70G, 70K, 70Q, 71D, 71H, 71P, 71V, 722, 72A, 72E, 72S, 731, 735, 73J, 73V, 742, 744, 751, 755, 75T, 762, 768, 76K, 76W, 77D, 77J, 77N, 77P, 77T, 78E, 78K, 78W, 797, 79D, 79H, 79T, 79V, 7AA, 7B7, 7BN, 7BP, 7BV, 7CK, ...
34	13, 17, 19, 1D, 1J, 1P, 1R, 1X, 23, 25, 2B, 2F, 2L, 2T, 2X, 31, 35, 37, 3B, 3P, 3T, 41, 43, 4D, 4F, 4L, 4R, 4V, 53, 59, 5B, 5L, 5N, 5R, 5T, 67, 6J, 6N, 6P, 6T, 71, 73, 7D, 7J, 7P, 7V, 7X, 85, 89, 8B, 8L, 91, 95, 97, 9B, 9P, 9V, A7, A9, AD, AJ, AR, AX, B5, B9, BF, BN, BR, C1, CB, CD, CN, CP, CV, D1, D7, DF, DJ, DL, DP, E3, EB, EF, EN, ER, EX, FB, FD, FV, G3, GD, GJ, GP, GR, GX, H9, HF, HL, HN, HT, I1, I5, I7, IJ, IT, IV, J1, J7, JD, JF, JR, JV, K3, KB, KL, KT, L5, LD, LJ, LP, LT, M3, M9, MD, ML, MP, N5, NF, NR, NT, O5, O7, OB, OD, ON, P3, P7, P9, PD, PR, PV, PX, Q3, QN, QR, R1, RB, RJ, RN, RT, S1, SF, SJ, SP, SV, T5, TB, TN, TR, TX, U1, UB, UD, UJ, UT, UV, V7, V9, VF, VX, W3, W5, W9, WF, WL, WT, X1, X7, XT, XV, 107, 10F, 10P, 10V, 113, 11B, 11N, 11R, 11X, 125, 127, 12D, 12P, 131, 13J, 13L, 13P, 13V, 13X, 145, 149, 14B, 14F, 14R, 14T, 151, 161, 167, 16D, 16L, 175, 17F, 17T, 17X, 181, 185, 18B, 18J, 18N, 18P, 18V, 199, 19J, 19L, 19P, 19R, 19V, 1A3, 1AF, 1AR, 1B1, 1BD, 1BJ, 1BN, 1BT, 1C3, 1C7, 1CF, 1CJ, 1CX, 1D3, 1D9, 1DB, 1DF, 1DL, 1DN, 1DT, 1E5, 1EP, 1EV, 1F1, 1F3, 1FR, 1FV, 1FX, 1G9, 1GL, 1GN, 1GX, 1H7, 1HD, 1HJ, 1HP, 1I9, 1IF, 1IJ, 1IL, 1IX, 1J9, 1JL, 1JT, 1KB, 1KP, 1KV, 1L1, 1L3, 1L7, 1L9, 1LJ, 1LV, 1M3, 1M9, 1MR, 1MT, 1NB, 1ND, 1O1, 1O7, 1OF, 1OL, 1OP, 1OR, 1OV, 1P5, 1PB, 1PL, 1PN, 1PX, 1QD, 1QN, 1QT, 1R7, 1R9, 1RD, 1RF, 1RP, 1S3, 1S5, 1SL, 1SN, 1ST, 1SX, 1T1, 1TB, 1TJ, 1U3, 1UR, 1UV, 1V3, 1VB, 1VR, 1VT, 1VX, 1W7, 1WN, 1WP, 1WT, 1X3, 1X9, 1XF, 1XJ, 1XV, 1XX, 20L, 20R, 20T, 211, 215, 21B, 21P, 21V, 221, 223, 229, 22D, 22J, 22V, 233, 239, 23N, 23R, 23X, 24B, 24J, 24P, 24T, 25L, 265, 26F, 26N, 26R, 26X, 271, 277, 27T, 287, 289, 28P, 28X, 293, 29F, 29T, 2A5, 2A7, 2AB, 2AJ, 2AP, 2AV, 2B1, 2B3, 2B7, 2BD, 2BL, 2BP, 2BR, 2BX, 2C9, 2CB, 2CL, 2CT, 2CX, 2DD, 2DN, 2E1, 2E3, 2E9, 2ED, 2EF, 2EV, 2FB, 2FF, 2FL, 2FT, 2G1, 2G5, 2GN, 2GV, 2H7, 2HD, 2HJ, 2HR, 2I3, 2IF, 2IT, 2IX, 2J5, 2JB, 2JD, 2K7, 2K9, 2KJ, 2KR, 2KV, 2LB, 2LF, 2LN, 2M1, 2M7, 2MJ, 2MN, 2MT, 2NF, 2NP, 2NR, 2O9, 2P1, 2P5, 2P7, 2PJ, 2PP, 2PT, 2Q7, 2QD, 2QL, 2QP, 2QX, 2RL, 2RN, 2RR, 2RT, 2S7, 2T1, 2T3, 2T9, 2TF, 2TL, 2TP, 2TV, 2TX, 2UB, 2UF, 2UR, 2UT, 2V5, 2V7, 2VN, 2VP, 2W7, 2WD, 2WX, 2XF, 2XN, 2XR, 2XT, 2XX, 301, 30N, 30V, 319, 31F, 31P, 31R, 31V, 323, 325, 32B, 32L, 32N, 331, 33B, 33D, 33N, 343, 349, 34D, 34J, 34R, 34X, 355, 35L, 35X, 361, 365, 36J, 36P, 36T, 373, 37D, 37L, 37R, 37X, 38L, 38R, 38T, 395, 39J, 39N, 39T, 3AD, 3AF, 3AP, 3B5, 3B9, 3BB, 3BL, 3C1, 3C5, 3CD, 3CV, 3D1, 3D7, 3D9, 3DD, 3DJ, 3DL, 3DX, 3E3, 3EN, 3FB, 3FN, 3FP, 3FT, 3G1, 3G7, 3G9, 3GF, 3H3, 3H5, 3HB, 3HR, 3HX, 3IB, 3ID, 3IJ, 3IV, 3JD, 3JF, 3JJ, 3JP, 3K5, 3K9, 3KB, 3KT, 3LJ, 3LT, 3M1, 3M3, 3MD, 3MF, 3MP, 3MR, 3N3, 3N9, 3NB, 3NL, 3NN, 3NX, 3O5, 3OD, 3P9, 3PJ, 3PL, 3PV, 3Q5, 3QB, 3QL, 3R5, 3RB, 3RN, 3S1, 3S3, 3SL, 3SR, 3SV, 3T3, 3T9, 3TR, 3TT, 3U5, 3UJ, 3UP, 3UT, 3UV, 3V1, 3VP, 3VR, 3W5, 3WB, 3WR, 3X1, 3X7, 3XD, 3XV, 40D, 40F, 40J, 40P, 40R, 40X, 415, 41F, 41L, 41X, 42B, 42T, 42V, 433, 437, 43P, 43X, 44N, 44R, 44T, 44X, 455, 457, 45J, 45N, 463, 46X, 479, 47F, 47R, 487, 48D, 48N, 491, 493, 497, 49D, 49L, 49R, 4A3, 4A5, 4A9, 4AN, 4AT, 4B1, 4B5, 4BB, 4BD, 4BN, 4BP, 4C7, 4CJ, 4CR, 4DB, 4DF, 4DL, 4DX, 4E1, 4E7, 4ED, 4EJ, 4FD, 4FJ, 4FX, 4G3, 4GB, 4GL, 4GT, 4H7, 4HP, 4HT, 4HV, 4I1, 4IP, 4J3, 4J9, 4JB, 4JR, 4JX, 4K5, 4KJ, 4KT, 4L9, 4LD, 4M9, 4MF, 4ML, 4MR, 4N1, 4N7, 4NB, 4ND, 4NP, 4NV, 4O1, 4O3, 4O9, 4OV, 4P3, 4P5, 4P9, 4PR, 4PT, 4PX, 4QB, 4QD, 4QJ, 4QN, 4RF, 4RL, 4RR, 4RV, 4S5, 4SF, 4TD, 4TT, 4TV, 4U3, 4U7, 4U9, 4UD, 4UF, 4UP, 4V5, 4VB, 4VF, 4VN, 4VX, 4W5, 4WP, 4WT, 4WV, 4X3, 4XX, 503, 50B, 50L, 50R, 50X, 517, 51D, 51P, 51T, 521, 523, 529, 52D, 52J, 52L, 52V, 52X, 53F, 53L, 547, 54B, 54N, 553, 55V, 563, 56N, 56R, 57B, 57J, 57P, 57T, 581, 58F, 58L, 58R, 593, 595, 59F, 59R, 5A1, 5AB, 5AD, 5AN, 5AV, 5B9, 5BJ, 5C9, 5CB, 5CF, 5CN, 5CT, 5CX, 5D7, 5DP, 5E1, 5E7, 5ED, 5EF, 5EL, 5EV, 5F9, 5FB, 5FL, 5FR, 5FX, 5G5, 5GD, 5GJ, 5GT, 5H1, 5H3, 5H9, 5HF, 5HL, 5HV, 5I5, 5IT, 5J1, 5JN, 5JP, 5K9, 5KD, 5KL, 5KV, 5LR, 5M1, 5MJ, 5MN, 5MP, 5N1, 5N7, 5N9, 5NF, 5NJ, 5O3, 5OB, 5ON, 5P7, 5PN, 5PT, 5PV, 5Q9, 5QF, 5QP, 5QR, 5R3, 5R5, 5RB, 5RL, 5S1, 5S5, 5ST, 5SV, 5TD, 5TF, 5TP, 5TR, 5U3, 5UN, 5UR, 5UT, 5UX, 5V7, 5VN, 5VT, 5W1, 5W3, 5WF, 5WV, 5X5, 5X9, 5XF, 60B, 60D, 60N, 60P, 60V, 611, 617, 61D, 61L, 61R, 61V, 629, 62F, 62N, 631, 635, 63J, 63V, 647, 64V, 653, 65F, 65L, 65N, 66B, 66J, 673, 67D, 67J, 67X, 683, 685, 68B, 68L, 68T, 691, 695, 69B, 6A7, 6AL, 6AV, 6AX, 6BB, 6BL, 6BN, 6C5, 6C7, 6CP, 6DF, 6DX, 6E5, 6EL, 6F5, 6FB, 6FD, 6FV, 6G1, 6G7, 6G9, 6GJ, 6GR, 6H3, 6H9, 6HF, 6HN, 6HR, 6HX, 6I1, 6IB, 6ID, 6IP, 6IT, 6J1, 6J7, 6J9, 6JL, 6JP, 6K5, 6KN, 6KR, 6KX, 6LJ, 6LN, 6LV, 6M3, 6M7, 6MF, 6MJ, 6MX, 6N5, 6N9, 6NN, 6O1, 6O5, 6O7, 6P3, 6P7, 6PV, 6Q3, 6Q9, 6QL, 6QX, 6RD, 6RJ, 6RN, 6RP, 6RT, 6SD, 6SJ, 6SV, 6T5, 6TB, 6TF, 6TR, 6TT, 6U7, 6V3, 6VJ, 6VL, 6VR, 6WF, ...
35	12, 16, 18, 1C, 1I, 1O, 1Q, 1W, 21, 23, 29, 2D, 2J, 2R, 2V, 2X, 32, 34, 38, 3M, 3Q, 3W, 3Y, 49, 4B, 4H, 4N, 4R, 4X, 54, 56, 5G, 5I, 5M, 5O, 61, 6D, 6H, 6J, 6N, 6T, 6V, 76, 7C, 7I, 7O, 7Q, 7W, 81, 83, 8D, 8R, 8V, 8X, 92, 9G, 9M, 9W, 9Y, A3, A9, AH, AN, AT, AX, B4, BC, BG, BO, BY, C1, CB, CD, CJ, CN, CT, D2, D6, D8, DC, DO, DW, E1, E9, ED, EJ, EV, EX, FG, FM, FW, G3, G9, GB, GH, GR, GX, H4, H6, HC, HI, HM, HO, I1, IB, ID, IH, IN, IT, IV, J8, JC, JI, JQ, K1, K9, KJ, KR, KX, L4, L8, LG, LM, LQ, LY, M3, MH, MR, N4, N6, NG, NI, NM, NO, NY, OD, OH, OJ, ON, P2, P6, P8, PC, PW, Q1, Q9, QJ, QR, QV, R2, R8, RM, RQ, RW, S3, SB, SH, ST, SX, T4, T6, TG, TI, TO, TY, U1, UB, UD, UJ, V2, V6, V8, VC, VI, VO, VW, W3, W9, WV, WX, X8, XG, XQ, XW, Y3, YB, YN, YR, YX, 104, 106, 10C, 10O, 10Y, 11H, 11J, 11N, 11T, 11V, 122, 126, 128, 12C, 12O, 12Q, 12W, 13V, 142, 148, 14G, 14Y, 159, 15N, 15R, 15T, 15X, 164, 16C, 16G, 16I, 16O, 171, 17B, 17D, 17H, 17J, 17N, 17T, 186, 18I, 18Q, 193, 199, 19D, 19J, 19R, 19V, 1A4, 1A8, 1AM, 1AQ, 1AW, 1AY, 1B3, 1B9, 1BB, 1BH, 1BR, 1CC, 1CI, 1CM, 1CO, 1DD, 1DH, 1DJ, 1DT, 1E6, 1E8, 1EI, 1EQ, 1EW, 1F3, 1F9, 1FR, 1FX, 1G2, 1G4, 1GG, 1GQ, 1H3, 1HB, 1HR, 1I6, 1IC, 1IG, 1II, 1IM, 1IO, 1IY, 1JB, 1JH, 1JN, 1K6, 1K8, 1KO, 1KQ, 1LD, 1LJ, 1LR, 1LX, 1M2, 1M4, 1M8, 1MG, 1MM, 1MW, 1MY, 1N9, 1NN, 1NX, 1O4, 1OG, 1OI, 1OM, 1OO, 1OY, 1PB, 1PD, 1PT, 1PV, 1Q2, 1Q6, 1Q8, 1QI, 1QQ, 1R9, 1RX, 1S2, 1S8, 1SG, 1SW, 1SY, 1T3, 1TB, 1TR, 1TT, 1TX, 1U6, 1UC, 1UI, 1UM, 1UY, 1V1, 1VN, 1VT, 1VV, 1W2, 1W6, 1WC, 1WQ, 1WW, 1X1, 1X3, 1X9, 1XD, 1XJ, 1XV, 1Y2, 1Y8, 1YM, 1YQ, 1YW, 209, 20H, 20N, 20R, 21I, 221, 22B, 22J, 22N, 22T, 22V, 232, 23O, 241, 243, 24J, 24R, 24V, 258, 25M, 25W, 25Y, 263, 26B, 26H, 26N, 26R, 26T, 26X, 274, 27C, 27G, 27I, 27O, 27Y, 281, 28B, 28J, 28N, 292, 29C, 29O, 29Q, 29W, 2A1, 2A3, 2AJ, 2AX, 2B2, 2B8, 2BG, 2BM, 2BQ, 2C9, 2CH, 2CR, 2CX, 2D4, 2DC, 2DM, 2DY, 2ED, 2EH, 2EN, 2ET, 2EV, 2FO, 2FQ, 2G1, 2G9, 2GD, 2GR, 2GV, 2H4, 2HG, 2HM, 2HY, 2I3, 2I9, 2IT, 2J4, 2J6, 2JM, 2KD, 2KH, 2KJ, 2KV, 2L2, 2L6, 2LI, 2LO, 2LW, 2M1, 2M9, 2MV, 2MX, 2N2, 2N4, 2NG, 2O9, 2OB, 2OH, 2ON, 2OT, 2OX, 2P4, 2P6, 2PI, 2PM, 2PY, 2Q1, 2QB, 2QD, 2QT, 2QV, 2RC, 2RI, 2S3, 2SJ, 2SR, 2SV, 2SX, 2T2, 2T4, 2TQ, 2TY, 2UB, 2UH, 2UR, 2UT, 2UX, 2V4, 2V6, 2VC, 2VM, 2VO, 2W1, 2WB, 2WD, 2WN, 2X2, 2X8, 2XC, 2XI, 2XQ, 2XW, 2Y3, 2YJ, 2YV, 2YX, 302, 30G, 30M, 30Q, 30Y, 319, 31H, 31N, 31T, 32G, 32M, 32O, 32Y, 33D, 33H, 33N, 346, 348, 34I, 34W, 351, 353, 35D, 35R, 35V, 364, 36M, 36Q, 36W, 36Y, 373, 379, 37B, 37N, 37R, 38C, 38Y, 39B, 39D, 39H, 39N, 39T, 39V, 3A2, 3AO, 3AQ, 3AW, 3BD, 3BJ, 3BV, 3BX, 3C4, 3CG, 3CW, 3CY, 3D3, 3D9, 3DN, 3DR, 3DT, 3EC, 3F1, 3FB, 3FH, 3FJ, 3FT, 3FV, 3G6, 3G8, 3GI, 3GO, 3GQ, 3H1, 3H3, 3HD, 3HJ, 3HR, 3IM, 3IW, 3IY, 3J9, 3JH, 3JN, 3JX, 3KG, 3KM, 3KY, 3LB, 3LD, 3LV, 3M2, 3M6, 3MC, 3MI, 3N1, 3N3, 3ND, 3NR, 3NX, 3O2, 3O4, 3O8, 3OW, 3OY, 3PB, 3PH, 3PX, 3Q6, 3QC, 3QI, 3R1, 3RH, 3RJ, 3RN, 3RT, 3RV, 3S2, 3S8, 3SI, 3SO, 3T1, 3TD, 3TV, 3TX, 3U4, 3U8, 3UQ, 3UY, 3VN, 3VR, 3VT, 3VX, 3W4, 3W6, 3WI, 3WM, 3X1, 3XV, 3Y6, 3YC, 3YO, 403, 409, 40J, 40V, 40X, 412, 418, 41G, 41M, 41W, 41Y, 423, 42H, 42N, 42T, 42X, 434, 436, 43G, 43I, 43Y, 44B, 44J, 452, 456, 45C, 45O, 45Q, 45W, 463, 469, 472, 478, 47M, 47Q, 47Y, 489, 48H, 48T, 49C, 49G, 49I, 49M, 4AB, 4AN, 4AT, 4AV, 4BC, 4BI, 4BO, 4C3, 4CD, 4CR, 4CV, 4DQ, 4DW, 4E3, 4E9, 4EH, 4EN, 4ER, 4ET, 4F6, 4FC, 4FG, 4FI, 4FO, 4GB, 4GH, 4GJ, 4GN, 4H6, 4H8, 4HC, 4HO, 4HQ, 4HW, 4I1, 4IR, 4IX, 4J4, 4J8, 4JG, 4JQ, 4KN, 4L4, 4L6, 4LC, 4LG, 4LI, 4LM, 4LO, 4LY, 4MD, 4MJ, 4MN, 4MV, 4N6, 4NC, 4NW, 4O1, 4O3, 4O9, 4P4, 4P8, 4PG, 4PQ, 4PW, 4Q3, 4QB, 4QH, 4QT, 4QX, 4R4, 4R6, 4RC, 4RG, 4RM, 4RO, 4RY, 4S1, 4SH, 4SN, 4T8, 4TC, 4TO, 4U3, 4UV, 4V2, 4VM, 4VQ, 4W9, 4WH, 4WN, 4WR, 4WX, 4XC, 4XI, 4XO, 4XY, 4Y1, 4YB, 4YN, 4YV, 506, 508, 50I, 50Q, 513, 51D, 522, 524, 528, 52G, 52M, 52Q, 52Y, 53H, 53R, 53X, 544, 546, 54C, 54M, 54Y, 551, 55B, 55H, 55N, 55T, 562, 568, 56I, 56O, 56Q, 56W, 573, 579, 57J, 57R, 58G, 58M, 599, 59B, 59T, 59X, 5A6, 5AG, 5BB, 5BJ, 5C2, 5C6, 5C8, 5CI, 5CO, 5CQ, 5CW, 5D1, 5DJ, 5DR, 5E4, 5EM, 5F3, 5F9, 5FB, 5FN, 5FT, 5G4, 5G6, 5GG, 5GI, 5GO, 5GY, 5HD, 5HH, 5I6, 5I8, 5IO, 5IQ, 5J1, 5J3, 5JD, 5JX, 5K2, 5K4, 5K8, 5KG, 5KW, 5L3, 5L9, 5LB, 5LN, 5M4, 5MC, 5MG, 5MM, 5NH, 5NJ, 5NT, 5NV, 5O2, 5O6, 5OC, 5OI, 5OQ, 5OW, 5P1, 5PD, 5PJ, 5PR, 5Q4, 5Q8, 5QM, 5QY, 5R9, 5RX, 5S4, 5SG, 5SM, 5SO, 5TB, 5TJ, 5U2, 5UC, 5UI, 5UW, 5V1, 5V3, 5V9, 5VJ, 5VR, 5VX, 5W2, 5W8, 5X3, 5XH, 5XR, 5XT, 5Y6, 5YG, 5YI, 5YY, 601, 60J, 618, 61Q, 61W, 62D, 62V, 632, 634, 63M, 63Q, 63W, 63Y, 649, 64H, 64R, 64X, 654, 65C, 65G, 65M, 65O, 65Y, 661, 66D, 66H, 66N, 66T, 66V, 678, 67C, 67Q, 689, 68D, 68J, 694, 698, 69G, 69M, 69Q, 69Y, 6A3, 6AH, 6AN, 6AR, 6B6, 6BI, 6BM, 6BO, 6CJ, 6CN, 6DC, 6DI, 6DO, 6E1, 6ED, 6ER, 6EX, 6F2, 6F4, 6F8, 6FQ, 6FW, 6G9, 6GH, 6GN, 6GR, 6H4, 6H6, 6HI, 6ID, 6IT, 6IV, 6J2, 6JO, ...
36	11, 15, 17, 1B, 1H, 1N, 1P, 1V, 1Z, 21, 27, 2B, 2H, 2P, 2T, 2V, 2Z, 31, 35, 3J, 3N, 3T, 3V, 45, 47, 4D, 4J, 4N, 4T, 4Z, 51, 5B, 5D, 5H, 5J, 5V, 67, 6B, 6D, 6H, 6N, 6P, 6Z, 75, 7B, 7H, 7J, 7P, 7T, 7V, 85, 8J, 8N, 8P, 8T, 97, 9D, 9N, 9P, 9T, 9Z, A7, AD, AJ, AN, AT, B1, B5, BD, BN, BP, BZ, C1, C7, CB, CH, CP, CT, CV, CZ, DB, DJ, DN, DV, DZ, E5, EH, EJ, F1, F7, FH, FN, FT, FV, G1, GB, GH, GN, GP, GV, H1, H5, H7, HJ, HT, HV, HZ, I5, IB, ID, IP, IT, IZ, J7, JH, JP, JZ, K7, KD, KJ, KN, KV, L1, L5, LD, LH, LV, M5, MH, MJ, MT, MV, MZ, N1, NB, NP, NT, NV, NZ, OD, OH, OJ, ON, P7, PB, PJ, PT, Q1, Q5, QB, QH, QV, QZ, R5, RB, RJ, RP, S1, S5, SB, SD, SN, SP, SV, T5, T7, TH, TJ, TP, U7, UB, UD, UH, UN, UT, V1, V7, VD, VZ, W1, WB, WJ, WT, WZ, X5, XD, XP, XT, XZ, Y5, Y7, YD, YP, YZ, ZH, ZJ, ZN, ZT, ZV, 101, 105, 107, 10B, 10N, 10P, 10V, 11T, 11Z, 125, 12D, 12V, 135, 13J, 13N, 13P, 13T, 13Z, 147, 14B, 14D, 14J, 14V, 155, 157, 15B, 15D, 15H, 15N, 15Z, 16B, 16J, 16V, 171, 175, 17B, 17J, 17N, 17V, 17Z, 18D, 18H, 18N, 18P, 18T, 18Z, 191, 197, 19H, 1A1, 1A7, 1AB, 1AD, 1B1, 1B5, 1B7, 1BH, 1BT, 1BV, 1C5, 1CD, 1CJ, 1CP, 1CV, 1DD, 1DJ, 1DN, 1DP, 1E1, 1EB, 1EN, 1EV, 1FB, 1FP, 1FV, 1FZ, 1G1, 1G5, 1G7, 1GH, 1GT, 1GZ, 1H5, 1HN, 1HP, 1I5, 1I7, 1IT, 1IZ, 1J7, 1JD, 1JH, 1JJ, 1JN, 1JV, 1K1, 1KB, 1KD, 1KN, 1L1, 1LB, 1LH, 1LT, 1LV, 1LZ, 1M1, 1MB, 1MN, 1MP, 1N5, 1N7, 1ND, 1NH, 1NJ, 1NT, 1O1, 1OJ, 1P7, 1PB, 1PH, 1PP, 1Q5, 1Q7, 1QB, 1QJ, 1QZ, 1R1, 1R5, 1RD, 1RJ, 1RP, 1RT, 1S5, 1S7, 1ST, 1SZ, 1T1, 1T7, 1TB, 1TH, 1TV, 1U1, 1U5, 1U7, 1UD, 1UH, 1UN, 1UZ, 1V5, 1VB, 1VP, 1VT, 1VZ, 1WB, 1WJ, 1WP, 1WT, 1XJ, 1Y1, 1YB, 1YJ, 1YN, 1YT, 1YV, 1Z1, 1ZN, 1ZZ, 201, 20H, 20P, 20T, 215, 21J, 21T, 21V, 21Z, 227, 22D, 22J, 22N, 22P, 22T, 22Z, 237, 23B, 23D, 23J, 23T, 23V, 245, 24D, 24H, 24V, 255, 25H, 25J, 25P, 25T, 25V, 26B, 26P, 26T, 26Z, 277, 27D, 27H, 27Z, 287, 28H, 28N, 28T, 291, 29B, 29N, 2A1, 2A5, 2AB, 2AH, 2AJ, 2BB, 2BD, 2BN, 2BV, 2BZ, 2CD, 2CH, 2CP, 2D1, 2D7, 2DJ, 2DN, 2DT, 2ED, 2EN, 2EP, 2F5, 2FV, 2FZ, 2G1, 2GD, 2GJ, 2GN, 2GZ, 2H5, 2HD, 2HH, 2HP, 2IB, 2ID, 2IH, 2IJ, 2IV, 2JN, 2JP, 2JV, 2K1, 2K7, 2KB, 2KH, 2KJ, 2KV, 2KZ, 2LB, 2LD, 2LN, 2LP, 2M5, 2M7, 2MN, 2MT, 2ND, 2NT, 2O1, 2O5, 2O7, 2OB, 2OD, 2OZ, 2P7, 2PJ, 2PP, 2PZ, 2Q1, 2Q5, 2QB, 2QD, 2QJ, 2QT, 2QV, 2R7, 2RH, 2RJ, 2RT, 2S7, 2SD, 2SH, 2SN, 2SV, 2T1, 2T7, 2TN, 2TZ, 2U1, 2U5, 2UJ, 2UP, 2UT, 2V1, 2VB, 2VJ, 2VP, 2VV, 2WH, 2WN, 2WP, 2WZ, 2XD, 2XH, 2XN, 2Y5, 2Y7, 2YH, 2YV, 2YZ, 2Z1, 2ZB, 2ZP, 2ZT, 301, 30J, 30N, 30T, 30V, 30Z, 315, 317, 31J, 31N, 327, 32T, 335, 337, 33B, 33H, 33N, 33P, 33V, 34H, 34J, 34P, 355, 35B, 35N, 35P, 35V, 367, 36N, 36P, 36T, 36Z, 37D, 37H, 37J, 381, 38P, 38Z, 395, 397, 39H, 39J, 39T, 39V, 3A5, 3AB, 3AD, 3AN, 3AP, 3AZ, 3B5, 3BD, 3C7, 3CH, 3CJ, 3CT, 3D1, 3D7, 3DH, 3DZ, 3E5, 3EH, 3ET, 3EV, 3FD, 3FJ, 3FN, 3FT, 3FZ, 3GH, 3GJ, 3GT, 3H7, 3HD, 3HH, 3HJ, 3HN, 3IB, 3ID, 3IP, 3IV, 3JB, 3JJ, 3JP, 3JV, 3KD, 3KT, 3KV, 3KZ, 3L5, 3L7, 3LD, 3LJ, 3LT, 3LZ, 3MB, 3MN, 3N5, 3N7, 3ND, 3NH, 3NZ, 3O7, 3OV, 3OZ, 3P1, 3P5, 3PB, 3PD, 3PP, 3PT, 3Q7, 3R1, 3RB, 3RH, 3RT, 3S7, 3SD, 3SN, 3SZ, 3T1, 3T5, 3TB, 3TJ, 3TP, 3TZ, 3U1, 3U5, 3UJ, 3UP, 3UV, 3UZ, 3V5, 3V7, 3VH, 3VJ, 3VZ, 3WB, 3WJ, 3X1, 3X5, 3XB, 3XN, 3XP, 3XV, 3Y1, 3Y7, 3YZ, 3Z5, 3ZJ, 3ZN, 3ZV, 405, 40D, 40P, 417, 41B, 41D, 41H, 425, 42H, 42N, 42P, 435, 43B, 43H, 43V, 445, 44J, 44N, 45H, 45N, 45T, 45Z, 467, 46D, 46H, 46J, 46V, 471, 475, 477, 47D, 47Z, 485, 487, 48B, 48T, 48V, 48Z, 49B, 49D, 49J, 49N, 4AD, 4AJ, 4AP, 4AT, 4B1, 4BB, 4C7, 4CN, 4CP, 4CV, 4CZ, 4D1, 4D5, 4D7, 4DH, 4DV, 4E1, 4E5, 4ED, 4EN, 4ET, 4FD, 4FH, 4FJ, 4FP, 4GJ, 4GN, 4GV, 4H5, 4HB, 4HH, 4HP, 4HV, 4I7, 4IB, 4IH, 4IJ, 4IP, 4IT, 4IZ, 4J1, 4JB, 4JD, 4JT, 4JZ, 4KJ, 4KN, 4KZ, 4LD, 4M5, 4MB, 4MV, 4MZ, 4NH, 4NP, 4NV, 4NZ, 4O5, 4OJ, 4OP, 4OV, 4P5, 4P7, 4PH, 4PT, 4Q1, 4QB, 4QD, 4QN, 4QV, 4R7, 4RH, 4S5, 4S7, 4SB, 4SJ, 4SP, 4ST, 4T1, 4TJ, 4TT, 4TZ, 4U5, 4U7, 4UD, 4UN, 4UZ, 4V1, 4VB, 4VH, 4VN, 4VT, 4W1, 4W7, 4WH, 4WN, 4WP, 4WV, 4X1, 4X7, 4XH, 4XP, 4YD, 4YJ, 4Z5, 4Z7, 4ZP, 4ZT, 501, 50B, 515, 51D, 51V, 51Z, 521, 52B, 52H, 52J, 52P, 52T, 53B, 53J, 53V, 54D, 54T, 54Z, 551, 55D, 55J, 55T, 55V, 565, 567, 56D, 56N, 571, 575, 57T, 57V, 58B, 58D, 58N, 58P, 58Z, 59J, 59N, 59P, 59T, 5A1, 5AH, 5AN, 5AT, 5AV, 5B7, 5BN, 5BV, 5BZ, 5C5, 5CZ, 5D1, 5DB, 5DD, 5DJ, 5DN, 5DT, 5DZ, 5E7, 5ED, 5EH, 5ET, 5EZ, 5F7, 5FJ, 5FN, 5G1, 5GD, 5GN, 5HB, 5HH, 5HT, 5HZ, 5I1, 5IN, 5IV, 5JD, 5JN, 5JT, 5K7, 5KB, 5KD, 5KJ, 5KT, 5L1, 5L7, 5LB, 5LH, 5MB, 5MP, 5MZ, 5N1, 5ND, 5NN, 5NP, 5O5, 5O7, 5OP, 5PD, 5PV, 5Q1, 5QH, 5QZ, 5R5, 5R7, 5RP, 5RT, 5RZ, 5S1, 5SB, 5SJ, 5ST, 5SZ, 5T5, 5TD, 5TH, 5TN, 5TP, 5TZ, 5U1, 5UD, 5UH, 5UN, 5UT, 5UV, 5V7, 5VB, 5VP, 5W7, 5WB, 5WH, 5X1, 5X5, 5XD, 5XJ, 5XN, 5XV, 5XZ, 5YD, 5YJ, 5YN, 5Z1, 5ZD, 5ZH, 5ZJ, 60D, 60H, 615, 61B, 61H, 61T, 625, 62J, 62P, 62T, 62V, 62Z, 63H, 63N, 63Z, 647, 64D, 64H, 64T, 64V, 657, 661, 66H, 66J, 66P, 67B, ...

The OEIS sequences for the base b representations of the prime numbers (of course, also includes the primes ≤ b) are: https://oeis.org/A004676 (b = 2), https://oeis.org/A001363 (b = 3), https://oeis.org/A004678 (b = 4), https://oeis.org/A004679 (b = 5), https://oeis.org/A004680 (b = 6), https://oeis.org/A004681 (b = 7), https://oeis.org/A004682 (b = 8), https://oeis.org/A004683 (b = 9), https://oeis.org/A000040 (b = 10), there are no OEIS sequences for b > 10 since OEIS disallows the alpha digits and only allows decimal characters (i.e. the 10 Arabic numerals (https://en.wikipedia.org/wiki/Arabic_numerals, https://mathworld.wolfram.com/ArabicNumeral.html)), see https://oeis.org/wiki/Disallowed_sequences#Sequences_of_rational_integers_with_digits_other_than_0_to_9, but there is a short OEIS sequence https://oeis.org/A004684 for b = 11, which stops exactly before the first term with a nondecimal character (i.e. the prime 43, which is written "3A" in base b = 11) and stops with the prime 41, which is written "38" in base b = 11.

Some bases 2 ≤ b ≤ 36 are notable: (fortunately, all of these bases except b = 36 are solved, except the primality proving for the probable prime 57₆₂₆₆₈ in base b = 11 and the probable primes C5₂₃₇₅₅C, 80₃₂₀₁₇111, 95₁₉₇₄₂₀, A3₅₉₂₁₉₇A in base b = 13)

b = 2: binary (https://en.wikipedia.org/wiki/Binary_number, https://www.rieselprime.de/ziki/Binary, https://mathworld.wolfram.com/Binary.html, https://oeis.org/A007088)
b = 3: ternary (https://en.wikipedia.org/wiki/Ternary_numeral_system, https://mathworld.wolfram.com/Ternary.html, https://oeis.org/A007089)
b = 4: quaternary (https://en.wikipedia.org/wiki/Quaternary_numeral_system, https://mathworld.wolfram.com/Quaternary.html, https://oeis.org/A007090)
b = 5: quinary (https://en.wikipedia.org/wiki/Quinary, https://oeis.org/A007091)
b = 6: senary (https://en.wikipedia.org/wiki/Senary, https://oeis.org/A007092)
b = 7: septenary (https://web.archive.org/web/20141218113439/https://en.wikipedia.org/wiki/Septenary, https://fr.wikipedia.org/wiki/Syst%C3%A8me_sept%C3%A9naire (in Franch), https://ja.wikipedia.org/wiki/%E4%B8%83%E9%80%B2%E6%B3%95 (in Japanese), https://oeis.org/A007093)
b = 8: octal (https://en.wikipedia.org/wiki/Octal, https://mathworld.wolfram.com/Octal.html, https://oeis.org/A007094)
b = 9: nonary (https://web.archive.org/web/20141218113440/https://en.wikipedia.org/wiki/Nonary, https://fr.wikipedia.org/wiki/Syst%C3%A8me_nonaire (in Franch), https://ja.wikipedia.org/wiki/%E4%B9%9D%E9%80%B2%E6%B3%95 (in Japanese), https://oeis.org/A007095)
b = 10: decimal (the standard system) (https://en.wikipedia.org/wiki/Decimal, https://www.rieselprime.de/ziki/Decimal, https://mathworld.wolfram.com/Decimal.html, https://oeis.org/A001477)
b = 11: undecimal (https://web.archive.org/web/20141218113441/https://en.wikipedia.org/wiki/Base_11, https://fr.wikipedia.org/wiki/Syst%C3%A8me_und%C3%A9cimal (in Franch), https://ja.wikipedia.org/wiki/%E5%8D%81%E4%B8%80%E9%80%B2%E6%B3%95 (in Japanese), https://oeis.org/A055649)
b = 12: duodecimal (https://en.wikipedia.org/wiki/Duodecimal, https://mathworld.wolfram.com/Duodecimal.html, https://oeis.org/A049872)
b = 13: tridecimal (https://web.archive.org/web/20141218113443/https://en.wikipedia.org/wiki/Base_13, https://fr.wikipedia.org/wiki/Syst%C3%A8me_trid%C3%A9cimal (in Franch), https://ja.wikipedia.org/wiki/%E5%8D%81%E4%B8%89%E9%80%B2%E6%B3%95 (in Japanese), https://oeis.org/A055648)
b = 14: tetradecimal (https://web.archive.org/web/20141218113444/https://en.wikipedia.org/wiki/Tetradecimal, https://oeis.org/A055647)
b = 15: pentadecimal (https://web.archive.org/web/20141218113445/https://en.wikipedia.org/wiki/Pentadecimal, https://ja.wikipedia.org/wiki/%E5%8D%81%E4%BA%94%E9%80%B2%E6%B3%95 (in Japanese), https://oeis.org/A055646)
b = 16: hexadecimal (https://en.wikipedia.org/wiki/Hexadecimal, https://mathworld.wolfram.com/Hexadecimal.html, https://oeis.org/A055645)
b = 20: vigesimal (https://en.wikipedia.org/wiki/Vigesimal, https://mathworld.wolfram.com/Vigesimal.html, https://oeis.org/A055644)
b = 24: quadravigesimal (https://ja.wikipedia.org/wiki/%E4%BA%8C%E5%8D%81%E5%9B%9B%E9%80%B2%E6%B3%95 (in Japanese))
b = 36: hexatrigesimal (https://web.archive.org/web/20150320103231/https://en.wikipedia.org/wiki/Base_36, https://fr.wikipedia.org/wiki/Syst%C3%A8me_%C3%A0_base_36 (in Franch), https://ja.wikipedia.org/wiki/%E4%B8%89%E5%8D%81%E5%85%AD%E9%80%B2%E6%B3%95 (in Japanese))

addition	multiplication
subtraction	division
0	1
negation	reciprocal
the set {1}	the set of the prime numbers
less than	divides
1 + 1 + 1 + ... + 1 with n 1's	the prime factorization of n (e.g. 360 = 2³ × 3² × 5)

(k + 2) × (1 − (w×z+h+j−q)² − ((g×k+2×g+k+1)×(h+j)+h−z)² − (2×n+p+q+z−e)² − (16×(k+1)³×(k+2)×(n+1)²+1−f²)² − (e³×(e+2)×(a+1)²+1−o²)² − ((a²−1)×y²+1−x²)² − (16×r²×y⁴×(a²−1)+1−u²)² − (((a+u²×(u²−a))²−1)×(n+4×d×y)²+1−(x+c×u)²)² - (n+l+v−y)² − ((a²−1)×l²+1−m²)² − (a×i+k+1−l−i)² − (p+l×(a−n−1)+b×(2×a×n+2×a−n²−2×n−2)−m)² − (q+y×(a−p−1)+s×(2×a×p+2×a−p²−2×p−2)−x)² − (z+p×l×(a−p)+t×(2×a×p−p²−1)−p×m)²)

Besides, the record for the lowest degree of such a polynomial is 4 (with 58 variables), and the record for the fewest variables of such a polynomial is 10 (with degree about 1.6×10⁴⁵)

subsequence ordering	divisibility ordering
the "prime numbers > b" digit strings" in base b	the integers > 1
the set of the minimal elements of the "prime numbers > b" digit strings" in base b under the subsequence ordering (which is exactly the target of this project)	the set of the minimal elements of the integers > 1 under the divisibility ordering (which is exactly the set of the prime numbers)
no common subsequence with length > 1	coprime (no common divisor > 1) (https://en.wikipedia.org/wiki/Coprime_integers, https://t5k.org/glossary/xpage/RelativelyPrime.html, https://www.rieselprime.de/ziki/Coprime, https://mathworld.wolfram.com/RelativelyPrime.html, http://www.numericana.com/answer/primes.htm#coprime)
proper subsequence with length > 1	proper factor (https://en.wikipedia.org/wiki/Proper_factor, https://mathworld.wolfram.com/ProperFactor.html, https://mathworld.wolfram.com/ProperDivisor.html) > 1
longest common subsequence (https://en.wikipedia.org/wiki/Longest_common_subsequence)	greatest common divisor (https://en.wikipedia.org/wiki/Greatest_common_divisor, https://mathworld.wolfram.com/GreatestCommonDivisor.html, http://www.numericana.com/answer/numbers.htm#gcd)
shortest common supersequence (https://en.wikipedia.org/wiki/Shortest_common_supersequence)	least common multiple (https://en.wikipedia.org/wiki/Least_common_multiple, https://mathworld.wolfram.com/LeastCommonMultiple.html, http://www.numericana.com/answer/numbers.htm#lcm)
pairwise incomparable strings (no string is a subsequence of another string)	pairwise incomparable numbers (no number divides another number)

(warning: the data in the Table 5 in https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf) has many errors, e.g. for base b = 53, k = 4 is remaining at n = 2500000 and k = 8 has first prime at n = 227183 (which should not be found when the article was written), but the table only lists {1816, 1838, 1862, 1892} for the "ks not yet eliminated" data for base b = 53, and for base b = 48, the correct "ks not yet eliminated" data (at n = 100000) is {29, 36, 62, 153, 561, 622, 701, 937, 1077, 1086, 1114, 1121, 1168}, but the table wrongly lists {29, 36, 62, 153, 422, 1174}, missing many k and wrongly includes k = 422 and k = 1174 (which are trivial k since gcd(k+1,48−1) for these two k are not 1), and for base b = 55, the correct "ks not yet eliminated" data (at n = 100000) is {36, 778, 2274}, but the table lists {1980, 2274}, this article allow k with partial or full algebraic factors to become the conjectures, thus the conjecture k for b = 55 in this article is 2500 instead of 4416 (which is the conjecture k for b = 55 in Conjectures 'R Us), and thus k = 3940 becomes a k > conjectured k and thus not considered, but the table still misses k = 36 and k = 778, and only includes k = 1980 = 36×55 (unlike Conjectures 'R Us, this article does not exclude the ks which are multiples of base (b) and where k+1 is composite))

(in fact, for any k (not only the k < b), there is always an r such that "the minimal prime in base b^r" covers "finding the smallest prime of the form k×bⁿ+1 and k×bⁿ−1 and bⁿ+k and bⁿ−k (or proving that such prime does not exist)" (also, no matter what is the lower bound (https://en.wikipedia.org/wiki/Lower_bound, https://mathworld.wolfram.com/LowerBound.html) of allowed n, the lower bound of allowed n need not to be 1 or 2), while this is not true for the original minimal prime problem (of course, there are bases b > 36 (which are not in this project) mentioned))

However, including the base (b) itself results in automatic elimination of all possible extension numbers with "0 after 1" from the set (when the base is prime, if the base is composite, then there is no difference to include the base (b) itself or not), which is quite restrictive (since when the base is prime, then the base (b) itself is the only prime ending with 0, i.e. having trailing zero (https://en.wikipedia.org/wiki/Trailing_zero), since in any base, all numbers ending with 0 (i.e. having trailing zero) are divisible by the base (b), thus cannot be prime unless it is equal the base (b), i.e. "10" in base b, note that the numbers cannot have leading zero (https://en.wikipedia.org/wiki/Leading_zero), since typically this is not the way we write numbers (in any base), thus for all primes in our sets (i.e. all primes > base (b)), all zero digits must be "between" other digits). (for the reference of this, see https://www.mersenneforum.org/showpost.php?p=531632&postcount=7)

Besides, this problem is better than the original minimal prime problem since this problem is regardless whether 1 is considered as prime or not, i.e. no matter 1 is considered as prime or not prime (https://t5k.org/notes/faq/one.html, https://primefan.tripod.com/Prime1ProCon.html, https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_24.pdf), http://www.numericana.com/answer/numbers.htm#one), the sets in this problem are the same, while the sets in the original minimal prime problem are different, e.g. in base 10, if 1 is considered as prime, then the set in the original minimal prime problem is {1, 2, 3, 5, 7, 89, 409, 449, 499, 6469, 6949, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049}, while if 1 is not considered as prime, then the set in the original minimal prime problem is {2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049}, however, in base 10, the set in this problem is always {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}, no matter 1 is considered as prime or not prime.

The third reason for excluding the single-digit primes is that they are trivial (https://en.wikipedia.org/wiki/Triviality_(mathematics), https://mathworld.wolfram.com/Trivial.html), like that Conjectures 'R Us Sierpinski/Riesel conjectures base b requires exponent n ≥ 1 for these primes (see https://www.mersenneforum.org/showpost.php?p=447679&postcount=27), n = 0 is not acceptable to avoid the trivial primes (e.g. 2×bⁿ+1, 4×bⁿ+1, 6×bⁿ+1, 10×bⁿ+1, 12×bⁿ+1, 16×bⁿ+1, 3×bⁿ−1, 4×bⁿ−1, 6×bⁿ−1, 8×bⁿ−1, 12×bⁿ−1, 14×bⁿ−1, ... cannot be quickly eliminated with n = 0, or the conjectures become much easier and uninteresting), for the same reason, this minimal prime puzzle requires ≥ b (i.e. ≥ 2 digits) for these primes, single-digit primes are not acceptable to avoid the trivial primes (e.g. families containing digit 2, 3, 5, 7, B, D, H, J, N, T, V, ... cannot be quickly eliminated with the single-digit prime, or the conjectures become much easier and uninteresting).

The fourth reason for excluding the primes ≤ b is that starting with b+1 makes the formula of the number of possible (first digit,last digit) combo of a minimal prime in base b more simple and smooth number (https://en.wikipedia.org/wiki/Smooth_number, https://mathworld.wolfram.com/SmoothNumber.html, https://oeis.org/A003586, https://oeis.org/A051037, https://oeis.org/A002473, https://oeis.org/A051038, https://oeis.org/A080197, https://oeis.org/A080681, https://oeis.org/A080682, https://oeis.org/A080683) (i.e. the greatest prime factor (http://mathworld.wolfram.com/GreatestPrimeFactor.html, https://oeis.org/A006530) is small), it is (b−1)×eulerphi(b) (https://oeis.org/A062955), where eulerphi is Euler's totient function (https://en.wikipedia.org/wiki/Euler%27s_totient_function, https://t5k.org/glossary/xpage/EulersPhi.html, https://mathworld.wolfram.com/TotientFunction.html, http://www.numericana.com/answer/modular.htm#phi, http://www.javascripter.net/math/calculators/eulertotientfunction.htm, https://oeis.org/A000010), since b−1 is the number of possible first digit (except 0, all digits can be first digit), and eulerphi(b) is the number of possible last digit (only digits coprime to b can be last digit), by rule of product (https://en.wikipedia.org/wiki/Rule_of_product), there are (b−1)×eulerphi(b) possible (first digit,last digit) combo, and if start with b, then when b is prime, there is an additional possible (first digit,last digit) combo: (1,0), and hence the formula will be (b−1)×eulerphi(b)+1 if b is prime, or (b−1)×eulerphi(b) if b is composite (the fully formula will be (b−1)×eulerphi(b)+isprime(b) or (b−1)×eulerphi(b)+floor((b−eulerphi(b)) / (b−1))), which is more complex, and if start with 1 (i.e. the original minimal prime problem), the formula is much more complex, since the prime digits (i.e. the single-digit primes) should be excluded, and (for such prime > b) the first digit has b−1−primepi(b) choices, and the last digit has eulerphi(b)−primepi(b)+omega(b) (https://oeis.org/A048864) choices, by the rule of product (https://en.wikipedia.org/wiki/Rule_of_product), there are (b−1−primepi(b))×(eulerphi(b)−primepi(b)+omega(b)) choices of the (first digit,last digit) combo (if for such prime ≥ b instead of > b, then the formula will be (b−1−primepi(b))×(eulerphi(b)−primepi(b)+omega(b))+1 if b is prime, or (b−1−primepi(b))×(eulerphi(b)−primepi(b)+omega(b)) if b is composite), which is much more complex, (also, the possible (first digit,last digit) combo for a prime > b in base b are exactly the (first digit,last digit) combos which there are infinitely many primes have, while this is not true when the requiring is prime ≥ b or prime ≥ 2 instead of prime > b, since this will contain the prime factors of b, which are not coprime to b and hence there is only this prime (and not infinitely many primes) have this (first digit,last digit) combo) thus the main problem in this project (i.e. the minimal prime (start with b+1) problem) is much better than the original minimal prime problem.

(in the section above, isprime(n) is the characteristic function (https://en.wikipedia.org/wiki/Indicator_function, https://mathworld.wolfram.com/CharacteristicFunction.html) of primes (i.e. 1 if n is prime, else 0) (https://oeis.org/A010051), floor is the floor function (https://en.wikipedia.org/wiki/Floor_function, https://t5k.org/glossary/xpage/FloorFunction.html, https://www.rieselprime.de/ziki/Floor_function, https://mathworld.wolfram.com/FloorFunction.html), primepi is the prime-counting function (https://en.wikipedia.org/wiki/Prime-counting_function, https://t5k.org/glossary/xpage/PrimeCountingFunction.html, https://mathworld.wolfram.com/PrimeCountingFunction.html, https://oeis.org/A000720, https://oeis.org/A006880, https://oeis.org/A007053, https://faculty.lynchburg.edu/~nicely/index.html, https://faculty.lynchburg.edu/~nicely/pi/pix_0000.htm, https://faculty.lynchburg.edu/~nicely/pi/pix_0001.htm, https://faculty.lynchburg.edu/~nicely/constell.zip, http://sweet.ua.pt/tos/primes.html, https://pzktupel.de/counting/PI_01.php, https://sweet.ua.pt/tos/bib/5.4.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_452.pdf), https://arxiv.org/pdf/1503.01839.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_453.pdf)), omega is the little prime omega function (https://en.wikipedia.org/wiki/Prime_omega_function, https://oeis.org/A001221))

The fifth reason (and the main reason) for excluding the primes ≤ b is that the possible last digits of a minimal prime in base b are exactly the last digits in base b such that there are infinitely many primes, by the Dirichlet's theorem (https://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions, https://t5k.org/glossary/xpage/DirichletsTheorem.html, https://mathworld.wolfram.com/DirichletsTheorem.html, http://www.numericana.com/answer/primes.htm#dirichlet), thus in this problem, we completely need not to consider the last digits which are not coprime (https://en.wikipedia.org/wiki/Coprime_integers, https://t5k.org/glossary/xpage/RelativelyPrime.html, https://www.rieselprime.de/ziki/Coprime, https://mathworld.wolfram.com/RelativelyPrime.html, http://www.numericana.com/answer/primes.htm#coprime) to b, while in the original minimal prime problem, this is false for the primes dividing b.

The sixth reason is that (heuristically) the more one-digit primes are contained in the set, the less primes have to be considered (since all numbers that contain one of these digits cannot be contained in the minimal set), thus one-digit primes will make this problem much easier and more uninteresting (and when single-digit primes are excluded, all base b digits may appear in large minimal primes in base b, e.g. when base b = 19 searched to length 100000, all base 19 digits except 2 and 8 still appear in the list of the 23 unsolved families), the reason is the same as why the article https://nntdm.net/papers/nntdm-25/NNTDM-25-1-036-047.pdf deals only with the minimal sets for eulerphi(n) + k (where eulerphi is the Euler's totient function (https://en.wikipedia.org/wiki/Euler%27s_totient_function, https://t5k.org/glossary/xpage/EulersPhi.html, https://mathworld.wolfram.com/TotientFunction.html, http://www.numericana.com/answer/modular.htm#phi, http://www.javascripter.net/math/calculators/eulertotientfunction.htm, https://oeis.org/A000010)) with k ≤ 5, since for k = 6, eulerphi(n) + 6 contains only two one-digit numbers (the author of that article wishes that the problem become easier, while I wish that this problem become much harder, thus I exclude the single-digit primes).

The seventh reason is that in this problem, for the linear families x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b) in base b which we search, y can be any base b digit except 1 (y can be 1 if and only if base b has no repunit primes), while in the original minimal prime problem, y cannot be any prime digit (and y can be 1 if and only if base b has no repunit primes).

The eighth reason is that for the numbers in the sets in this problem, the greatest common divisor (https://en.wikipedia.org/wiki/Greatest_common_divisor, https://mathworld.wolfram.com/GreatestCommonDivisor.html, http://www.numericana.com/answer/numbers.htm#gcd) of the digits of these numbers must be 1, and the last digit must be coprime (https://en.wikipedia.org/wiki/Coprime_integers, https://t5k.org/glossary/xpage/RelativelyPrime.html, https://www.rieselprime.de/ziki/Coprime, https://mathworld.wolfram.com/RelativelyPrime.html, http://www.numericana.com/answer/primes.htm#coprime) to the base (b), since a prime p (when written in base b) have both "greatest common divisor (https://en.wikipedia.org/wiki/Greatest_common_divisor, https://mathworld.wolfram.com/GreatestCommonDivisor.html, http://www.numericana.com/answer/numbers.htm#gcd) of the digits of these numbers is 1" and "last digit is coprime (https://en.wikipedia.org/wiki/Coprime_integers, https://t5k.org/glossary/xpage/RelativelyPrime.html, https://www.rieselprime.de/ziki/Coprime, https://mathworld.wolfram.com/RelativelyPrime.html, http://www.numericana.com/answer/primes.htm#coprime) to the base (b)" if and only if p > b, thus it is not true for the numbers in the sets in the original minimal prime problem.

In fact, I create this problem because I think that the single-digit primes are trivial (https://en.wikipedia.org/wiki/Triviality_(mathematics), https://mathworld.wolfram.com/Trivial.html) (like strictly non-palindromic number (https://en.wikipedia.org/wiki/Strictly_non-palindromic_number, http://www.mathpages.com/home/kmath359.htm, https://oeis.org/A016038), single-digit numbers are trivially palindromic (https://en.wikipedia.org/wiki/Palindromic_number, https://en.wikipedia.org/wiki/Palindromic_prime, https://t5k.org/glossary/xpage/PalindromicPrime.html, https://mathworld.wolfram.com/PalindromicNumber.html, https://mathworld.wolfram.com/PalindromicPrime.html, https://www.numbersaplenty.com/set/palindromic_number/, https://t5k.org/top20/page.php?id=53, https://t5k.org/primes/search.php?Comment=Palindrome&OnList=all&Number=1000000&Style=HTML, https://oeis.org/A002113, https://oeis.org/A002385), thus to test whether a number n is strictly non-palindromic, we do not consider the bases b > n, since in these bases, n is a single-digit number, thus trivially palindromic, note that all strictly non-palindromic numbers > 6 are primes), thus I do not count them. (There is someone else who also exclude the single-digit primes, but his research is about substring (https://en.wikipedia.org/wiki/Substring) instead of subsequence, see https://www.mersenneforum.org/showpost.php?p=235383&postcount=42, subsequences can contain consecutive elements which were not consecutive in the original sequence, a subsequence which consists of a consecutive run of elements from the original sequence, such as 234 from 123456, is a substring, substring is a refinement of the subsequence, subsequence is a generalization of substring, substring must be subsequence, but subsequence may not be substring, 514 is a subsequence of 352148, but not a substring of 352148, see the list below of the comparation of "subsequence" and "substring")

subsequence	substring
https://oeis.org/A071062	https://oeis.org/A033274
https://oeis.org/A130448	https://oeis.org/A238334
https://oeis.org/A039995	https://oeis.org/A039997
https://oeis.org/A039994	https://oeis.org/A039996
https://oeis.org/A094535	https://oeis.org/A093301
https://oeis.org/A350508	https://oeis.org/A038103
https://oeis.org/A354113	https://oeis.org/A354114
https://t5k.org/glossary/xpage/MinimalPrime.html	https://www.mersenneforum.org/showpost.php?p=235098&postcount=5
longest common subsequence (https://en.wikipedia.org/wiki/Longest_common_subsequence)	longest common substring (https://en.wikipedia.org/wiki/Longest_common_substring)

The longest common subsequence problem (https://en.wikipedia.org/wiki/Longest_common_subsequence) and the longest common substring problem (https://en.wikipedia.org/wiki/Longest_common_substring) are two hard problems on strings (https://en.wikipedia.org/wiki/String_(computer_science), https://mathworld.wolfram.com/String.html), the former is NP-complete (https://en.wikipedia.org/wiki/NP-complete, https://mathworld.wolfram.com/NP-CompleteProblem.html) and NP-hard (https://en.wikipedia.org/wiki/NP-hard, https://mathworld.wolfram.com/NP-HardProblem.html), while the latter is not.

(we do not research substring in this project, because for substring ordering, "the set of the minimal elements of the base 10 representations of the prime numbers > 10" are very likely to be infinite (and thus almost unsolvable), since all primes of the form 1{0}3 (i.e. https://oeis.org/A159352, for the exponents see https://oeis.org/A049054, also see https://stdkmd.net/nrr/1/10003.htm) or 3{0}1 (i.e. https://oeis.org/A259866, for the exponents see https://oeis.org/A056807, also see https://stdkmd.net/nrr/3/30001.htm) are minimal elements of the base 10 representations of the prime numbers > 10 under the substring ordering, and there is likely infinitely many primes of the form 1{0}3 and infinitely many primes of the form 3{0}1, see https://web.archive.org/web/20100628035147/http://www.math.niu.edu/~rusin/known-math/98/exp_primes and https://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Mathematics/2023_September_25#Are_there_infinitely_many_primes_of_the_form_1000%E2%80%A60007,_333%E2%80%A63331,_7111%E2%80%A6111,_or_3444%E2%80%A64447_in_base_10? and https://arxiv.org/pdf/2307.07894.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_203.pdf) and https://web.archive.org/web/20231002020455/http://yves.gallot.pagesperso-orange.fr/papers/weight.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_216.pdf) and https://www.mersenneforum.org/showpost.php?p=564786&postcount=3 and https://www.mersenneforum.org/showpost.php?p=461665&postcount=7 and https://www.mersenneforum.org/showpost.php?p=354505&postcount=5 and https://www.mersenneforum.org/showpost.php?p=344985&postcount=293 and https://www.mersenneforum.org/showpost.php?p=625978&postcount=1027, https://www.primegrid.com/forum_thread.php?id=5093&nowrap=true#66471 and https://www.primegrid.com/forum_thread.php?id=4935&nowrap=true#63813)

(of course, you can also try to extend the main problem in this project to bases 2 ≤ b ≤ 50 or 2 ≤ b ≤ 100 (I cannot imagine the effort needed for bases b around 500 or 1000, even if strong probable primes are allowed) (in fact, the GMP (https://gmplib.org/, https://en.wikipedia.org/wiki/GNU_Multiple_Precision_Arithmetic_Library) program supports bases 2 ≤ b ≤ 50, but I only ran for bases 2 ≤ b ≤ 36) (suggestion to use the character ":" to saparate the digits for bases b > 36 (and just use decimal to write the digits), just like https://baseconvert.com/ and https://baseconvert.com/high-precision), but warning: these problems will be extremely hard (especially the bases b such that (b−1)×eulerphi(b) (https://oeis.org/A062955) is larger)!!! The difficulty of base b is roughly (https://en.wikipedia.org/wiki/Asymptotic_analysis, https://t5k.org/glossary/xpage/AsymptoticallyEqual.html, https://mathworld.wolfram.com/Asymptotic.html) e^{γ×(b−1)×eulerphi(b)}, and e^{γ×(b−1)×eulerphi(b)} is an exponential sequence (https://en.wikipedia.org/wiki/Exponential_growth, https://mathworld.wolfram.com/ExponentialGrowth.html) for (b−1)×eulerphi(b) (https://oeis.org/A062955))

The value (b−1)×eulerphi(b) (https://oeis.org/A062955) is the number of possible (first digit,last digit) (also called (initial digit,final digit)) combos (ordered pair (https://en.wikipedia.org/wiki/Ordered_pair, https://mathworld.wolfram.com/OrderedPair.html)) of a minimal prime in base b (these (first digit,last digit) combos are also all possible (first digit,last digit) combos (ordered pair (https://en.wikipedia.org/wiki/Ordered_pair, https://mathworld.wolfram.com/OrderedPair.html)) of a prime > b in base b) (these (first digit,last digit) combos for decimal (base b = 10) are listed in OEIS sequence https://oeis.org/A085820, except the single-digit numbers (i.e. 1, 3, 7, 9) (i.e. first digit is 0, and hence the number has leading zeros (https://en.wikipedia.org/wiki/Leading_zero)) in this sequence, the smallest primes with these (first digit,last digit) combos listed in https://oeis.org/A085820 (except the single-digit numbers (i.e. 1, 3, 7, 9) in this sequence) are (italic for primes which are not minimal primes): 11, 13, 17, 19, 211, 23, 227, 29, 31, 313, 37, 349, 41, 43, 47, 409, 521, 53, 547, 59, 61, 613, 67, 619, 71, 73, 727, 79, 811, 83, 827, 89, 911, 953, 97, 919, and the smallest minimal primes with these (first digit,last digit) combos listed in https://oeis.org/A085820 (except the single-digit numbers (i.e. 1, 3, 7, 9) in this sequence) are (0 if no such minimal prime exists): 11, 13, 17, 19, 251, 23, 227, 29, 31, 0, 37, 349, 41, 43, 47, 409, 521, 53, 557, 59, 61, 0, 67, 6469, 71, 73, 727, 79, 821, 83, 827, 89, 991, 0, 97, 9049) (they are only all "possible" (first digit,last digit) combos (ordered pair (https://en.wikipedia.org/wiki/Ordered_pair, https://mathworld.wolfram.com/OrderedPair.html)) of a minimal prime in base b, this does not mean that they must be realized, e.g. there are no minimal primes with (first digit,last digit) = (2,2) in base b = 3, and there are no minimal primes with (first digit,last digit) = (3,3), (6,3), or (9,3) in base b = 10, but it is conjectured that there are only finitely many such examples (i.e. for every sufficiently large (https://en.wikipedia.org/wiki/Sufficiently_large, https://mathworld.wolfram.com/SufficientlyLarge.html) base b, for any given such (first digit,last digit) combo, there is a minimal prime with this (first digit,last digit) combo), also, it is conjectured that all such examples have gcd(first digit, last digit, b−1) > 1 (i.e. there is a prime number which divides first digit, last digit, and b−1 simultaneously), since the first digit has b−1 choices (all digits except 0 can be the first digit), and the last digit has eulerphi(b) choices (only digits coprime (https://en.wikipedia.org/wiki/Coprime_integers, https://t5k.org/glossary/xpage/RelativelyPrime.html, https://www.rieselprime.de/ziki/Coprime, https://mathworld.wolfram.com/RelativelyPrime.html, http://www.numericana.com/answer/primes.htm#coprime) to b (i.e. the digits in the reduced residue system (https://en.wikipedia.org/wiki/Reduced_residue_system, https://mathworld.wolfram.com/ReducedResidueSystem.html) mod b) can be the last digit), by the rule of product (https://en.wikipedia.org/wiki/Rule_of_product), there are (b−1)×eulerphi(b) choices of the (first digit,last digit) combo.

b	number of possible first digits of a prime > b in base b (equal b−1, since all digits except 0 can be the first digit)	number of possible last digits of a prime > b in base b (equal eulerphi(b), since only digits coprime to b (i.e. the digits in the reduced residue system mod b) can be the last digit)	number of possible (first digit,last digit) combos of a prime > b in base b (equal (b−1)×eulerphi(b), by the rule of product), also the relative hardness for the "minimal prime problem" in base b
2	1	1	1
3	2	2	4
4	3	2	6
5	4	4	16
6	5	2	10
7	6	6	36
8	7	4	28
9	8	6	48
10	9	4	36
11	10	10	100
12	11	4	44
13	12	12	144
14	13	6	78
15	14	8	112
16	15	8	120
17	16	16	256
18	17	6	102
19	18	18	324
20	19	8	152
21	20	12	240
22	21	10	210
23	22	22	484
24	23	8	184
25	24	20	480
26	25	12	300
27	26	18	468
28	27	12	324
29	28	28	784
30	29	8	232
31	30	30	900
32	31	16	496
33	32	20	640
34	33	16	528
35	34	24	816
36	35	12	420

(Note: Not all (first digit,last digit) combos must be realized for a minimal prime in base b, e.g. there are no minimal primes with (first digit,last digit) = (2,2) in base 3, and there are no minimal primes with (first digit,last digit) = (3,3), (6,3), or (9,3) in base 10)

The lengths of the minimal primes in base b (e.g. in decimal (base b = 10) the lengths of the 77 minimal primes are {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 8, 8, 8, 8, 8, 12, 31}, respectively, and in base b = 16 the lengths of the 2347 minimal (probable) primes are {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 25, 25, 25, 25, 25, 26, 26, 26, 27, 27, 27, 27, 29, 29, 29, 30, 30, 31, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38, 38, 38, 40, 40, 40, 41, 41, 42, 42, 44, 45, 45, 46, 47, 47, 49, 49, 49, 50, 50, 51, 54, 54, 56, 58, 60, 61, 62, 66, 67, 68, 73, 74, 79, 89, 101, 105, 105, 125, 130, 130, 132, 137, 146, 179, 186, 205, 210, 214, 220, 243, 249, 265, 265, 294, 307, 426, 547, 547, 796, 1053, 1066, 1519, 1717, 1965, 3545, 3703, 17806, 32235, 72787, 116139}, respectively) appear to follow the Zipf's law (https://en.wikipedia.org/wiki/Zipf%27s_law, https://mathworld.wolfram.com/ZipfsLaw.html) (which is similar to the Benford's law (https://en.wikipedia.org/wiki/Benford%27s_law, https://t5k.org/glossary/xpage/BenfordsLaw.html, https://mathworld.wolfram.com/BenfordsLaw.html, https://www.mathpages.com/home/kmath302/kmath302.htm, https://t5k.org/notes/faq/BenfordsLaw.html, https://www.ams.org/publications/journals/notices/201702/rnoti-p132.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_261.pdf)), for n ≥ 2, the number of n-digit minimal primes in base b is inversely proportional (https://en.wikipedia.org/wiki/Inversely_proportional, https://mathworld.wolfram.com/InverselyProportional.html) to n−1 (i.e. the expected value (https://en.wikipedia.org/wiki/Expected_value, https://mathworld.wolfram.com/ExpectationValue.html) is c/(n−1), where c is a fixed constant) (i.e. the graph of the points (x,y = the number of x-digit minimal primes in base b) in the xy-plane is near to the graph of y = c/(x−1) in the xy-plane for a fixed real number c), for any fixed base b, also, for n ≥ 1, the length of the nth largest minimal prime in base b is inversely proportional (https://en.wikipedia.org/wiki/Inversely_proportional, https://mathworld.wolfram.com/InverselyProportional.html) to n (i.e. the expected value (https://en.wikipedia.org/wiki/Expected_value, https://mathworld.wolfram.com/ExpectationValue.html) is c/n, where c is a fixed constant) (i.e. the graph of the points (x,y = the length of the xth largest minimal prime in base b) in the xy-plane is near to the graph of y = c/x in the xy-plane for a fixed real number c), for any fixed base b. (for more information of the Zipf's law and the Benford's law, see https://oeis.org/A008952 and https://oeis.org/A008963 and https://oeis.org/A060956 and https://oeis.org/A241299 and https://oeis.org/A244059 and https://oeis.org/A363746 and http://www.cut-the-knot.org/do_you_know/zipfLaw.shtml and https://www.fq.math.ca/Scanned/13-4/webb.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_281.pdf) and https://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_282.pdf) and https://arxiv.org/pdf/cond-mat/0412004.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_283.pdf))

We can use the sense of https://web.archive.org/web/20231002020455/http://yves.gallot.pagesperso-orange.fr/papers/weight.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_216.pdf) to say: (note that some of the left families may cover another left family, e.g. the base 19 left family 5{H}5 covers another base 19 left family 5{H}05, and if the smallest prime in family 5{H}5 in base 19 has length n, and the family 5{H}05 in base 19 has no prime with length ≤ n, then family 5{H}05 in base 19 can be removed from the unsolved families for base 19, however, if the smallest prime in family 5{H}5 in base 19 has length n, but the family 5{H}05 in base 19 is not tested to length n or more, then family 5{H}05 in base 19 should not be removed from the unsolved families for base 19, since a number in family 5{H}05 covers the prime in family 5{H}5 with length n if and only if the length of this number is ≥ n+1; besides, the base 19 left family FH0{H} covers another base 19 left family FHHH0{H}, and if the smallest prime in family FH0{H} in base 19 has length n, and the family FHHH0{H} in base 19 has no prime with length ≤ n+1, then family FHHH0{H} in base 19 can be removed from the unsolved families for base 19, however, if the smallest prime in family FH0{H} in base 19 has length n, but the family FHHH0{H} in base 19 is not tested to length n+1 or more, then family FHHH0{H} in base 19 should not be removed from the unsolved families for base 19, since a number in family FHHH0{H} covers the prime in family FH0{H} with length n if and only if the length of this number is ≥ n+2; besides, the base 21 left family {9}D covers another base 21 left family F{9}D, and if the smallest prime in family {9}D in base 21 has length n, and the family F{9}D in base 21 has no prime with length ≤ n, then family F{9}D in base 21 can be removed from the unsolved families for base 21, however, if the smallest prime in family {9}D in base 21 has length n, but the family F{9}D in base 21 is not tested to length n or more, then family F{9}D in base 21 should not be removed from the unsolved families for base 21, since a number in family F{9}D covers the prime in family {9}D with length n if and only if the length of this number is ≥ n+1 (if a family has no primes, then we say "the smallest prime in this family has length ∞ (https://en.wikipedia.org/wiki/Infinity, https://t5k.org/glossary/xpage/Infinite.html, https://mathworld.wolfram.com/Infinity.html) (instead of 0 or −1)", see http://gladhoboexpress.blogspot.com/2019/05/prime-sandwiches-made-with-one-derbread.html and http://chesswanks.com/seq/a306861.txt (for the OEIS sequence https://oeis.org/A306861) and http://chesswanks.com/seq/a269254.txt (for the OEIS sequence https://oeis.org/A269254) (since this is more convenient, e.g. the n of the smallest prime in the base 21 family 9_nD, this family has been searched to n = 100000 with no prime or probable prime found, we can use ">100000" for the n of the smallest prime in the base 21 family 9_nD (while for the n of the smallest prime in the base 13 family A3_nA, it is 592199), ">100000" includes infinity (since infinity is > 100000) but does not includes 0 or −1, it is still possible that there is no prime in the base 21 family 9_nD, although by the heuristic argument (https://en.wikipedia.org/wiki/Heuristic_argument, https://t5k.org/glossary/xpage/Heuristic.html, https://mathworld.wolfram.com/Heuristic.html, https://web.archive.org/web/20230911032453/https://www.utm.edu/staff/caldwell/preprints/Heuristics.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_112.pdf), https://arxiv.org/pdf/2103.04483.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_113.pdf)) above, this is very impossible, also "the smallest n ≥ 1 such that (a×bⁿ+c)/gcd(a+c,b−1) is prime" should be the infimum (https://en.wikipedia.org/wiki/Infimum, https://mathworld.wolfram.com/Infimum.html) of the set S of the numbers n ≥ 1 such that (a×bⁿ+c)/gcd(a+c,b−1) is prime, and if there is no n ≥ 1 such that (a×bⁿ+c)/gcd(a+c,b−1) is prime, then this set S is the empty set (https://en.wikipedia.org/wiki/Empty_set, https://mathworld.wolfram.com/EmptySet.html), and by the definition of "inf", the infimum of the empty set is ∞), ∞ is > any finite number, e.g. "the smallest n ≥ 1 such that k×2ⁿ+1 is prime" is ∞ for k = 78557, 157114, 271129, 271577, 314228, 322523, 327739, 482719, ..., while it is 31172165 for k = 10223 and 13018586 for k = 19249, another example is "the smallest n such that (bⁿ−1)/(b−1) is prime" is ∞ for b = 9, 25, 32, 49, 64, 81, 121, 125, 144, 169, 216, 225, 243, 289, 324, 343, 361, 441, 484, 529, 625, 729, 784, 841, 900, 961, 1000, ..., while it is 62903 for b = 691 and 41189 for b = 693))

e.g. for bases b = 23 and b = 25:

We have a 50% chance of solving the "minimal prime problem" at length 10²⁵.
We have a 5% chance of solving the "minimal prime problem" at length 10¹⁶.
We have a 95% chance of solving the "minimal prime problem" at length 10⁴⁸.
The chances at lengths 10⁶, 10⁷, 10⁸ are respectively 10⁻⁸⁶, 10⁻⁵², and 10⁻³³.

(The chance that an unproven probable prime in the sets is in fact composite is less than 10⁻²⁰⁰⁰, see https://t5k.org/notes/prp_prob.html and https://www.ams.org/journals/mcom/1989-53-188/S0025-5718-1989-0982368-4/S0025-5718-1989-0982368-4.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_22.pdf))

It is extremely likely that the largest minimal prime in base b is larger than the currently largest known prime (the world record prime) (i.e. 2^82589933−1, with 24862048 decimal digits) (https://en.wikipedia.org/wiki/Largest_known_prime_number, https://mathworld.wolfram.com/LargePrime.html, https://t5k.org/largest.html, https://t5k.org/top20/page.php?id=3, http://www.numericana.com/answer/primes.htm#history, https://t5k.org/primes/page.php?id=125874, https://www.rieselprime.de/ziki/M51, http://factordb.com/index.php?id=1100000001257221107&open=prime, https://oeis.org/A344984), for bases b = 19, 23, 25, 27, 29, 31, 32, 33, 34, 35, i.e. they will broke the world record (https://en.wikipedia.org/wiki/World_record) like Guinness World Records (https://guinnessworldrecords.com/, https://en.wikipedia.org/wiki/Guinness_World_Records), similar example is the project "Do You Feel Lucky?" (https://www.primegrid.com/forum_thread.php?id=8422) in PrimeGrid (https://www.primegrid.com/, https://en.wikipedia.org/wiki/PrimeGrid, https://www.rieselprime.de/ziki/PrimeGrid, https://t5k.org/bios/page.php?id=950), which searches primes of the form b^2²²+1 for bases b ≥ 846398, such primes will be larger than the currently largest known prime (the world record prime) (i.e. 2^82589933−1, with 24862048 decimal digits) (https://en.wikipedia.org/wiki/Largest_known_prime_number, https://mathworld.wolfram.com/LargePrime.html, https://t5k.org/largest.html, https://t5k.org/top20/page.php?id=3, http://www.numericana.com/answer/primes.htm#history, https://t5k.org/primes/page.php?id=125874, https://www.rieselprime.de/ziki/M51, http://factordb.com/index.php?id=1100000001257221107&open=prime, https://oeis.org/A344984).

We can imagine an alien force, vastly more powerful than us, landing on Earth and demanding the set of all minimal primes in base b = 17 (or 21, 26, 36) (including primality proving of all primes in this set) or they will destroy our planet. In that case, I claim, we should marshal all our computers and all our mathematicians and attempt to find the set and to prove the primality of all numbers in this set. But suppose, instead, that they ask for the set of all minimal primes in base b = 19 (or 23, 25, 27, 29, 31, 32, 33, 34, 35). In that case, I believe, we should attempt to destroy the aliens. (Maybe only the God knows the set of all minimal primes in base b = 19 (or 23, 25, 27, 29, 31, 32, 33, 34, 35)!) (just like Paul Erdős for the Ramsey numbers (https://en.wikipedia.org/wiki/Ramsey_number, https://mathworld.wolfram.com/RamseyNumber.html), I do not think that finding the set of all minimal primes in bases b = 17, 19, 21, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 36 is easier than finding the Ramsey numbers R(m,n) for m > 4, n > 4)

This problem covers finding the smallest prime in these families in the same base b (or proving that such prime does not exist), since the smallest prime in these families (if exists) must be a minimal prime in base b (since these families are of the form {x}, x{y}, {x}y, x{0}y (where x and y are any digits in base b) in base b, and the repeating digit is not 1 for all bases b > 2 (or all bases b > 3 for the family (bⁿ+1)/2 for odd b) except the family (bⁿ−1)/(b−1), which is the form {1}) (thus the main problem in this project covers finding the smallest prime in these families (or proving that such prime does not exist) in bases 2 ≤ b ≤ 36, since all bases b < "smallest allowed b" (i.e. the bases b < k+1 for the families of the form k×bⁿ±1 with fixed 2 ≤ k ≤ 12 and the families of the form bⁿ±k with fixed 2 ≤ k ≤ 4) either have a prime < 2×10¹⁷ (only count the numbers > b) or can be proven to have no primes (only count the numbers > b), the largest of the smallest prime in these families is 11×8¹⁸−1 = 198158383604301823, which is the smallest prime of the form 11×8ⁿ−1 with n ≥ 1): (while the original minimal prime problem does not cover some of these forms for some bases (or all bases) b)

(of course, there are bases b > 36 (which are not in this project) mentioned in the "smaller bases b such that this family can be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them)
bases b: why this family contain no primes > b" column and the "smaller bases b with the smallest (probable) prime in this family has length > 100: b (length)" column, but I will not run the bases b > 36 in the main problem in this project, since base 2 ≤ b ≤ 36 are the bases which the main problem in this project decide to go, and you can also try to extend the main problem in this project to bases 2 ≤ b ≤ 50 or 2 ≤ b ≤ 100 (I cannot imagine the effort needed for bases b around 500 or 1000, even if strong probable primes are allowed) (in fact, the GMP (https://gmplib.org/, https://en.wikipedia.org/wiki/GNU_Multiple_Precision_Arithmetic_Library) program supports bases 2 ≤ b ≤ 50, but I only ran for bases 2 ≤ b ≤ 36) (suggestion to use the character ":" to saparate the digits for bases b > 36 (and just use decimal to write the digits), just like https://baseconvert.com/ and https://baseconvert.com/high-precision), but warning: these problems will be extremely hard (especially the bases b such that (b−1)×eulerphi(b) (https://oeis.org/A062955) is larger)!!! The difficulty of base b is roughly (https://en.wikipedia.org/wiki/Asymptotic_analysis, https://t5k.org/glossary/xpage/AsymptoticallyEqual.html, https://mathworld.wolfram.com/Asymptotic.html) e^{γ×(b−1)×eulerphi(b)}, and e^{γ×(b−1)×eulerphi(b)} is an exponential sequence (https://en.wikipedia.org/wiki/Exponential_growth, https://mathworld.wolfram.com/ExponentialGrowth.html) for (b−1)×eulerphi(b) (https://oeis.org/A062955))

(in fact, I know exactly which bases 2 ≤ b ≤ 1024 have the families listed in the table below as unsolved families, all these families in all bases 2 ≤ b ≤ 1024 have been searched to length ≥ 10000)

family	corresponding form ({x} or x{y} or {x}y or x{0}y)	the value of x	the value of y	smallest allowed b	smallest allowed n	OEIS sequences for the smallest n such that this form is prime for fixed base b (such n always exist unless these families can be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them) if my conjecture is true)	OEIS sequences for the smallest base b such that this form is prime for fixed n (such base b always exist unless these families can be ruled out as only containing composites (by single prime factor or algebraic factorization) if the Bunyakovsky conjecture (https://en.wikipedia.org/wiki/Bunyakovsky_conjecture, https://mathworld.wolfram.com/BouniakowskyConjecture.html) is true, in fact, if the Bunyakovsky conjecture (https://en.wikipedia.org/wiki/Bunyakovsky_conjecture, https://mathworld.wolfram.com/BouniakowskyConjecture.html) is true, then all numbers not in the OEIS sequence https://oeis.org/A121719 are primes in infinitely many bases b, since if the Bunyakovsky conjecture (https://en.wikipedia.org/wiki/Bunyakovsky_conjecture, https://mathworld.wolfram.com/BouniakowskyConjecture.html) is true, then all irreducible polynomials (https://en.wikipedia.org/wiki/Irreducible_polynomial, https://mathworld.wolfram.com/IrreduciblePolynomial.html) a_nxⁿ+a_n−1xⁿ⁻¹+a_n−2xⁿ⁻²+...+a₂x²+a₁x+a₀ which have no fixed prime factors (in fact, such prime factors must be ≤ n, i.e. ≤ the degree (https://en.wikipedia.org/wiki/Degree_of_a_polynomial, https://mathworld.wolfram.com/PolynomialDegree.html) of the polynomial) for all integers x contain infinitely many primes, see https://oeis.org/A354718 and https://oeis.org/A337164) (although these primes need not to be minimal primes in base b, I include this only because these OEIS sequences are usable references of the primes in these families)	references	current smallest base b such that this family is an unsolved family (i.e. have no known prime (or strong probable prime) members > b, nor can be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them))	search limit of the length of this family in this base b	bases b such that this family can be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them) bases b: why this family contains no primes > b (only list reasons such that there are bases 2 ≤ b ≤ 2048 which the reason is realized)	smaller bases b with the smallest (probable) prime in this family has length > 100: b (length)
(bⁿ−1)/(b−1)	{x}	1	–	2	2	https://oeis.org/A084740 https://oeis.org/A084738 (corresponding primes) https://oeis.org/A246005 (odd b) https://oeis.org/A065854 (prime b) https://oeis.org/A279068 (prime b, corresponding primes) https://oeis.org/A360738 (n replaced by n−1) https://oeis.org/A279069 (prime b, n replaced by n−1) https://oeis.org/A065813 (prime b, n replaced by (n−1)/2) https://oeis.org/A128164 (n = 2 not allowed) https://oeis.org/A285642 (n = 2 not allowed, corresponding primes)	https://oeis.org/A066180 https://oeis.org/A084732 (corresponding primes) (if this form is prime, then n must be a prime, see https://t5k.org/notes/proofs/Theorem2.html for the proof, this proof can be generalized to any base b, see https://en.wikipedia.org/wiki/Repunit#Properties)	http://www.fermatquotient.com/PrimSerien/GenRepu.txt (in German) https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html http://www.primenumbers.net/Henri/us/MersFermus.htm http://www.bitman.name/math/table/379 (in Italian) https://www.ams.org/journals/mcom/1993-61-204/S0025-5718-1993-1185243-9/S0025-5718-1993-1185243-9.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_4.pdf) https://www.ams.org/journals/mcom/1979-33-148/S0025-5718-1979-0537980-7/S0025-5718-1979-0537980-7.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_119.pdf)	185	275419	b = m²: difference-of-two-squares factorization b = m³: difference-of-two-cubes factorization b = m⁵: difference-of-two-5th-powers factorization b = m⁷: difference-of-two-7th-powers factorization (note: although bases b = 4, 8, 16, 27, 36, 100, 128 have algebraic factorization (if the numbers are factored as F × G / d), F (or G) is equal to d and G (or F) is prime > b, to make the factorizations be trivial, thus these bases b have only one very small prime > b instead of "can be ruled out as only containing composites (only count the numbers > b)", thus the only smaller bases b such that this family can be ruled out as only containing composites (only count the numbers > b) are 9, 25, 32, 49, 64, 81, 121, 125, 144, 169)	35 (313) 39 (349) 47 (127) 51 (4229) 91 (4421) 92 (439) 124 (599) 135 (1171) 139 (163) 142 (1231) 152 (270217) 171 (181) 174 (3251) 182 (167) 183 (223) 184 (16703)
bⁿ+1	x{0}y	1	1	2	1	https://oeis.org/A079706 https://oeis.org/A084712 (corresponding primes) https://oeis.org/A228101 (n replaced by log₂n) https://oeis.org/A123669 (n = 1 not allowed, corresponding primes)	https://oeis.org/A056993 https://oeis.org/A123599 (corresponding primes) (if this form is prime, then n must be a power of 2, see https://web.archive.org/web/20231001191526/http://yves.gallot.pagesperso-orange.fr/primes/math.html for the proof, this proof can be generalized to any base b, see https://www.mersenneforum.org/showpost.php?p=95745&postcount=3 and https://www.mersenneforum.org/showpost.php?p=96001&postcount=95)	http://jeppesn.dk/generalized-fermat.html http://www.noprimeleftbehind.net/crus/GFN-primes.htm https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html https://web.archive.org/web/20231003030159/http://yves.gallot.pagesperso-orange.fr/primes/results.html https://web.archive.org/web/20231001191355/http://yves.gallot.pagesperso-orange.fr/primes/stat.html https://genefer.great-site.net/	38	33554432	b == 1 mod 2: always divisible by 2 b = m³: sum-of-two-cubes factorization b = m⁵: sum-of-two-5th-powers factorization	(none)
(bⁿ+1)/2	{x}y	(b−1)/2	(b+1)/2	3 (only odd b)	2		https://oeis.org/A275530 (if this form is prime, then n must be a power of 2, see https://web.archive.org/web/20231001191526/http://yves.gallot.pagesperso-orange.fr/primes/math.html for the proof, this proof can be generalized to any base b, see https://www.mersenneforum.org/showpost.php?p=95745&postcount=3 and https://www.mersenneforum.org/showpost.php?p=96001&postcount=95)	http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt (in German)	31	16777215	b = m³: sum-of-two-cubes factorization	(none)
2×bⁿ+1	x{0}y	2	1	3	1	https://oeis.org/A119624 https://oeis.org/A253178 (only bases b which have possible primes) https://oeis.org/A098872 (b divisible by 6)		https://www.mersenneforum.org/showthread.php?t=6918 https://www.mersenneforum.org/showthread.php?t=19725 (b == 11 mod 12) https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	365	500000	b == 1 mod 3: always divisible by 3	38 (2730) 47 (176) 101 (192276) 104 (1234) 117 (287) 122 (756) 137 (328) 147 (155) 167 (6548) 203 (106) 206 (46206) 218 (333926) 236 (161230) 248 (322) 257 (12184) 263 (958) 287 (5468) 305 (16808) 347 (124) 353 (2314)
2×bⁿ−1	x{y}	1	b−1	3	1	https://oeis.org/A119591 https://oeis.org/A098873 (b divisible by 6)	https://oeis.org/A157922	https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&d=1567314217 https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	581	600000	(none)	29 (137) 67 (769) 74 (133) 107 (21911) 152 (797) 161 (229) 170 (166429) 191 (971) 215 (1073) 224 (109) 233 (8621) 235 (181) 254 (2867) 260 (121) 276 (2485) 278 (43909) 284 (417) 298 (4203) 303 (40175) 308 (991) 347 (523) 380 (3787) 382 (2325) 383 (20957) 393 (108) 395 (397) 401 (113) 418 (472) 422 (541) 431 (529) 434 (1167) 449 (175) 457 (103) 473 (661) 480 (145) 503 (861) 513 (299) 515 (58467) 522 (62289) 524 (165) 536 (841) 550 (1381) 551 (2719) 572 (3805) 578 (129469)
bⁿ+2	x{0}y	1	2	3	1	https://oeis.org/A138066 https://oeis.org/A084713 (corresponding primes) https://oeis.org/A138067 (n = 1 not allowed)	https://oeis.org/A087576 https://oeis.org/A095302 (corresponding primes)		167	100000	b == 0 mod 2: always divisible by 2 b == 1 mod 3: always divisible by 3	47 (114) 89 (256) 159 (137)
bⁿ−2	{x}y	b−1	b−2	3	2	https://oeis.org/A250200 https://oeis.org/A255707 (n = 1 allowed) https://oeis.org/A084714 (n = 1 allowed, corresponding primes) https://oeis.org/A292201 (prime b, n = 1 allowed)	https://oeis.org/A095303 https://oeis.org/A095304 (corresponding primes)	https://www.primepuzzles.net/puzzles/puzz_887.htm (n = 1 allowed)	305	30000	b == 0 mod 2: always divisible by 2	81 (130) 97 (747) 197 (164) 209 (126) 215 (134) 221 (552) 287 (3410)
3×bⁿ+1	x{0}y	3	1	4	1	https://oeis.org/A098877 (b divisible by 6)		https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	718	300000	b == 1 mod 2: always divisible by 2	108 (271) 314 (281) 358 (9561) 386 (184) 424 (1106) 458 (108) 492 (157) 636 (142) 646 (159) 648 (647) 652 (621) 654 (217) 690 (358)
3×bⁿ−1	x{y}	2	b−1	4	1	https://oeis.org/A098876 (b divisible by 6)		https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	588	500000	b == 1 mod 2: always divisible by 2	42 (2524) 202 (263) 212 (283) 238 (105) 422 (191) 432 (16003) 446 (4851) 452 (335) 464 (219) 522 (347) 532 (136) 572 (377) 582 (445)
bⁿ+3	x{0}y	1	3	4	1		https://oeis.org/A087577		718	10000	b == 1 mod 2: always divisible by 2 b == 0 mod 3: always divisible by 3	382 (256) 388 (109) 412 (137) 530 (1399) 548 (118) 646 (9314)
bⁿ−3	{x}y	b−1	b−3	4	2				1192	6000	b == 1 mod 2: always divisible by 2 b == 0 mod 3: always divisible by 3	52 (105) 94 (204) 152 (346) 154 (396) 290 (111) 302 (1061) 478 (1410) 512 (1600) 542 (1944) 676 (141) 698 (306) 754 (120) 760 (120) 1000 (330) 1006 (124) 1010 (226) 1022 (102) 1094 (1508) 1096 (135)
4×bⁿ+1	x{0}y	4	1	5	1		(such base b does not exist if n is divisible by 4 because of the Aurifeuillean factorization of x⁴+4×y⁴)	https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	32	1717986918	b == 1 mod 5: always divisible by 5 b == 14 mod 15: always divisible by some element of {3,5} b = m⁴: Aurifeuillean factorization of x⁴+4×y⁴	23 (343)
4×bⁿ−1	x{y}	3	b−1	5	1		(such base b does not exist if n is even because of the difference-of-two-squares factorization)	https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	275	600000	b == 1 mod 3: always divisible by 3 b == 14 mod 15: always divisible by some element of {3,5} b = m²: difference-of-two-squares factorization b == 4 mod 5: combine of factor 5 and difference-of-two-squares factorization	47 (1556) 72 (1119850) 107 (252) 167 (1866) 212 (34414) 218 (23050) 236 (940) 240 (1402) 251 (272) 261 (820) 270 (89662)
bⁿ+4	x{0}y	1	4	5	1		(such base b does not exist if n is divisible by 4 because of the Aurifeuillean factorization of x⁴+4×y⁴)		139	18000	b == 0 mod 2: always divisible by 2 b == 1 mod 5: always divisible by 5 b == 14 mod 15: always divisible by some element of {3,5} b = m⁴: Aurifeuillean factorization of x⁴+4×y⁴	53 (13403) 113 (10647)
bⁿ−4	{x}y	b−1	b−4	5	2		(such base b does not exist if n is even because of the difference-of-two-squares factorization)		207	12000	b == 0 mod 2: always divisible by 2 b == 1 mod 3: always divisible by 3 b == 14 mod 15: always divisible by some element of {3,5} b = m²: difference-of-two-squares factorization b == 4 mod 5: combine of factor 5 and difference-of-two-squares factorization	65 (175) 93 (105) 123 (299) 135 (165) 137 (147) 141 (395) 173 (135) 183 (113) 191 (319) 203 (107)
5×bⁿ+1	x{0}y	5	1	6	1			https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	512	1000000	b == 1 mod 2: always divisible by 2 b == 1 mod 3: always divisible by 3	122 (136) 170 (176) 200 (768) 248 (262) 266 (510) 308 (309756) 318 (127) 326 (400786) 332 (106) 350 (20392) 356 (596) 368 (208) 392 (152) 410 (108) 440 (826)
5×bⁿ−1	x{y}	4	b−1	6	1			https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	338	300000	b == 1 mod 2: always divisible by 2	14 (19699) 68 (13575) 112 (133) 116 (157) 196 (9850) 206 (109) 254 (15451) 320 (233)
6×bⁿ+1	x{0}y	6	1	7	1			https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	212	1400000	b == 1 mod 7: always divisible by 7 b == 34 mod 35: always divisible by some element of {5,7}	53 (144) 67 (4533) 93 (521) 108 (16318) 129 (16797) 144 (783) 163 (1304) 185 (171) 193 (149)
6×bⁿ−1	x{y}	5	b−1	7	1			https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	234	1000000	b == 1 mod 5: always divisible by 5 b == 34 mod 35: always divisible by some element of {5,7} b = 6×m² with m == 2, 3 mod 5: combine of factor 5 and difference-of-two-squares factorization	48 (295) 118 (211) 119 (666) 154 (1990) 178 (119) 188 (951)
7×bⁿ+1	x{0}y	7	1	8	1			https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	1136	10000	b == 1 mod 2: always divisible by 2	50 (517) 62 (309) 170 (179) 194 (281) 224 (689) 236 (347) 308 (107) 338 (793) 380 (475) 382 (519) 386 (121) 398 (17473) 434 (321) 466 (181) 500 (1997) 520 (198) 522 (235) 524 (127) 598 (423) 632 (8447) 638 (265) 644 (3379) 652 (185) 674 (181) 682 (796) 724 (388) 734 (189) 764 (189) 836 (5701) 868 (274) 892 (157) 920 (491) 926 (523) 930 (218) 958 (169) 960 (128) 974 (1589) 982 (313) 1004 (54849) 1082 (2113) 1102 (820)
7×bⁿ−1	x{y}	6	b−1	8	1			https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	308	300000	b == 1 mod 2: always divisible by 2 b == 1 mod 3: always divisible by 3	68 (25396) 182 (210) 198 (117) 248 (3180) 260 (826)
8×bⁿ+1	x{0}y	8	1	9	1		(such base b does not exist if n is divisible by 3 because of the sum-of-two-cubes factorization)	https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	86	1000000	b == 1 mod 3: always divisible by 3 b == 20 mod 21: always divisible by some element of {3,7} b == 47, 83 mod 195: always divisible by some element of {3,5,13} b == 467, 4343, 9887, 25448, 35978, 41522, 42647, 57083 mod 73815: always divisible by some element of {3,5,7,19,37} b == 722, 83813, 206672, 239432, 322523, 1283843, 1519577, 1522553 mod 1551615: always divisible by some element of {3,5,13,73,109} b = m³: sum-of-two-cubes factorization b = 2^r such that the equation 2^x == 3 mod r has no solution: no possible prime, since 8×(2^r)ⁿ+1 = 2^n×r+3+1, and if 2^n×r+3+1 is prime, then n×r+3 must be a power of 2 (otherwise, if n×r+3 has an odd prime factor p, then 2^n×r+3+1 has a sum-of-two-pth-powers factorization), and this power of 2 must be == 3 mod r, for such r which are primes see https://oeis.org/A123988, unfortunately there is no OEIS sequence for all such r or all such odd r (they are in fact combine of sum-of-two-pth-powers factorization for infinitely many odd primes p, for such r which are primes, it is combine of sum-of-two-pth-powers factorization for the odd primes p which are not q^sth power residue (we only need consider the prime powers (https://oeis.org/A246655, https://en.wikipedia.org/wiki/Prime_power, https://mathworld.wolfram.com/PrimePower.html) q^s dividing r−1, for q^s = 2 this is quadratic residue (https://en.wikipedia.org/wiki/Quadratic_residue, https://t5k.org/glossary/xpage/QuadraticResidue.html, https://www.rieselprime.de/ziki/Quadratic_residue, https://mathworld.wolfram.com/QuadraticResidue.html), for q^s = 3 this is cubic residue (https://en.wikipedia.org/wiki/Cubic_residue, https://mathworld.wolfram.com/CubicResidue.html), for q^s = 4 this is quartic residue (https://en.wikipedia.org/wiki/Quartic_reciprocity, https://mathworld.wolfram.com/BiquadraticResidue.html), for q^s = 8 this is octic residue (https://en.wikipedia.org/wiki/Octic_reciprocity), for other q^s see power residue symbol (https://en.wikipedia.org/wiki/Power_residue_symbol) and Dirichlet character (https://en.wikipedia.org/wiki/Dirichlet_character, https://mathworld.wolfram.com/NumberTheoreticCharacter.html, https://www.lmfdb.org/Character/Dirichlet/) and Eisenstein reciprocity (https://en.wikipedia.org/wiki/Eisenstein_reciprocity) and Artin reciprocity (https://en.wikipedia.org/wiki/Artin_reciprocity, https://mathworld.wolfram.com/ArtinsReciprocityTheorem.html)) mod r for all prime powers (https://oeis.org/A246655, https://en.wikipedia.org/wiki/Prime_power, https://mathworld.wolfram.com/PrimePower.html) q^s dividing https://oeis.org/A001917 at the entry of the prime r but not dividing https://oeis.org/A094593 at the entry of the prime r, e.g. the case of b = 128 (i.e. r = 7) is combine of sum-of-two-pth-powers factorization for the odd primes p which are not quadratic residues (https://en.wikipedia.org/wiki/Quadratic_residue, https://t5k.org/glossary/xpage/QuadraticResidue.html, https://www.rieselprime.de/ziki/Quadratic_residue, https://mathworld.wolfram.com/QuadraticResidue.html) mod 7 (i.e. the odd primes p == 3, 5, 6 mod 7) (i.e. the odd primes p in https://oeis.org/A003625), and the case of b = 131072 (i.e. r = 17) is combine of sum-of-two-pth-powers factorization for the odd primes p which are not quadratic residues (https://en.wikipedia.org/wiki/Quadratic_residue, https://t5k.org/glossary/xpage/QuadraticResidue.html, https://www.rieselprime.de/ziki/Quadratic_residue, https://mathworld.wolfram.com/QuadraticResidue.html) mod 17 (i.e. the odd primes p == 3, 5, 6, 7, 10, 11, 12, 14 mod 17) (i.e. the odd primes p in https://oeis.org/A038890), and the case of b = 2147483648 (i.e. r = 31) is combine of sum-of-two-pth-powers factorization for the odd primes p which are not quadratic residues (https://en.wikipedia.org/wiki/Quadratic_residue, https://t5k.org/glossary/xpage/QuadraticResidue.html, https://www.rieselprime.de/ziki/Quadratic_residue, https://mathworld.wolfram.com/QuadraticResidue.html) mod 31 (i.e. the odd primes p == 3, 6, 11, 12, 13, 15, 17, 21, 22, 23, 24, 26, 27, 29, 30 mod 31) (i.e. the odd primes p in https://oeis.org/A191067), also combine of sum-of-two-pth-powers factorization for the odd primes p which are not cubic residues (https://en.wikipedia.org/wiki/Cubic_residue, https://mathworld.wolfram.com/CubicResidue.html) mod 31 (i.e. the odd primes p == 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28 mod 31), etc. and by the Dirichlet's theorem (https://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions, https://t5k.org/glossary/xpage/DirichletsTheorem.html, https://mathworld.wolfram.com/DirichletsTheorem.html, http://www.numericana.com/answer/primes.htm#dirichlet), all of these sequences contain infinitely many odd primes)	23 (119216) 53 (227184) 68 (320)
8×bⁿ−1	x{y}	7	b−1	9	1		(such base b does not exist if n is divisible by 3 because of the difference-of-two-cubes factorization)	https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	321	600000	b == 1 mod 7: always divisible by 7 b == 20 mod 21: always divisible by some element of {3,7} b == 83, 307 mod 455: always divisible by some element of {5,7,13} b = m³: difference-of-two-cubes factorization b == 1266, 13593, 27292, 46353 mod 63973: combine of factors {7,13,19,37} and difference-of-two-cubes factorization	97 (192336) 101 (113) 112 (269) 131 (197) 145 (6369) 170 (15423) 194 (38361) 202 (155772) 217 (179) 237 (528) 245 (501) 252 (6288) 270 (108) 277 (1229) 282 (21413) 283 (164769) 284 (5267)
9×bⁿ+1	x{0}y	9	1	10	1			https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	724	600000	b == 1 mod 2: always divisible by 2 b == 1 mod 5: always divisible by 5	94 (264) 134 (184) 182 (264) 244 (1836) 248 (39511) 332 (311) 334 (340) 344 (306) 364 (166) 400 (265) 402 (127) 422 (106) 448 (372) 454 (136) 490 (469) 534 (106) 544 (4706) 592 (96870) 622 (127) 634 (190) 664 (290)
9×bⁿ−1	x{y}	8	b−1	10	1		(such base b does not exist if n is even because of the difference-of-two-squares factorization)	https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	378	300000	b == 1 mod 2: always divisible by 2 b = m²: difference-of-two-squares factorization b == 4 mod 5: combine of factor 5 and difference-of-two-squares factorization	88 (172) 112 (5718) 116 (250) 130 (468) 138 (35686) 188 (3888) 198 (304) 218 (178) 258 (106) 286 (164) 292 (2928) 328 (606) 332 (946) 346 (130) 360 (316) 366 (238)
10×bⁿ+1	x{0}y	10	1	11	1	https://oeis.org/A088782 https://oeis.org/A088622 (corresponding primes)	https://oeis.org/A089319 https://oeis.org/A089318 (corresponding primes)	https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	185	1000000	b == 1 mod 11: always divisible by 11 b == 32 mod 33: always divisible by some element of {3,11}	17 (1357) 61 (166) 74 (139) 101 (1507) 137 (103) 142 (408) 173 (264235) 176 (147) 179 (337)
10×bⁿ−1	x{y}	9	b−1	11	1			https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	233	1000000	b == 1 mod 3: always divisible by 3 b == 32 mod 33: always divisible by some element of {3,11}	17 (118) 80 (423716) 89 (250) 185 (6784) 194 (3150) 215 (144)
11×bⁿ+1	x{0}y	11	1	12	1			https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	560	100000	b == 1 mod 2: always divisible by 2 b == 1 mod 3: always divisible by 3 b == 14 mod 15: always divisible by some element of {3,5}	68 (3948) 108 (190) 110 (162) 152 (838) 222 (101) 236 (154) 294 (365) 320 (1264) 384 (491) 392 (412) 432 (226) 440 (146) 462 (762) 506 (270) 528 (249) 534 (689) 542 (4910)
11×bⁿ−1	x{y}	10	b−1	12	1			https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	214	1000000	b == 1 mod 2: always divisible by 2 b == 1 mod 5: always divisible by 5 b == 14 mod 15: always divisible by some element of {3,5} b = 11×m² with m == 2, 3 mod 5: combine of factor 5 and difference-of-two-squares factorization	38 (767) 68 (199) 72 (2446) 80 (209) 102 (2071) 140 (109) 170 (109) 178 (178) 188 (183)
12×bⁿ+1	x{0}y	12	1	13	1			https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	163	500000	b == 1 mod 13: always divisible by 13 b == 142 mod 143: always divisible by some element of {11,13} b == 562, 828, 900, 1166 mod 1729: always divisible by some element of {7,13,19} b == 597, 1143 mod 1885: always divisible by some element of {5,13,29} b == 296, 901, 1759, 3090, 4553, 5521, 5807, 6016, 6984, 7094, 7270, 7380, 7479, 8447, 8557, 8733, 8843, 9910, 10020, 10196, 10306, 11483, 11769, 12737, 14200, 15531, 16994, 18457 mod 19019: always divisible by some element of {7,11,13,19} b == 563, 1433, 13212, 15097, 19848, 20718, 32497, 34382, 39133, 51782, 53667, 58418, 58452, 60337, 60883, 71067, 72952, 77737, 79622, 80168, 94267, 97022, 98583, 98907, 113552, 116307, 117868, 118192, 131967, 132513, 132837, 134398, 151252, 151798, 152122, 153683, 170537, 171083, 172968, 177753, 179638, 189822, 190368, 192253, 192287, 197038, 198923, 211572, 213568, 216323, 218208, 229987, 232853, 235608, 237493, 249272 mod 250705: always divisible by some element of {5,7,13,19,29}	30 (1024) 65 (685) 67 (136) 68 (656922) 82 (108) 87 (1215) 102 (2740) 106 (139) 159 (122)
12×bⁿ−1	x{y}	11	b−1	13	1			https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n https://www.mersenneforum.org/showthread.php?t=10354	263	314000	b == 1 mod 11: always divisible by 11 b == 142 mod 143: always divisible by some element of {11,13} b == 307, 1143 mod 1595: always divisible by some element of {5,11,29} b == 901, 6016, 7479, 18457 mod 19019: always divisible by some element of {7,11,13,19}	43 (204) 65 (1194) 98 (3600) 129 (229) 147 (113) 153 (21660) 186 (112718) 193 (117) 230 (188)
(b−1)×bⁿ+1	x{0}y	b−1	1	2	1	https://oeis.org/A305531 https://oeis.org/A087139 (prime b, n replaced by n+1)	(such base b does not exist if n == 1 mod 6 except n = 1 because such numbers are divisible by b²−b+1)	https://www.rieselprime.de/ziki/Williams_prime_MP_least https://www.rieselprime.de/ziki/Williams_prime_MP_table https://pzktupel.de/Primetables/TableWilliams2.php https://pzktupel.de/Primetables/Williams_2.txt https://web.archive.org/web/20240126201446/https://pzktupel.de/Primetables/Williams2DB.txt https://sites.google.com/view/williams-primes http://www.bitman.name/math/table/477 (in Italian)	342	300000	(none)	53 (961) 65 (947) 77 (829) 88 (3023) 122 (6217) 123 (865891) 127 (166) 136 (280) 158 (1621) 180 (2485) 182 (397) 185 (209) 197 (521) 202 (46774) 214 (119) 248 (605) 249 (1852) 251 (102979) 257 (1345) 269 (1437) 272 (16681) 275 (981) 282 (277) 297 (14314) 298 (60671) 307 (204) 317 (129) 319 (565) 326 (64757) 328 (1627) 329 (481) 332 (113) 338 (273) 340 (325)
(b−1)×bⁿ−1	x{y}	b−2	b−1	2	1	https://oeis.org/A122396 (prime b, n replaced by n+1)	(such base b does not exist if n == 4 mod 6 because such numbers are divisible by b²−b+1)	https://harvey563.tripod.com/wills.txt https://www.rieselprime.de/ziki/Williams_prime_MM_least https://www.rieselprime.de/ziki/Williams_prime_MM_table https://pzktupel.de/Primetables/TableWilliams1.php https://pzktupel.de/Primetables/Williams_1.txt https://web.archive.org/web/20240126201427/https://pzktupel.de/Primetables/Williams1DB.txt https://sites.google.com/view/williams-primes http://matwbn.icm.edu.pl/ksiazki/aa/aa39/aa3912.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_9.pdf) https://www.ams.org/journals/mcom/2000-69-232/S0025-5718-00-01212-6/S0025-5718-00-01212-6.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_10.pdf) http://www.bitman.name/math/table/484 (in Italian)	128	2450000	(none)	26 (134) 38 (136212) 62 (900) 83 (21496) 91 (520) 93 (477) 98 (4984) 108 (411) 113 (286644) 125 (8740)
bⁿ+(b−1)	x{0}y	1	b−1	2	1	https://oeis.org/A076845 https://oeis.org/A076846 (corresponding primes) https://oeis.org/A078178 (n = 1 not allowed) https://oeis.org/A078179 (n = 1 not allowed, corresponding primes)	https://oeis.org/A248079 (such base b does not exist if n == 5 mod 6 because such numbers are divisible by b²−b+1)	https://pzktupel.de/Primetables/TableWilliams6.php https://pzktupel.de/Primetables/W6DB.txt https://web.archive.org/web/20231015225001/https://pzktupel.de/Primetables/Williams6DB.txt https://sites.google.com/view/williams-primes http://www.bitman.name/math/table/795 (in Italian)	257	17000	(none)	32 (109) 80 (195) 107 (1401) 113 (20089) 123 (64371) 128 (505) 161 (105) 173 (11429) 179 (3357) 197 (977) 212 (109) 224 (259) 227 (157) 237 (110) 238 (117)
bⁿ−(b−1)	{x}y	b−1	1	2	2	https://oeis.org/A113516 https://oeis.org/A343589 (corresponding primes)	https://oeis.org/A113517 (such base b does not exist if n == 2 mod 6 except n = 2 because such numbers are divisible by b²−b+1)	https://pzktupel.de/Primetables/TableWilliams5.php https://pzktupel.de/Primetables/W5DB.txt https://web.archive.org/web/20231015225036/https://pzktupel.de/Primetables/Williams5DB.txt https://sites.google.com/view/williams-primes http://www.bitman.name/math/table/792 (in Italian) https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html (prime b) http://www.bitman.name/math/table/435 (in Italian) (prime b)	93	60000	(none)	71 (3019) 82 (169) 83 (965) 88 (2848)

In fact, this problem covers finding the smallest prime of these form in the same base b: (where x, y, z are any digits in base b)

x{0}y (see https://arxiv.org/pdf/2307.07894.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_203.pdf) for the case b = 2, this is exactly the case x×bⁿ+y, the case y = 1 is exactly x×bⁿ+1 (exactly the generalized Sierpinski problem to base b with k = x), also see https://math.stackexchange.com/questions/805465/is-my-proof-correct-regarding-the-non-primality-of-2-cdot-17a-1, and the case x = 1 is exactly bⁿ+y (exactly the generalized dual Sierpinski problem to base b with k = y), see https://mathoverflow.net/questions/268918/density-of-primes-in-sequences-of-the-form-anb and https://math.stackexchange.com/questions/597234/least-prime-of-the-form-38n31 and https://math.stackexchange.com/questions/760966/is-324455n-ever-prime)
x{y} (unless y = 1) (see https://stdkmd.net/nrr/abbbb.htm for the case b = 10)
{x}y (unless x = 1) (see https://stdkmd.net/nrr/aaaab.htm for the case b = 10)
x{0}yz (unless there is a prime of the form x{0}y or x{0}z) (this is exactly the case x×bⁿ+yz, the case x = 1 is exactly bⁿ+yz (exactly the generalized dual Sierpinski problem to base b with k = yz))
xy{0}z (unless there is a prime of the form x{0}z or y{0}z) (this is exactly the case xy×bⁿ+z, the case z = 1 is exactly xy×bⁿ+1 (exactly the generalized Sierpinski problem to base b with k = xy))
xy{x} (unless either x = 1 or there is a prime of the form y{x} (or both)) (see https://stdkmd.net/nrr/abaaa.htm for the case b = 10)
{x}yx (unless either x = 1 or there is a prime of the form {x}y (or both)) (see https://stdkmd.net/nrr/aaaba.htm for the case b = 10)

Proving that "the set of the minimal elements of the base b representations of the prime numbers > b under the subsequence ordering" = the set S is equivalent to (https://en.wikipedia.org/wiki/Logical_equivalence):

Prove that all elements in S, when read as base b representation, are primes > b.
Prove that all proper subsequence of all elements in S, when read as base b representation, which are > b, are composite (https://en.wikipedia.org/wiki/Composite_number, https://t5k.org/glossary/xpage/Composite.html, https://www.rieselprime.de/ziki/Composite_number, https://mathworld.wolfram.com/CompositeNumber.html, https://oeis.org/A002808).
Prove that all primes > b, when written in base b, contain at least one element in S as subsequence (equivalently, prove that all strings not containing any element in S as subsequence, when read as base b representation, which are > b, are composite).

("the set of the minimal elements of the base b representations of the prime numbers > b under the subsequence ordering" = S is proved if and only if all these three problems are proved, i.e. "the set of the minimal elements of the base b representations of the prime numbers > b under the subsequence ordering" = S is a theorem if and only if all these three "conjectures" are theorems)

e.g. proving that "the set of the minimal elements of the base 10 representations of the prime numbers > 10 under the subsequence ordering" = {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}, is equivalent to:

Prove that all of 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027 are primes > 10.
Prove that all proper subsequence of all elements in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} which are > 10 are composite.
Prove that all primes > 10 contain at least one element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} as subsequence (equivalently, prove that all numbers > 10 not containing any element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} as subsequence are composite, since they are contraposition (https://en.wikipedia.org/wiki/Contraposition), P ⟶ Q and ¬Q ⟶ ¬P are logically equivalent (https://en.wikipedia.org/wiki/Logical_equivalence)).

(since for base b = 10, all these three problems are proved, i.e. all they are theorems, thus, "the set of the minimal elements of the base 10 representations of the prime numbers > 10 under the subsequence ordering" = {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} is also proved, i.e. "the set of the minimal elements of the base 10 representations of the prime numbers > 10 under the subsequence ordering" = {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} is also a theorem)

Theorem (https://en.wikipedia.org/wiki/Theorem, https://mathworld.wolfram.com/Theorem.html, https://t5k.org/notes/proofs/): The set of the minimal elements of the base 10 representations of the prime numbers > 10 under the subsequence ordering is {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}

Proof (https://en.wikipedia.org/wiki/Mathematical_proof, https://mathworld.wolfram.com/Proof.html, https://t5k.org/notes/proofs/): (this proof uses the notation in http://www.cs.uwaterloo.ca/~shallit/Papers/minimal5.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_11.pdf), i.e. "X ◁ Y" means "X is a subsequence of Y") (below, 𝜆 is the empty string (https://en.wikipedia.org/wiki/Empty_string)) (bold for minimal primes)

Assume p is a prime > 10, and the last digit of p must lie in {1,3,7,9}

Case 1: p ends with 1.

In this case we can write p = x1. If x contains 1, 3, 4, 6, or 7, then (respectively) 11 ◁ p, 31 ◁ p, 41 ◁ p, 61 ◁ p, or 71 ◁ p. Hence we may assume all digits of x are 0, 2, 5, 8, or 9.

Case 1.1: p begins with 2.

In this case we can write p = 2y1. If 5 ◁ y, then 251 ◁ p. If 8 ◁ y, then 281 ◁ p. If 9 ◁ y, then 29 ◁ p. Hence we may assume all digits of y are 0 or 2.

If 22 ◁ y, then 2221 ◁ p. Hence we may assume y contains zero or one 2's.

If y contains no 2's, then p ∈ 2{0}1. But then, since the sum of the digits of p is 3, p is divisible by 3, so p cannot be prime.

If y contains exactly one 2, then we can write p = 2z2w1, where z,w ∈ {0}. If 0 ◁ z and 0 ◁ w, then 20201 ◁ p. Hence we may assume either z or w is empty.

If z is empty, then p ∈ 22{0}1, and the smallest prime p ∈ 22{0}1 is 22000001.

If w is empty, then p ∈ 2{0}21, and the smallest prime p ∈ 2{0}21 is 20021.

Case 1.2: p begins with 5.

In this case we can write p = 5y1. If 2 ◁ y, then 521 ◁ p. If 9 ◁ y, then 59 ◁ p. Hence we may assume all digits of y are 0, 5, or 8.

If 05 ◁ y, then 5051 ◁ p. If 08 ◁ y, then 5081 ◁ p. If 50 ◁ y, then 5501 ◁ p. If 58 ◁ y, then 5581 ◁ p. If 80 ◁ y, then 5801 ◁ p. If 85 ◁ y, then 5851 ◁ p. Hence we may assume y ∈ {0} ∪ {5} ∪ {8}.

If y ∈ {0}, then p ∈ 5{0}1. But then, since the sum of the digits of p is 6, p is divisible by 3, so p cannot be prime.

If y ∈ {5}, then p ∈ 5{5}1 = {5}1, and the smallest prime p ∈ 5{5}1 = {5}1 is 555555555551.

If y ∈ {8}, since if 88 ◁ y, then 881 ◁ p, hence we may assume y ∈ {𝜆, 8}, and thus p ∈ {51, 581}, but 51 and 581 are both composite.

Case 1.3: p begins with 8.

In this case we can write p = 8y1. If 2 ◁ y, then 821 ◁ p. If 8 ◁ y, then 881 ◁ p. If 9 ◁ y, then 89 ◁ p. Hence we may assume all digits of y are 0 or 5.

If 50 ◁ y, then 8501 ◁ p. Hence we may assume y ∈ {0}{5}.

If 005 ◁ y, then 80051 ◁ p. Hence we may assume y ∈ {0} ∪ {5} ∪ 0{5}.

If y ∈ {0}, then p ∈ 8{0}1. But then, since the sum of the digits of p is 9, p is divisible by 3, so p cannot be prime.

If y ∈ {5}, since if 55555555555 ◁ y, then 555555555551 ◁ p, hence we may assume y ∈ {𝜆, 5, 55, 555, 5555, 55555, 555555, 5555555, 55555555, 555555555, 5555555555}, and thus p ∈ {81, 851, 8551, 85551, 855551, 8555551, 85555551, 855555551, 8555555551, 85555555551, 855555555551}, but all of these numbers are composite.

If y ∈ 0{5}, since if 55555555555 ◁ y, then 555555555551 ◁ p, hence we may assume y ∈ {0, 05, 055, 0555, 05555, 055555, 0555555, 05555555, 055555555, 0555555555, 05555555555}, and thus p ∈ {801, 8051, 80551, 805551, 8055551, 80555551, 805555551, 8055555551, 80555555551, 805555555551, 8055555555551}, and of these numbers only 80555551 and 8055555551 are primes, but 80555551 ◁ 8055555551, thus only 80555551 is minimal prime.

Case 1.4: p begins with 9.

In this case we can write p = 9y1. If 9 ◁ y, then 991 ◁ p. Hence we may assume all digits of y are 0, 2, 5, or 8.

If 00 ◁ y, then 9001 ◁ p. If 22 ◁ y, then 9221 ◁ p. If 55 ◁ y, then 9551 ◁ p. If 88 ◁ y, then 881 ◁ p. Hence we may assume y contains at most one 0, at most one 2, at most one 5, and at most one 8.

If y only contains at most one 0 and does not contain any of {2, 5, 8}, then y ∈ {𝜆, 0}, and thus p ∈ {91, 901}, but 91 and 901 are both composite. If y only contains at most one 0 and only one of {2, 5, 8}, then the sum of the digits of p is divisible by 3, p is divisible by 3, so p cannot be prime. Hence we may assume y contains at least two of {2, 5, 8}.

If 25 ◁ y, then 251 ◁ p. If 28 ◁ y, then 281 ◁ p. If 52 ◁ y, then 521 ◁ p. If 82 ◁ y, then 821 ◁ p. Hence we may assume y contains no 2's (since if y contains 2, then y cannot contain either 5's or 8's, which is a contradiction).

If 85 ◁ y, then 9851 ◁ p. Hence we may assume y ∈ {58, 580, 508, 058}, and thus p ∈ {9581, 95801, 95081, 90581}, and of these numbers only 95801 is prime, but 95801 is not minimal prime since 5801 ◁ 95801.

Case 2: p ends with 3.

In this case we can write p = x3. If x contains 1, 2, 4, 5, 7, or 8, then (respectively) 13 ◁ p, 23 ◁ p, 43 ◁ p, 53 ◁ p, 73 ◁ p, or 83 ◁ p. Hence we may assume all digits of x are 0, 3, 6, or 9, and thus all digits of p are 0, 3, 6, or 9. But then, since the digits of p all have a common factor 3, p is divisible by 3, so p cannot be prime.

Case 3: p ends with 7.

In this case we can write p = x7. If x contains 1, 3, 4, 6, or 9, then (respectively) 17 ◁ p, 37 ◁ p, 47 ◁ p, 67 ◁ p, or 97 ◁ p. Hence we may assume all digits of x are 0, 2, 5, 7, or 8.

Case 3.1: p begins with 2.

In this case we can write p = 2y7. If 2 ◁ y, then 227 ◁ p. If 5 ◁ y, then 257 ◁ p. If 7 ◁ y, then 277 ◁ p. Hence we may assume all digits of y are 0 or 8.

If 08 ◁ y, then 2087 ◁ p. If 88 ◁ y, then 887 ◁ p. Hence we may assume y ∈ {0} ∪ 8{0}.

If y ∈ {0}, then p ∈ 2{0}7. But then, since the sum of the digits of p is 9, p is divisible by 3, so p cannot be prime.

If y ∈ 8{0}, then p ∈ 28{0}7. But then p is divisible by 7, since for n ≥ 0 we have 7 × 40_n1 = 280_n7, so p cannot be prime.

Case 3.2: p begins with 5.

In this case we can write p = 5y7. If 5 ◁ y, then 557 ◁ p. If 7 ◁ y, then 577 ◁ p. If 8 ◁ y, then 587 ◁ p. Hence we may assume all digits of y are 0 or 2.

If 22 ◁ y, then 227 ◁ p. Hence we may assume y contains zero or one 2's.

If y contains no 2's, then p ∈ 5{0}7. But then, since the sum of the digits of p is 12, p is divisible by 3, so p cannot be prime.

If y contains exactly one 2, then we can write p = 5z2w7, where z,w ∈ {0}. If 0 ◁ z and 0 ◁ w, then 50207 ◁ p. Hence we may assume either z or w is empty.

If z is empty, then p ∈ 52{0}7, and the smallest prime p ∈ 52{0}7 is 5200007.

If w is empty, then p ∈ 5{0}27, and the smallest prime p ∈ 5{0}27 is 5000000000000000000000000000027.

Case 3.3: p begins with 7.

In this case we can write p = 7y7. If 2 ◁ y, then 727 ◁ p. If 5 ◁ y, then 757 ◁ p. If 8 ◁ y, then 787 ◁ p. Hence we may assume all digits of y are 0 or 7, and thus all digits of p are 0 or 7. But then, since the digits of p all have a common factor 7, p is divisible by 7, so p cannot be prime.

Case 3.4: p begins with 8.

In this case we can write p = 8y7. If 2 ◁ y, then 827 ◁ p. If 5 ◁ y, then 857 ◁ p. If 7 ◁ y, then 877 ◁ p. If 8 ◁ y, then 887 ◁ p. Hence we may assume y ∈ {0}, and thus p ∈ 8{0}7. But then, since the sum of the digits of p is 15, p is divisible by 3, so p cannot be prime.

Case 4: p ends with 9.

In this case we can write p = x9. If x contains 1, 2, 5, 7, or 8, then (respectively) 19 ◁ p, 29 ◁ p, 59 ◁ p, 79 ◁ p, or 89 ◁ p. Hence we may assume all digits of x are 0, 3, 4, 6, or 9.

If 44 ◁ x, then 449 ◁ p. Hence we may assume x contains zero or one 4's.

If x contains no 4's, then all digits of x are 0, 3, 6, or 9, and thus all digits of p are 0, 3, 6, or 9. But then, since the digits of p all have a common factor 3, p is divisible by 3, so p cannot be prime. Hence we may assume that x contains exactly one 4.

Case 4.1: p begins with 3.

In this case we can write p = 3y4z9, where all digits of y, z are 0, 3, 6, or 9. We must have 349 ◁ p.

Case 4.2: p begins with 4.

In this case we can write p = 4y9, where all digits of y are 0, 3, 6, or 9. If 0 ◁ y, then 409 ◁ p. If 3 ◁ y, then 43 ◁ p. If 9 ◁ y, then 499 ◁ p. Hence we may assume y ∈ {6}, and thus p ∈ 4{6}9. But then p is divisible by 7, since for n ≥ 0 we have 7 × 6_n7 = 46_n9, so p cannot be prime.

Case 4.3: p begins with 6.

In this case we can write p = 6y4z9, where all digits of y, z are 0, 3, 6, or 9. If 0 ◁ z, then 409 ◁ p. If 3 ◁ z, then 43 ◁ p. If 6 ◁ z, then 6469 ◁ p. If 9 ◁ z, then 499 ◁ p. Hence we may assume z is empty.

If 3 ◁ y, then 349 ◁ p. If 9 ◁ y, then 6949 ◁ p. Hence we may assume all digits of y are 0 or 6.

If 06 ◁ y, then 60649 ◁ p. Hence we may assume y ∈ {6}{0}.

If 666 ◁ y, then 666649 ◁ p. If 00000 ◁ y, then 60000049 ◁ p. Hence we may assume y ∈ {𝜆, 0, 00, 000, 0000, 6, 60, 600, 6000, 60000, 66, 660, 6600, 66000, 660000}, and thus p ∈ {649, 6049, 60049, 600049, 6000049, 6649, 66049, 660049, 6600049, 66000049, 66649, 666049, 6660049, 66600049, 666000049}, and of these numbers only 66000049 and 66600049 are primes.

Case 4.4: p begins with 9.

In this case we can write p = 9y4z9, where all digits of y, z are 0, 3, 6, or 9. If 0 ◁ y, then 9049 ◁ p. If 3 ◁ y, then 349 ◁ p. If 6 ◁ y, then 9649 ◁ p. If 9 ◁ y, then 9949 ◁ p. Hence we may assume y is empty.

If 0 ◁ z, then 409 ◁ p. If 3 ◁ z, then 43 ◁ p. If 9 ◁ z, then 499 ◁ p. Hence we may assume z ∈ {6}, and thus p ∈ 94{6}9, and the smallest prime p ∈ 94{6}9 is 946669.

I left as an exercise to the readers to write the proof for bases b = 2, 3, 4, 5, 6, 7, 8, 9, 12, 14, 18 (bases b = 14 and b = 18 have 650 and 549 minimal primes, respectively, they are "a little" many, thus they are "a little" difficult, but you may try them!) like http://www.cs.uwaterloo.ca/~shallit/Papers/minimal5.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_11.pdf) for base b = 10 and https://scholar.colorado.edu/downloads/hh63sw661 (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_16.pdf) for bases 2 ≤ b ≤ 10 (warning: the datas for bases 8 and 10 have errors, the data for base 8 misses the prime 6101 and the data for base 10 misses the primes 9001 and 9049 and instead wrongly includes the primes 90001, 90469, and 9000049, and the correct values of S_m for bases 8 and 10 are 15 and 26 (instead of 14 and 27), respectively, also, the "number of minimal primes base b" and the "length of the largest minimal prime base b" are not the same sizes of b but the same sizes of e^{γ×(b−1)×eulerphi(b)}, this article has this error is because it only search bases 2 ≤ b ≤ 10, and for the data of 2 ≤ b ≤ 10 for the original minimal problem, you may think that they are the same sizes of b (however, if you extend the data to b = 11, 13, 16, then you will know that they are not the same sizes of b), since bases b = 7 and b = 9 have very large differences of the "number of minimal primes base b" between the original minimal problem and this new minimal prime problem (b = 7: 9 v.s. 71, b = 9: 12 v.s. 151), and bases b = 5 and b = 8 and b = 9 have very large differences of the "length of the largest minimal prime base b" between the original minimal problem and this new minimal prime problem (b = 5: 5 v.s. 96, b = 8: 9 v.s. 221, b = 9: 4 v.s. 1161)) for the original minimal prime problems, of course, the proof for base b = 2 is trivial, since all primes p > 2 must start and end with 1 in base 2, thus we must have 11 ◁ p, however, for some bases b like 24 (the currently "proven" base b (including the primality proving for the primes in the set) with the most number of minimal primes) and 22 (the currently "proven" base b (if unproven probable primes are allowed) with the most number of minimal primes), it is almost impossible to write the proof by hand, since base b = 24 and b = 22 have too many (3409 and 8003, respectively) minimal primes to write the proof (not to mention the "extremely hard" unproven bases b, i.e. bases b = 19, 23, 25, 27, 29, 31, 32, 33, 34, 35, you will write the proof (up to the unsolved families) until the end of time!), thus the C++ program code (for computer to compute (https://en.wikipedia.org/wiki/Computing) the proof) is made.

Any repunit in any base b having a composite number of digits is necessarily composite. Only repunits (in any base b) having a prime number of digits might be prime. This is a necessary but not sufficient condition, e.g. 11111111111111111111111111111111111 (the repunit with 35 (= 5 × 7, which is composite) digits) = 11111 × 1000010000100001000010000100001 = 1111111 × 10000001000000100000010000001, since 35 = 5 × 7 = 7 × 5, and this repunit factorization does not depend on the base b in which the repunit is expressed. (note that the value of the repunit (in any base b) having 1 digit is 1, and 1 is not prime (https://t5k.org/notes/faq/one.html, https://primefan.tripod.com/Prime1ProCon.html, https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_24.pdf), http://www.numericana.com/answer/numbers.htm#one)).

This is the list of the known generalized repunit (probable) primes in bases 2 ≤ b ≤ 36 (italic for unproven probable primes (https://en.wikipedia.org/wiki/Probable_prime, https://t5k.org/glossary/xpage/PRP.html, https://www.rieselprime.de/ziki/Probable_prime, https://mathworld.wolfram.com/ProbablePrime.html, http://www.primenumbers.net/prptop/prptop.php, https://web.archive.org/web/20240202224722/https://stdkmd.net/nrr/records.htm#probableprimenumbers, https://stdkmd.net/nrr/repunit/prpfactors.htm, https://www.mersenne.ca/prp.php?show=1, https://www.alfredreichlg.de/10w7/prp.html, http://factordb.com/listtype.php?t=1)): (references: http://www.fermatquotient.com/PrimSerien/GenRepu.txt (in German), https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379 (in Italian), https://www.ams.org/journals/mcom/1993-61-204/S0025-5718-1993-1185243-9/S0025-5718-1993-1185243-9.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_4.pdf), https://www.ams.org/journals/mcom/1979-33-148/S0025-5718-1979-0537980-7/S0025-5718-1979-0537980-7.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_119.pdf))

b	lengths of the generalized repunit primes in base b (written in base 10)	search limit	OEIS sequence
2	2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161, ..., 74207281, ..., 77232917, ..., 82589933, ... (the Mersenne primes (https://en.wikipedia.org/wiki/Mersenne_prime, https://t5k.org/glossary/xpage/MersenneNumber.html, https://t5k.org/glossary/xpage/Mersennes.html, https://www.rieselprime.de/ziki/Mersenne_number, https://www.rieselprime.de/ziki/Mersenne_prime, https://mathworld.wolfram.com/MersenneNumber.html, https://mathworld.wolfram.com/MersennePrime.html, https://pzktupel.de/Primetables/TableMersenne.php, https://t5k.org/top20/page.php?id=4, https://t5k.org/primes/search.php?Comment=Mersenne%20[[:digit:]]&OnList=all&Number=1000000&Style=HTML, https://www.mersenne.org/, https://www.mersenne.ca/, https://www.mersenne.org/primes/, https://www.mersenne.ca/prime.php, https://t5k.org/mersenne/), all are definitely primes, i.e. not merely probable primes)	68450071	https://oeis.org/A000043
3	3, 7, 13, 71, 103, 541, 1091, 1367, 1627, 4177, 9011, 9551, 36913, 43063, 49681, 57917, 483611, 877843, 2215303, 2704981, 3598867, 7973131, 8530117, ...	8530117	https://oeis.org/A028491
4	2 (this is all, since (4ⁿ−1)/3 = (2ⁿ−1) × (2ⁿ+1) / 3, and both 2ⁿ−1 and 2ⁿ+1 are > 3 for n > 2, thus this factorization is nontrivial for n > 2)	(infinity)	–
5	3, 7, 11, 13, 47, 127, 149, 181, 619, 929, 3407, 10949, 13241, 13873, 16519, 201359, 396413, 1888279, 3300593, 4939471, 5154509, ...	5154509	https://oeis.org/A004061
6	2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099, 1365019, 3360347, ...	3360347	https://oeis.org/A004062
7	5, 13, 131, 149, 1699, 14221, 35201, 126037, 371669, 1264699, ...	1264699	https://oeis.org/A004063
8	3 (this is all, since (8ⁿ−1)/7 = (2ⁿ−1) × (4ⁿ+2ⁿ+1) / 7, and both 2ⁿ−1 and 4ⁿ+2ⁿ+1 are > 7 for n > 3, thus this factorization is nontrivial for n > 3, it only remains to check the cases n = 2 and n = 3, but (8²−1)/7 = 9 = 3² is not prime)	(infinity)	–
9	not exist (since (9ⁿ−1)/8 = (3ⁿ−1) × (3ⁿ+1) / 8, and both 3ⁿ−1 and 3ⁿ+1 are > 8 for n > 2, thus this factorization is nontrivial for n > 2, it only remains to check the case n = 2, but (9²−1)/8 = 10 = 2 × 5 is not prime)	(infinity)	–
10	2, 19, 23, 317, 1031, 49081, 86453, 109297, 270343, 5794777, 8177207, ...	10800000	https://oeis.org/A004023
11	17, 19, 73, 139, 907, 1907, 2029, 4801, 5153, 10867, 20161, 293831, 1868983, ...	1868983	https://oeis.org/A005808
12	2, 3, 5, 19, 97, 109, 317, 353, 701, 9739, 14951, 37573, 46889, 769543, ...	1000000	https://oeis.org/A004064
13	5, 7, 137, 283, 883, 991, 1021, 1193, 3671, 18743, 31751, 101089, 1503503, ...	1503503	https://oeis.org/A016054
14	3, 7, 19, 31, 41, 2687, 19697, 59693, 67421, 441697, ...	1000000	https://oeis.org/A006032
15	3, 43, 73, 487, 2579, 8741, 37441, 89009, 505117, 639833, ...	1000000	https://oeis.org/A006033
16	2 (this is all, since (16ⁿ−1)/15 = (4ⁿ−1) × (4ⁿ+1) / 15, and both 4ⁿ−1 and 4ⁿ+1 are > 15 for n > 2, thus this factorization is nontrivial for n > 2)	(infinity)	–
17	3, 5, 7, 11, 47, 71, 419, 4799, 35149, 54919, 74509, 1990523, ...	1990523	https://oeis.org/A006034
18	2, 25667, 28807, 142031, 157051, 180181, 414269, 1270141, ...	1270141	https://oeis.org/A133857
19	19, 31, 47, 59, 61, 107, 337, 1061, 9511, 22051, 209359, ...	1000000	https://oeis.org/A006035
20	3, 11, 17, 1487, 31013, 48859, 61403, 472709, 984349, ...	1000000	https://oeis.org/A127995
21	3, 11, 17, 43, 271, 156217, 328129, ...	1000000	https://oeis.org/A127996
22	2, 5, 79, 101, 359, 857, 4463, 9029, 27823, ...	1000000	https://oeis.org/A127997
23	5, 3181, 61441, 91943, 121949, 221411, ...	1000000	https://oeis.org/A204940
24	3, 5, 19, 53, 71, 653, 661, 10343, 49307, 115597, 152783, ...	1000000	https://oeis.org/A127998
25	not exist (since (25ⁿ−1)/24 = (5ⁿ−1) × (5ⁿ+1) / 24, and both 5ⁿ−1 and 5ⁿ+1 are > 24 for n > 2, thus this factorization is nontrivial for n > 2, it only remains to check the case n = 2, but (25²−1)/24 = 26 = 2 × 13 is not prime)	(infinity)	–
26	7, 43, 347, 12421, 12473, 26717, ...	1000000	https://oeis.org/A127999
27	3 (this is all, since (27ⁿ−1)/26 = (3ⁿ−1) × (9ⁿ+3ⁿ+1) / 26, and both 3ⁿ−1 and 9ⁿ+3ⁿ+1 are > 26 for n > 3, thus this factorization is nontrivial for n > 3, it only remains to check the cases n = 2 and n = 3, but (27²−1)/26 = 28 = 2²×7 is not prime)	(infinity)	–
28	2, 5, 17, 457, 1423, 115877, ...	1000000	https://oeis.org/A128000
29	5, 151, 3719, 49211, 77237, ...	1000000	https://oeis.org/A181979
30	2, 5, 11, 163, 569, 1789, 8447, 72871, 78857, 82883, ...	1000000	https://oeis.org/A098438
31	7, 17, 31, 5581, 9973, 54493, 101111, 535571, ...	1000000	https://oeis.org/A128002
32	not exist (since (32ⁿ−1)/31 = (2ⁿ−1) × (16ⁿ+8ⁿ+4ⁿ+2ⁿ+1) / 31, and both 2ⁿ−1 and 16ⁿ+8ⁿ+4ⁿ+2ⁿ+1 are > 31 for n > 5, thus this factorization is nontrivial for n > 5, it only remains to check the cases n = 2 and n = 3 and n = 4 and n = 5, but (32²−1)/31 = 33 = 3 × 11 and (32³−1)/31 = 1057 = 7 × 151 and (32⁴−1)/31 = 33825 = 3 × 5² × 11 × 41 and (32⁵−1)/31 = 1082401 = 601 × 1801 are not primes)	(infinity)	–
33	3, 197, 3581, 6871, 183661, ...	1000000	https://oeis.org/A209120
34	13, 1493, 5851, 6379, 125101, ...	1000000	https://oeis.org/A185073
35	313, 1297, 568453, ...	1000000	https://oeis.org/A348170
36	2 (this is all, since (36ⁿ−1)/35 = (6ⁿ−1) × (6ⁿ+1) / 35, and both 6ⁿ−1 and 6ⁿ+1 are > 35 for n > 2, thus this factorization is nontrivial for n > 2)	(infinity)	–

The following is a "semi-algorithm" (https://en.wikipedia.org/wiki/Semi-algorithm) that is guaranteed to produce the minimal elements of a arbitrary set of strings under the subsequence ordering, but it is not so easy to implement:

M := ∅
while (L ≠ ∅) do
choose x, a shortest string in L
M := M ∪ {x}
L := L − sup({x})

In practice, for arbitrary L, we cannot feasibly carry out step 5. Instead, we work with L', some regular overapproximation to L, until we can show L' = ∅ (which implies L = ∅). In practice, L' is usually chosen to be a finite union of sets of the form L₁{L₂}L₃, where each of L₁, L₂, L₃ is finite. In the case we consider in this project, we then have to determine whether such a family contains a prime > b or not.

To solve this problem (i.e. to compute (https://en.wikipedia.org/wiki/Computing) the set of the minimal elements of the base b representations of the prime numbers > b under the subsequence ordering), we need to determine whether a given family contains a prime. In practice, if family x{Y}z (where x and z are strings (may be empty) of digits in base b, Y is a set of digits in base b) could not be ruled out as only containing composites and Y contains two or more digits, then a relatively small prime > b could always be found in this family. Intuitively, this is because there are a large number of small strings in such a family, and at least one is likely to be prime (e.g. there are 2ⁿ⁻² strings of length n in the family 1{3,7}9, and there are over a thousand strings of length 12 in the family 1{3,7}9, thus it is very impossible that these numbers are all composite). In the case Y contains only one digit, this family is of the form x{y}z, and there is only a single string of each length > (the length of x + the length of z), and it is not known if the following decision problem (https://en.wikipedia.org/wiki/Decision_problem, https://mathworld.wolfram.com/DecisionProblem.html) is recursively solvable:

(Currently, whether 65537 is the largest Fermat prime, whether there are infinitely many Mersenne primes, whether 78557 is the smallest Sierpinski number, whether 509203 is the smallest Riesel number, are all unsolved problems (https://en.wikipedia.org/wiki/Open_problem, https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics, https://t5k.org/glossary/xpage/OpenQuestion.html, https://mathworld.wolfram.com/UnsolvedProblems.html, http://www.numericana.com/answer/open.htm, https://t5k.org/notes/conjectures/))

x	y	z	answer	factorization of the first 200 numbers in this family (n is the number of digits in the "{}", start with the smallest allowed n in the table (usually n = 0, unless other n are mentioned))
5028	0	1	Yes! But the smallest such prime is very large, it is 50280₈₃₉₈₁1, its algebraic form is 5028×10⁸³⁹⁸²+1, its factordb entry is http://factordb.com/index.php?id=1100000000765961536, it can be proven prime by the N−1 primality proving (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1)	http://factordb.com/index.php?query=5028*10%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7018	9	𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string))	Yes! But the smallest such prime is very large, it is 70189₈₈₁₃₀₉, its algebraic form is 7019×10⁸⁸¹³⁰⁹−1, its factordb entry is http://factordb.com/index.php?id=1100000000628445542, it can be proven prime by the N+1 primality proving (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2)	http://factordb.com/index.php?query=7019*10%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9175	0	1	No! All numbers of this form is divisible by some element of {7,11,13,37}, since the algebraic form of this family is 9175×10ⁿ⁺¹+1, it is divisible by 7 if n == 3 mod 6, divisible by 11 if n == 0 mod 2, divisible by 13 if n == 1 mod 6, divisible by 37 if n == 2 mod 3	http://factordb.com/index.php?query=9175*10%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
10175	9	𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string))	No! All numbers of this form is divisible by some element of {7,11,13,37}, since the algebraic form of this family is 10176×10ⁿ−1, it is divisible by 7 if n == 1 mod 6, divisible by 11 if n == 0 mod 2, divisible by 13 if n == 5 mod 6, divisible by 37 if n == 0 mod 3	http://factordb.com/index.php?query=10176*10%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7666	0	1	Nobody knows! We cannot find a prime in this family, nor can prove that this family only contain composites (by covering congruence, algebraic factorization, or combine of them), the algebraic form of this family is 7666×10ⁿ⁺¹+1, and if such prime exists, then it must have n > 5000000	http://factordb.com/index.php?query=7666*10%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
4420	9	𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string))	Nobody knows! We cannot find a prime in this family, nor can prove that this family only contain composites (by covering congruence, algebraic factorization, or combine of them), the algebraic form of this family is 4421×10ⁿ−1, and if such prime exists, then it must have n > 4100000	http://factordb.com/index.php?query=4421*10%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	1	7	Yes! But the smallest such prime is very large, it is 71₁₀₉₀₅7, its algebraic form is (64×10¹⁰⁹⁰⁶+53)/9, its factordb entry is http://factordb.com/index.php?id=1000000000008860930, its primality certificate is http://factordb.com/cert.php?id=1000000000008860930 and https://stdkmd.net/nrr/cert/7/71117_10906.zip	http://factordb.com/index.php?query=%2864*10%5E%28n%2B1%29%2B53%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	4	9	No! All numbers of this form is divisible by some element of {3,7,11,13}, since the algebraic form of this family is (85×10ⁿ⁺¹+41)/9, it is divisible by 3 if n == 0 mod 3, divisible by 7 if n == 5 mod 6, divisible by 11 if n == 0 mod 2, divisible by 13 if n == 1 mod 6	http://factordb.com/index.php?query=%2885*10%5E%28n%2B1%29%2B41%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
1	0 (at least two 0)	1	Nobody knows! We cannot find a prime in this family, nor can prove that this family only contain composites (by covering congruence, algebraic factorization, or combine of them), the algebraic form of this family is 10ⁿ⁺¹+1, and if such prime exists, then it must have n ≥ 2147483648	http://factordb.com/index.php?query=10%5E%28n%2B1%29%2B1&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
56	1	𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string))	Yes! But the smallest such prime is very large, it is 561₁₈₄₇₀, its algebraic form is (505×10¹⁸⁴⁷⁰−1)/9, its factordb entry is http://factordb.com/index.php?id=1100000000301454592, its primality certificate is http://factordb.com/cert.php?id=1100000000301454592 and https://stdkmd.net/nrr/cert/5/56111_18470.zip	http://factordb.com/index.php?query=%28505*10%5En-1%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
38	1	𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string))	No! All numbers of this form is either divisible by some element of {3,37} or has a difference-of-two-cubes factorization, since the algebraic form of this family is (343×10ⁿ−1)/9, it is divisible by 3 if n == 1 mod 3, divisible by 37 if n == 2 mod 3, and can be factored to (343×10ⁿ−1)/9 = (7×10^n/3−1) × (49×10^2×n/3+7×10^n/3+1) / 9 if n == 0 mod 3	http://factordb.com/index.php?query=%28343*10%5En-1%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
176	1	𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string))	No! All numbers of this form is divisible by some element of {3,7,11,13}, since the algebraic form of this family is (1585×10ⁿ−1)/9, it is divisible by 3 if n == 1 mod 3, divisible by 7 if n == 5 mod 6, divisible by 11 if n == 0 mod 2, divisible by 13 if n == 3 mod 6	http://factordb.com/index.php?query=%281585*10%5En-1%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
603	1	𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string))	Nobody knows! We cannot find a prime in this family, nor can prove that this family only contain composites (by covering congruence, algebraic factorization, or combine of them), the algebraic form of this family is (5428×10ⁿ−1)/9, and if such prime exists, then it must have n > 300000	http://factordb.com/index.php?query=%285428*10%5En-1%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string))	2	99	Yes! But the smallest such prime is very large, it is 2₁₉₁₅₁99, its algebraic form is (2×10¹⁹¹⁵³+691)/9, its factordb entry is http://factordb.com/index.php?id=1100000000301493137, its primality certificate is http://factordb.com/cert.php?id=1100000000301493137 and https://stdkmd.net/nrr/cert/2/2w99_19153.zip	http://factordb.com/index.php?query=%282*10%5E%28n%2B2%29%2B691%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string))	5 (at least one 5)	37	No! All numbers of this form is divisible by some element of {3,7,13,37}, since the algebraic form of this family is (5×10ⁿ⁺²−167)/9, it is divisible by 3 if n == 1 mod 3, divisible by 7 if n == 2 mod 6, divisible by 13 if n == 5 mod 6, divisible by 37 if n == 0 mod 3	http://factordb.com/index.php?query=%285*10%5E%28n%2B2%29-167%29%2F9&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
44	9 (at least two 9)	𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string))	Yes! But the smallest such prime is very large, it is 449₁₁₉₅₉, its algebraic form is 45×10¹¹⁹⁵⁹−1, its factordb entry is http://factordb.com/index.php?id=1100000000291927010, it can be proven prime by the N+1 primality proving (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2)	http://factordb.com/index.php?query=45*10%5En-1&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
421	0	3	Almost surely Yes! But the smallest such (probable) prime is very large, it is 4210₁₆₀₁₉3, its algebraic form is 421×10¹⁶⁰²⁰+3, its factordb entry is http://factordb.com/index.php?id=1100000002392921307, but since this number is only a probable prime and not definitely prime, we cannot definitely say "Yes!" (this family has no known definitely prime)	http://factordb.com/index.php?query=421*10%5E%28n%2B1%29%2B3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
404	0	3	No! All numbers of this form is divisible by some element of {7,11,13,37}, since the algebraic form of this family is 404×10ⁿ⁺¹+3, it is divisible by 7 if n == 5 mod 6, divisible by 11 if n == 0 mod 2, divisible by 13 if n == 1 mod 6, divisible by 37 if n == 0 mod 3	http://factordb.com/index.php?query=404*10%5E%28n%2B1%29%2B3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
99	4	99	Almost surely Yes! But the smallest such (probable) prime is very large, it is 994₃₄₀₁₉99, its algebraic form is (895×10³⁴⁰²¹+491)/9, its factordb entry is http://factordb.com/index.php?id=1100000002454717990, but since this number is only a probable prime and not definitely prime, we cannot definitely say "Yes!" (this family has no known definitely prime)	http://factordb.com/index.php?query=%28895*10%5E%28n%2B2%29%2B491%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
2	5	67	Nobody knows! We cannot find a prime in this family, nor can prove that this family only contain composites (by covering congruence, algebraic factorization, or combine of them), the algebraic form of this family is (23×10ⁿ⁺²+103)/9, and if such prime exists, then it must have n > 30000	http://factordb.com/index.php?query=%2823*10%5E%28n%2B2%29%2B103%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	1	83	Almost surely Yes! But the smallest such (probable) prime is very large, it is 71₁₈₄₆₆83, its algebraic form is (64×10¹⁸⁴⁶⁸+647)/9, its factordb entry is http://factordb.com/index.php?id=1100000000301454024, but since this number is only a probable prime and not definitely prime, we cannot definitely say "Yes!" (this family has no known definitely prime)	http://factordb.com/index.php?query=%2864*10%5E%28n%2B2%29%2B647%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
3	2	01	No! All numbers of this form is divisible by some element of {3,7,11,13}, since the algebraic form of this family is (29×10ⁿ⁺²−191)/9, it is divisible by 3 if n == 1 mod 3, divisible by 7 if n == 0 mod 6, divisible by 11 if n == 1 mod 2, divisible by 13 if n == 2 mod 6	http://factordb.com/index.php?query=%2829*10%5E%28n%2B2%29-191%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show

(however, it can be shown that there is no base b ≥ 2 and family xy_nz (with fixed strings x, z (may be empty), fixed digit y, and variable n) in base b (x does not start with the digit 0, z ends with a digit which coprime to b, y is not 0 if x is empty, y is coprime to b if z is empty) which only contains primes, moreover, it can be shown that there is no base b ≥ 2 and family xy_nz (with fixed strings x, z (may be empty), fixed digit y, and variable n) in base b (x does not start with the digit 0, z ends with a digit which coprime to b, y is not 0 if x is empty, y is coprime to b if z is empty) which is prime for almost all (https://en.wikipedia.org/wiki/Almost_all, https://mathworld.wolfram.com/AlmostAll.html) n, since the number xy_nz with the smallest n making xy_nz > b (if n = 0 already makes xy_nz > b, then n = 0) (i.e. n = 2 if both x and z are empty, n = 1 if one of x and z is empty, the other has length 1, n = 0 otherwise) is > b and coprime to b, thus xy_nz must have a prime factor p which does not divide b, and if p divides b−1, then p divides xy_k×p+nz for all natural number k, otherwise, p divides xy_{k×ord_p(b)+n}z for all natural number k (where ord_p(b) is the multiplicative order (https://en.wikipedia.org/wiki/Multiplicative_order, https://t5k.org/glossary/xpage/Order.html, https://mathworld.wolfram.com/MultiplicativeOrder.html, http://www.numbertheory.org/php/order.html, https://oeis.org/A250211, https://oeis.org/A139366, https://oeis.org/A323376, https://oeis.org/A057593, https://oeis.org/A086145) of b mod p), thus there must be infinitely many composites in the family xy_nz, this theorem also proves that there is no (first kind or second kind) Cunningham chain (https://en.wikipedia.org/wiki/Cunningham_chain, https://t5k.org/glossary/xpage/CunninghamChain.html, https://mathworld.wolfram.com/CunninghamChain.html, https://t5k.org/top20/page.php?id=19, https://t5k.org/top20/page.php?id=20, https://t5k.org/primes/search.php?Comment=Cunningham%20chain&OnList=all&Number=1000000&Style=HTML, https://www.pzktupel.de/JensKruseAndersen/CC.php, http://www.primerecords.dk/Cunningham_Chain_records.htm, http://www.primenumbers.net/Henri/us/NouvTh1us.htm, https://web.archive.org/web/20050406075848/http://ksc9.th.com/warut/cunningham.html, https://oeis.org/A005602, https://oeis.org/A005603, https://oeis.org/A057331, https://oeis.org/A057330) with infinite length, since the first kind Cunningham chain is b = 2, y = 1, z = 𝜆 (the empty string (https://en.wikipedia.org/wiki/Empty_string)), with any given x, and the second kind Cunningham chain is b = 2, y = 0, z = 1, with any given x, also, for a proof for the special case of b = 2, y = 0, either x or z (or both) is 1, of this theorem, see https://oeis.org/A076336/a076336.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_377.pdf))

My conjecture: If family xy_nz (with fixed strings x, z (may be empty), fixed digit y, and variable n) in base b (with fixed b ≥ 2) (x does not start with the digit 0, z ends with a digit which coprime to b, y is not 0 if x is empty, y is coprime to b if z is empty) cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then family xy_nz in base b contains infinitely many primes (this is equivalent to: If form (a×bⁿ+c)/gcd(a+c,b−1) (with fixed integers a ≥ 1, b ≥ 2, c ≠ 0 (with gcd(a,c) = 1 and gcd(b,c) = 1), and variable n) cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then form (a×bⁿ+c)/gcd(a+c,b−1) contains infinitely many primes)

(of course, I hope that this conjecture is true, but this conjecture appears to be harder than the Schinzel's hypothesis H (https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H, https://mathworld.wolfram.com/SchinzelsHypothesis.html, http://www.numericana.com/answer/open.htm#h) and even the Bateman–Horn conjecture (https://en.wikipedia.org/wiki/Bateman%E2%80%93Horn_conjecture), and in fact, no single case is proven to contain infinitely many primes, like the Bunyakovsky conjecture (https://en.wikipedia.org/wiki/Bunyakovsky_conjecture, https://mathworld.wolfram.com/BouniakowskyConjecture.html) and the Dickson's conjecture (https://en.wikipedia.org/wiki/Dickson%27s_conjecture, https://t5k.org/glossary/xpage/DicksonsConjecture.html), no single case is proven to contain infinitely many primes, except the cases in the Dirichlet's theorem (https://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions, https://t5k.org/glossary/xpage/DirichletsTheorem.html, https://mathworld.wolfram.com/DirichletsTheorem.html, http://www.numericana.com/answer/primes.htm#dirichlet) (i.e. the polynomials with degree (https://en.wikipedia.org/wiki/Degree_of_a_polynomial, https://mathworld.wolfram.com/PolynomialDegree.html) 1 in the Bunyakovsky conjecture, or the set with 1 polynomial in the Dickson's conjecture))

(Note: Families with higher Nash weight (https://www.rieselprime.de/ziki/Nash_weight, http://irvinemclean.com/maths/nash.htm, http://www.brennen.net/primes/ProthWeight.html, https://www.mersenneforum.org/showthread.php?t=11844, https://www.mersenneforum.org/showthread.php?t=2645, https://www.mersenneforum.org/showthread.php?t=7213, https://www.mersenneforum.org/showthread.php?t=18818, https://www.mersenneforum.org/showpost.php?p=50442&postcount=1, https://www.mersenneforum.org/showpost.php?p=50444&postcount=1, https://www.mersenneforum.org/showpost.php?p=201642&postcount=1, https://www.mersenneforum.org/attachment.php?attachmentid=13663&d=1451910741, https://github.com/happy5214/nash, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/allnash, https://www.rieselprime.de/ziki/Riesel_2_Low-weight, https://www.rieselprime.de/ziki/Proth_2_Low-weight, https://www.rieselprime.de/ziki/Category:Riesel_2_Low-weight, https://www.rieselprime.de/ziki/Category:Proth_2_Low-weight, https://www.rieselprime.de/ziki/Category:Riesel_5_Low-weight, https://www.rieselprime.de/ziki/Category:Proth_5_Low-weight, https://web.archive.org/web/20230928115952/http://www.noprimeleftbehind.net/crus/vstats_new/riesel_weights.txt, https://web.archive.org/web/20230928120009/http://www.noprimeleftbehind.net/crus/vstats_new/sierpinski_weights.txt, https://arxiv.org/pdf/2307.07894.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_203.pdf), https://web.archive.org/web/20231002020455/http://yves.gallot.pagesperso-orange.fr/papers/weight.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_216.pdf)) (or difficulty (https://stdkmd.net/nrr/prime/prime_difficulty.htm, https://stdkmd.net/nrr/prime/prime_difficulty.txt, https://web.archive.org/web/20240305201107/https://stdkmd.net/nrr/prime/primedifficulty.htm, https://web.archive.org/web/20240305201027/https://stdkmd.net/nrr/prime/primedifficulty.txt, http://www.noprimeleftbehind.net/crus/vstats_new/crus-unproven.htm, https://web.archive.org/web/20230928120025/http://www.noprimeleftbehind.net/crus/vstats_new/riesel_difficulty.txt, https://web.archive.org/web/20230928120047/http://www.noprimeleftbehind.net/crus/vstats_new/sierpinski_difficulty.txt)) usually have smaller first prime (since the expected number of primes in a given range of n is larger, thus the expected number of the smallest n such that this family gives prime is smaller), but not always, e.g. the base 16 family {3}AF has Nash weight (or difficulty) higher than the base 16 family {4}DD, but the base 16 family {3}AF has the first (probable) prime at length 116139, while the base 16 family {4}DD has the first (probable) prime at length 72787)

(Note: Although most mathematician think that there are only finitely many Fermat primes, and possibly there are only the five known ones (i.e. 3, 5, 17, 257, 65537), and more generally, there are only finitely many generalized Fermat primes to any even base b, and there are only finitely many generalized half Fermat primes to any odd base b (if there are only finitely many generalized Fermat primes to any even base b, and there are only finitely many generalized half Fermat primes to any odd base b, then the unsolved family {F}G in base b = 31 and then the unsolved family 4{0}1 in base b = 32 and then the unsolved family G{0}1 in base b = 32 may have no primes), see https://www.mersenneforum.org/showpost.php?p=116415&postcount=1 and https://www.mersenneforum.org/showpost.php?p=447711&postcount=5 and https://www.mersenneforum.org/showpost.php?p=412191&postcount=3 and https://www.mersenneforum.org/showpost.php?p=447998&postcount=38 and https://www.mersenneforum.org/showpost.php?p=586121&postcount=16 and http://jeppesn.dk/generalized-fermat.html and https://www.primepuzzles.net/conjectures/conj_004.htm and https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf) and https://arxiv.org/pdf/1605.01371.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_29.pdf) and https://oeis.org/A171381 and https://oeis.org/A182331 and https://oeis.org/A078680 and https://oeis.org/history?seq=A257495 (the discussion by Thomas Ordowski at Wed Jun 05 01:18), but I do not think that, since I do not believe that in the sea of infinity, there are no single n > 4 such that 2^2ⁿ+1 is prime, also, all of "Is there an n > 0 such that 38ⁿ+1 is prime?", "Is there an n > 0 such that 50ⁿ+1 is prime?", "Is there an n > 0 such that 21181×2ⁿ+1 is prime?", "Is there an n > 0 such that 1597×6ⁿ−1 is prime?", "Is there an n > 0 such that 4×32ⁿ+1 is prime?", "Is there an n > 0 such that 4×53ⁿ+1 is prime?", "Is there an n > 0 such that 23ⁿ+458 is prime?", "Is there an n > 0 such that 38ⁿ+31 is prime?" are open problems (https://en.wikipedia.org/wiki/Open_problem, https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics, https://t5k.org/glossary/xpage/OpenQuestion.html, https://mathworld.wolfram.com/UnsolvedProblems.html, http://www.numericana.com/answer/open.htm, https://t5k.org/notes/conjectures/), since currently there is no known n > 0 such that these formulas give primes, and currently it cannot be proven that there is no n > 0 such that these formulas give primes, their situation are completely the same (for all these forms, nobody knows whether there is such an n or not!), while "Is there an n > 0 such that 78557×2ⁿ+1 is prime?", "Is there an n > 0 such that 84687×6ⁿ−1 is prime?", "Is there an n > 0 such that 8ⁿ+1 is prime?", "Is there an n > 0 such that 4×9ⁿ−1 is prime?", "Is there an n > 0 such that 25×12ⁿ−1 is prime?", "Is there an n > 0 such that (9ⁿ−1)/8 is prime?", "Is there an n > 0 such that 10223×2ⁿ+1 is prime?", "Is there an n > 0 such that 36772×6ⁿ−1 is prime?", "Is there an n > 0 such that 8×23ⁿ+1 is prime?", "Is there an n > 0 such that 25×30ⁿ−1 is prime?", "Is there an n > 0 such that 17ⁿ+32 is prime?", "Is there an n > 0 such that 29ⁿ+10 is prime?" are not open problems (https://en.wikipedia.org/wiki/Open_problem, https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics, https://t5k.org/glossary/xpage/OpenQuestion.html, https://mathworld.wolfram.com/UnsolvedProblems.html, http://www.numericana.com/answer/open.htm, https://t5k.org/notes/conjectures/), since the answer of them are currently known ("No" for the first four, "Yes" for the last four), and there are known proofs (https://en.wikipedia.org/wiki/Mathematical_proof, https://mathworld.wolfram.com/Proof.html, https://t5k.org/notes/proofs/) of them, thus they are solved problems, maybe the smallest n > 4 such that 2^2ⁿ+1 is prime is around googol (https://en.wikipedia.org/wiki/Googol, https://mathworld.wolfram.com/Googol.html), or around googolplex (https://en.wikipedia.org/wiki/Googolplex, https://mathworld.wolfram.com/Googolplex.html), or around Graham's number (https://en.wikipedia.org/wiki/Graham%27s_number, https://mathworld.wolfram.com/GrahamsNumber.html), or around TREE(3) (https://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem, https://mathworld.wolfram.com/KruskalsTreeTheorem.html)? I think that every family xy_nz (with fixed strings x, z (may be empty), fixed digit y, and variable n) in every base b (with fixed b ≥ 2) contains infinitely many primes unless this family can be proven to only contain composites or only contain finitely many primes, by covering congruence, algebraic factorization, or combine of them (of course, there are also generalized Fermat forms and generalized half Fermat forms which can be proven to only contain composites (whose situation are different to other generalized Fermat forms and generalized half Fermat forms, and the same to other forms which can be proven to only contain composites or only contain finitely many primes, e.g. the situation of 78557×2ⁿ+1 and 84687×6ⁿ−1 and 8ⁿ+1 and 4×9ⁿ−1 are the same (since all of them can be proven to only contain composites, although the reason of they can be proven to only contain composites are not completely the same, the reason is "covering congruence" for the first two and "algebraic factorization" for the last two), while the situation of 8ⁿ+1 and 38ⁿ+1 are different (since 8ⁿ+1 can be proven to only contain composites, while 38ⁿ+1 cannot), the situation of 38ⁿ+1 and 21181×2ⁿ+1 and 1597×6ⁿ−1 and 4×32ⁿ+1 are the same (since whether they contain a prime are open problems, currently there is no known n such that they give primes, and currently it cannot be proven that there is no n such that they give primes)), note the difference of them, see https://www.mersenneforum.org/showpost.php?p=210408&postcount=45 and https://www.mersenneforum.org/showpost.php?p=199373&postcount=67), see https://web.archive.org/web/20160418084212/http://staff.spd.dcu.ie/johnbcos/download/Fermat%20material/Fermat%206/Fermat_6.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_465.pdf) and https://oeis.org/A234285 (the comment by Farideh Firoozbakht, although this comment is not true, there is no prime for s = 509203 and s = −78557, s = 509203 has a covering set of {3, 5, 7, 13, 17, 241}, and s = −78557 has a covering set of {3, 5, 7, 13, 19, 37, 73}))

(this conjecture is for exponential sequences (https://en.wikipedia.org/wiki/Exponential_growth, https://mathworld.wolfram.com/ExponentialGrowth.html) (a×bⁿ+c)/gcd(a+c,b−1) (with fixed integers a ≥ 1, b ≥ 2, c ≠ 0, gcd(a, c) = 1, gcd(b, c) = 1, and variable n), there is also a similar conjecture for polynomial sequences (https://en.wikipedia.org/wiki/Polynomial, https://mathworld.wolfram.com/Polynomial.html) a₀+a₁x+a₂x²+a₃x³+...+a_n−1xⁿ⁻¹+a_nxⁿ (with fixed n, a₀, a₁, a₂, ..., a_n and variable x): the Bunyakovsky conjecture (https://en.wikipedia.org/wiki/Bunyakovsky_conjecture, https://mathworld.wolfram.com/BouniakowskyConjecture.html), the condition is similar to this conjecture (divisible by small primes and algebraic factorizations), the main difference is that polynomial sequence cannot have a covering congruence with > 1 primes, nor have a combine of covering congruence and algebraic factorization)

This conjecture will imply:

There are infinitely many Mersenne primes (i.e. primes of the form 2^p−1 with prime p) (https://en.wikipedia.org/wiki/Mersenne_prime, https://t5k.org/glossary/xpage/MersenneNumber.html, https://t5k.org/glossary/xpage/Mersennes.html, https://www.rieselprime.de/ziki/Mersenne_number, https://www.rieselprime.de/ziki/Mersenne_prime, https://mathworld.wolfram.com/MersenneNumber.html, https://mathworld.wolfram.com/MersennePrime.html, https://pzktupel.de/Primetables/TableMersenne.php, https://t5k.org/top20/page.php?id=4, https://t5k.org/primes/search.php?Comment=Mersenne%20[[:digit:]]&OnList=all&Number=1000000&Style=HTML, https://www.mersenne.org/, https://www.mersenne.ca/, https://www.mersenne.org/primes/, https://www.mersenne.ca/prime.php, https://t5k.org/mersenne/) (https://oeis.org/A001348, https://oeis.org/A000668, https://oeis.org/A000043)
There are infinitely many Fermat primes (i.e. primes of the form 2^2ⁿ+1) (https://en.wikipedia.org/wiki/Fermat_number, https://t5k.org/glossary/xpage/FermatNumber.html, https://www.rieselprime.de/ziki/Fermat_number, https://mathworld.wolfram.com/FermatNumber.html, https://mathworld.wolfram.com/FermatPrime.html, https://pzktupel.de/Primetables/TableFermat.php, http://www.prothsearch.com/fermat.html, https://t5k.org/top20/page.php?id=8, https://t5k.org/primes/search.php?Comment=Divides&OnList=all&Number=1000000&Style=HTML, http://www.fermatsearch.org/, https://64ordle.au/fermat/, https://64ordle.au/fermat/small/, https://www.primegrid.com/forum_thread.php?id=8778, https://www.primegrid.com/stats_div_llr.php, https://www.primegrid.com/primes/primes.php?project=DIV&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.rieselprime.de/ziki/PrimeGrid_Fermat_Divisor_Search, http://www.fermatsearch.org/factors/faclist.php, http://www.fermatsearch.org/factors/composite.php) (https://oeis.org/A000215, https://oeis.org/A019434)
There are infinitely many generalized repunit primes (i.e. primes of the form (b^p−1)/(b−1) with prime p) (https://en.wikipedia.org/wiki/Repunit, https://en.wikipedia.org/wiki/List_of_repunit_primes, https://t5k.org/glossary/xpage/Repunit.html, https://t5k.org/glossary/xpage/GeneralizedRepunitPrime.html, https://www.rieselprime.de/ziki/Repunit, https://www.rieselprime.de/ziki/Generalized_Repunit, https://mathworld.wolfram.com/Repunit.html, https://mathworld.wolfram.com/RepunitPrime.html, https://pzktupel.de/Primetables/TableRepunit.php, https://pzktupel.de/Primetables/TableRepunitGen.php, https://pzktupel.de/Primetables/TableRepunitGen.txt, https://stdkmd.net/nrr/prime/prime_rp.htm, https://stdkmd.net/nrr/prime/prime_rp.txt, https://www.numbersaplenty.com/set/repunit/, https://stdkmd.net/nrr/repunit/repunitnote.htm#repunit, https://web.archive.org/web/20021001222643/http://www.users.globalnet.co.uk/~aads/index.html, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, https://web.archive.org/web/20021114005730/http://www.users.globalnet.co.uk/~aads/titans.html, https://web.archive.org/web/20021015210104/http://www.users.globalnet.co.uk/~aads/faclist.html, https://web.archive.org/web/20131019185910/http://www.primes.viner-steward.org/andy/titans.html, https://web.archive.org/web/20120227163453/http://phi.redgolpe.com/, https://web.archive.org/web/20120227163614/http://phi.redgolpe.com/5.asp, https://web.archive.org/web/20120227163508/http://phi.redgolpe.com/4.asp, https://web.archive.org/web/20120227163610/http://phi.redgolpe.com/3.asp, https://web.archive.org/web/20120227163512/http://phi.redgolpe.com/2.asp, https://web.archive.org/web/20120227163521/http://phi.redgolpe.com/1.asp, http://www.elektrosoft.it/matematica/repunit/repunit.htm, http://www.fermatquotient.com/PrimSerien/GenRepu.txt (in German), http://www.primenumbers.net/Henri/us/MersFermus.htm, https://jpbenney.blogspot.com/2022/04/another-sequence-of-note.html, http://perplexus.info/show.php?pid=8661&cid=51696, https://benvitalenum3ers.wordpress.com/2013/07/24/repunit-11111111111111-in-other-bases/, https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906, http://www.bitman.name/math/article/380/231/, http://www.bitman.name/math/table/379, https://www.ams.org/journals/mcom/1993-61-204/S0025-5718-1993-1185243-9/S0025-5718-1993-1185243-9.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_4.pdf), https://www.ams.org/journals/mcom/1979-33-148/S0025-5718-1979-0537980-7/S0025-5718-1979-0537980-7.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_119.pdf), https://t5k.org/top20/page.php?id=57, https://t5k.org/top20/page.php?id=16, https://t5k.org/primes/search.php?Comment=^Repunit&OnList=all&Number=1000000&Style=HTML, https://t5k.org/primes/search.php?Comment=Generalized%20repunit&OnList=all&Number=1000000&Style=HTML, https://oeis.org/A002275, https://oeis.org/A004022, https://oeis.org/A053696, https://oeis.org/A085104, https://oeis.org/A179625) to every base b ≥ 2 which is not a perfect power (i.e. of the form m^r with r > 1) (https://oeis.org/A001597, https://en.wikipedia.org/wiki/Perfect_power, https://mathworld.wolfram.com/PerfectPower.html, https://www.numbersaplenty.com/set/perfect_power/) (https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A246005, https://oeis.org/A065854, https://oeis.org/A279068, https://oeis.org/A360738, https://oeis.org/A279069, https://oeis.org/A065813, https://oeis.org/A128164, https://oeis.org/A285642)
There are infinitely many generalized Wagstaff primes (i.e. primes of the form (b^p+1)/(b+1) with odd prime p) (https://en.wikipedia.org/wiki/Wagstaff_prime, https://t5k.org/glossary/xpage/WagstaffPrime.html, https://mathworld.wolfram.com/WagstaffPrime.html, https://pzktupel.de/Primetables/TableWagstaff.php, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://pzktupel.de/Primetables/TableWagstaffGen.txt, https://web.archive.org/web/20211031110623/http://mprime.s3-website.us-west-1.amazonaws.com/wagstaff/, http://www.fermatquotient.com/PrimSerien/GenRepuP.txt (in German), http://www.primenumbers.net/Henri/us/MersFermus.htm, https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906, http://www.bitman.name/math/table/488, https://cs.uwaterloo.ca/journals/JIS/VOL3/DUBNER/dubner.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_5.pdf), http://primenumbers.net/Documents/TestNP.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_486.pdf), https://t5k.org/top20/page.php?id=67, https://t5k.org/primes/search.php?Comment=Wagstaff&OnList=all&Number=1000000&Style=HTML, https://oeis.org/A007583, https://oeis.org/A000979, https://oeis.org/A000978, https://oeis.org/A059054, https://oeis.org/A059055) to every base b ≥ 2 which is neither a perfect odd power (i.e. of the form m^r with odd r > 1) (http://mathworld.wolfram.com/OddPower.html, https://oeis.org/A070265) nor of the form 4×m⁴ (https://oeis.org/A141046) (https://oeis.org/A084742, https://oeis.org/A084741, https://oeis.org/A126659, https://oeis.org/A065507)
There are infinitely many generalized Fermat primes (i.e. primes of the form b^2ⁿ+1 with even b) (https://t5k.org/glossary/xpage/GeneralizedFermatNumber.html, https://t5k.org/glossary/xpage/GeneralizedFermatPrime.html, https://www.rieselprime.de/ziki/Generalized_Fermat_number, https://mathworld.wolfram.com/GeneralizedFermatNumber.html, https://web.archive.org/web/20231002145700/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN2.html, https://web.archive.org/web/20231003013719/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN4.html, https://web.archive.org/web/20231002025450/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN8.html, https://web.archive.org/web/20231002191037/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN16.html, https://web.archive.org/web/20231001124718/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN32.html, https://web.archive.org/web/20231002052635/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN64.html, https://web.archive.org/web/20231001214959/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN128.html, https://web.archive.org/web/20231002034106/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN256.html, https://web.archive.org/web/20231002050146/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN512.html, https://web.archive.org/web/20231001232540/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN1024.html, https://web.archive.org/web/20231002232625/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN2048.html, https://web.archive.org/web/20231002045835/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN4096.html, https://web.archive.org/web/20231002020236/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN8192.html, https://web.archive.org/web/20231002043908/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN16384.html, https://web.archive.org/web/20231001231140/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN32768.html, https://web.archive.org/web/20231003010910/https://yves.gallot.pagesperso-orange.fr/primes/GFN/GFN65536.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://web.archive.org/web/20230323021722/https://pzktupel.de/Primetables/TableFermatGF09.php, https://web.archive.org/web/20230323021722/https://pzktupel.de/Primetables/TableFermatGF10.php, https://pzktupel.de/Primetables/TableFermatGF11.php, https://pzktupel.de/Primetables/TableFermatGF12.php, https://pzktupel.de/Primetables/TableFermatGF13.php, https://pzktupel.de/Primetables/TableFermatGF14.php, https://pzktupel.de/Primetables/TableFermatGF15.php, https://pzktupel.de/Primetables/TableFermatGF16.php, https://pzktupel.de/Primetables/TableFermatGF17.php, https://pzktupel.de/Primetables/TableFermatGF1820.php, http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://web.archive.org/web/20231003030159/http://yves.gallot.pagesperso-orange.fr/primes/results.html, https://web.archive.org/web/20231001191355/http://yves.gallot.pagesperso-orange.fr/primes/stat.html, https://genefer.great-site.net/, https://www.primegrid.com/forum_thread.php?id=3980, https://www.primegrid.com/forum_thread.php?id=5674, https://www.primegrid.com/stats_genefer.php, https://www.primegrid.com/primes/primes.php?project=GFN&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.primegrid.com/primes/primes.php?project=GFN32768&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.primegrid.com/primes/primes.php?project=GFN65536&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.primegrid.com/primes/primes.php?project=GFN131072&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.primegrid.com/primes/primes.php?project=GFN262144&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.primegrid.com/primes/primes.php?project=GFN524288&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.primegrid.com/primes/primes.php?project=GFN1048576&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, http://boincvm.proxyma.ru:30080/test4vm/index.php, https://t5k.org/top20/page.php?id=12, https://t5k.org/primes/search.php?Comment=Generalized%20Fermat&OnList=all&Number=1000000&Style=HTML, http://www.prothsearch.com/fermat.html, http://www.prothsearch.com/GFN06.html, http://www.prothsearch.com/GFN10.html, http://www.prothsearch.com/GFN12.html, http://www.prothsearch.com/GFNfacs.html, http://www.prothsearch.com/GFNsmall.html, http://www.prothsearch.com/OriginalGFNs.html, https://web.archive.org/web/20070910080730/http://members.cox.net/jfoug/GFNFacts_Riesel.html, https://web.archive.org/web/20070914091821/http://members.cox.net/jfoug/GFNFacts_SearchLimits.html, https://web.archive.org/web/20070914092135/http://members.cox.net/jfoug/GFNFacts_ECMComposites.html, http://www.fermatsearch.org/factors/faclist.php, http://www.fermatsearch.org/factors/composite.php, https://www.alpertron.com.ar/MODFERM.HTM, https://web.archive.org/web/20160603062044/http://staff.spd.dcu.ie/johnbcos/fermat6.htm, https://www.rieselprime.de/ziki/PrimeGrid_Generalized_Fermat_Prime_Search, https://t5k.org/top20/page.php?id=8, https://t5k.org/top20/page.php?id=9, https://t5k.org/top20/page.php?id=10, https://t5k.org/top20/page.php?id=11, https://t5k.org/top20/page.php?id=18, https://t5k.org/top20/page.php?id=37, https://t5k.org/primes/search.php?Comment=Divides&OnList=all&Number=1000000&Style=HTML, https://oeis.org/A005574, https://oeis.org/A000068, https://oeis.org/A006314, https://oeis.org/A006313, https://oeis.org/A006315, https://oeis.org/A006316, https://oeis.org/A056994, https://oeis.org/A056995, https://oeis.org/A057465, https://oeis.org/A057002, https://oeis.org/A088361, https://oeis.org/A088362, https://oeis.org/A226528, https://oeis.org/A226529, https://oeis.org/A226530, https://oeis.org/A251597, https://oeis.org/A253854, https://oeis.org/A244150, https://oeis.org/A243959, https://oeis.org/A321323, https://oeis.org/A002496, https://oeis.org/A037896, https://oeis.org/A258805, https://oeis.org/A272137, https://oeis.org/A140797, https://oeis.org/A245730, https://oeis.org/A297625) to every even base b ≥ 2 which is not a perfect odd power (i.e. of the form m^r with odd r > 1) (http://mathworld.wolfram.com/OddPower.html, https://oeis.org/A070265) (https://oeis.org/A228101, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A123669)
There are infinitely many generalized half-Fermat primes (i.e. primes of the form (b^2ⁿ+1)/2 with odd b) (http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt (in German), http://www.prothsearch.com/GFN03.html, http://www.prothsearch.com/GFN05.html, http://www.prothsearch.com/GFN07.html, http://www.prothsearch.com/GFN11.html, http://www.prothsearch.com/GFNfacs.html, http://www.prothsearch.com/GFNsmall.html, http://www.prothsearch.com/OriginalGFNs.html, https://web.archive.org/web/20070910080730/http://members.cox.net/jfoug/GFNFacts_Riesel.html, https://web.archive.org/web/20070914091821/http://members.cox.net/jfoug/GFNFacts_SearchLimits.html, https://web.archive.org/web/20070914092135/http://members.cox.net/jfoug/GFNFacts_ECMComposites.html, https://t5k.org/top20/page.php?id=28, https://t5k.org/top20/page.php?id=29, https://t5k.org/top20/page.php?id=18, https://t5k.org/primes/search.php?Comment=Divides&OnList=all&Number=1000000&Style=HTML, https://oeis.org/A002731, https://oeis.org/A096169, https://oeis.org/A027862, https://oeis.org/A096170) to every odd base b ≥ 2 which is not a perfect odd power (i.e. of the form m^r with odd r > 1) (http://mathworld.wolfram.com/OddPower.html, https://oeis.org/A070265)
There are infinitely many Williams primes of the first kind (i.e. primes of the form (b−1)×bⁿ−1) (https://harvey563.tripod.com/wills.txt, https://www.rieselprime.de/ziki/Williams_prime_MM_least, https://www.rieselprime.de/ziki/Williams_prime_MM_table, https://pzktupel.de/Primetables/TableWilliams1.php, https://pzktupel.de/Primetables/Williams_1.txt, https://web.archive.org/web/20240126201427/https://pzktupel.de/Primetables/Williams1DB.txt, https://sites.google.com/view/williams-primes, http://matwbn.icm.edu.pl/ksiazki/aa/aa39/aa3912.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_9.pdf), https://www.ams.org/journals/mcom/2000-69-232/S0025-5718-00-01212-6/S0025-5718-00-01212-6.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_10.pdf), http://www.bitman.name/math/table/484 (in Italian)) to every base b ≥ 2 (https://oeis.org/A122396)
There are infinitely many Williams primes of the second kind (i.e. primes of the form (b−1)×bⁿ+1) (https://www.rieselprime.de/ziki/Williams_prime_MP_least, https://www.rieselprime.de/ziki/Williams_prime_MP_table, https://pzktupel.de/Primetables/TableWilliams2.php, https://pzktupel.de/Primetables/Williams_2.txt, https://web.archive.org/web/20240126201446/https://pzktupel.de/Primetables/Williams2DB.txt, https://sites.google.com/view/williams-primes, http://www.bitman.name/math/table/477 (in Italian)) to every base b ≥ 2 (https://oeis.org/A305531, https://oeis.org/A087139) (warning: this may be false, (b−1)×bⁿ+1 may be able to be proven to only contain composites by combine of covering congruence and algebraic factorization when b−1 is either a perfect odd power (i.e. of the form m^r with odd r > 1) (http://mathworld.wolfram.com/OddPower.html, https://oeis.org/A070265) or of the form 4×m⁴ (https://oeis.org/A141046), but the smallest such base b will be very large, however, this is at least true for bases b such that b−1 is neither a perfect odd power (i.e. of the form m^r with odd r > 1) (http://mathworld.wolfram.com/OddPower.html, https://oeis.org/A070265) nor of the form 4×m⁴ (https://oeis.org/A141046), also at least true for bases b ≤ 10⁶)
There are infinitely many Williams primes of the third kind (i.e. primes of the form (b+1)×bⁿ−1) (https://www.rieselprime.de/ziki/Williams_prime_PM_least, https://www.rieselprime.de/ziki/Williams_prime_PM_table, https://pzktupel.de/Primetables/TableWilliams3.php, https://pzktupel.de/Primetables/Williams_3.txt, https://web.archive.org/web/20240126201502/https://pzktupel.de/Primetables/Williams3DB.txt, https://sites.google.com/view/williams-primes, http://www.bitman.name/math/table/471 (in Italian)) to every base b ≥ 2
There are infinitely many Williams primes of the fourth kind (i.e. primes of the form (b+1)×bⁿ+1) (https://www.rieselprime.de/ziki/Williams_prime_PP_least, https://www.rieselprime.de/ziki/Williams_prime_PP_table, https://pzktupel.de/Primetables/TableWilliams4.php, https://pzktupel.de/Primetables/Williams_4.txt, https://web.archive.org/web/20240126201521/https://pzktupel.de/Primetables/Williams4DB.txt, https://sites.google.com/view/williams-primes, http://www.bitman.name/math/table/474 (in Italian)) to every base b ≥ 2 which is not == 1 mod 3 (warning: this may be false, (b+1)×bⁿ+1 may be able to be proven to only contain composites by covering congruence, like the case of 2×bⁿ+1 and bⁿ+2 for b = 201446503145165177, which has a covering set {3, 5, 17, 257, 641, 65537, 6700417}, however, this is at least true for bases b ≤ 10⁶)
There are infinitely many dual Williams primes of the first kind (i.e. primes of the form bⁿ−(b−1)) (https://pzktupel.de/Primetables/TableWilliams5.php, https://pzktupel.de/Primetables/W5DB.txt, https://web.archive.org/web/20231015225036/https://pzktupel.de/Primetables/Williams5DB.txt, https://sites.google.com/view/williams-primes, https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/792 (in Italian), http://www.bitman.name/math/table/435 (in Italian)) to every base b ≥ 2 (https://oeis.org/A113516, https://oeis.org/A343589)
There are infinitely many dual Williams primes of the second kind (i.e. primes of the form bⁿ+(b−1)) (https://pzktupel.de/Primetables/TableWilliams6.php, https://pzktupel.de/Primetables/W6DB.txt, https://web.archive.org/web/20231015225001/https://pzktupel.de/Primetables/Williams6DB.txt, https://sites.google.com/view/williams-primes, http://www.bitman.name/math/table/795 (in Italian)) to every base b ≥ 2 (https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179) (warning: this may be false, bⁿ+(b−1) may be able to be proven to only contain composites by combine of covering congruence and algebraic factorization when b−1 is either a perfect odd power (i.e. of the form m^r with odd r > 1) (http://mathworld.wolfram.com/OddPower.html, https://oeis.org/A070265) or of the form 4×m⁴ (https://oeis.org/A141046), but the smallest such base b will be very large, however, this is at least true for bases b such that b−1 is neither a perfect odd power (i.e. of the form m^r with odd r > 1) (http://mathworld.wolfram.com/OddPower.html, https://oeis.org/A070265) nor of the form 4×m⁴ (https://oeis.org/A141046), also at least true for bases b ≤ 10⁶)
There are infinitely many dual Williams primes of the third kind (i.e. primes of the form bⁿ−(b+1)) (https://pzktupel.de/Primetables/TableWilliams7.php, https://pzktupel.de/Primetables/W7DB.txt, https://web.archive.org/web/20231015224950/https://pzktupel.de/Primetables/Williams7DB.txt, https://sites.google.com/view/williams-primes, http://www.bitman.name/math/table/798 (in Italian)) to every base b ≥ 2 (https://oeis.org/A178250)
There are infinitely many dual Williams primes of the fourth kind (i.e. primes of the form bⁿ+(b+1)) (https://pzktupel.de/Primetables/TableWilliams8.php, https://pzktupel.de/Primetables/W8DB.txt, https://web.archive.org/web/20231015224944/https://pzktupel.de/Primetables/Williams8DB.txt, https://sites.google.com/view/williams-primes, http://www.bitman.name/math/table/801 (in Italian)) to every base b ≥ 2 which is not == 1 mod 3 (https://oeis.org/A346149, https://oeis.org/A346154) (warning: this may be false, bⁿ+(b+1) may be able to be proven to only contain composites by covering congruence, like the case of 2×bⁿ+1 and bⁿ+2 for b = 201446503145165177, which has a covering set {3, 5, 17, 257, 641, 65537, 6700417}, however, this is at least true for bases b ≤ 10⁶)
78557 is the smallest Sierpinski number (i.e. numbers k such that k×2ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base2.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), http://www.prothsearch.com/sierp.html, https://www.primegrid.com/forum_thread.php?id=1647, https://www.primegrid.com/forum_thread.php?id=972, https://www.primegrid.com/forum_thread.php?id=1750, https://www.primegrid.com/forum_thread.php?id=5758, https://www.primegrid.com/stats_sob_llr.php, https://www.primegrid.com/stats_psp_llr.php, https://www.primegrid.com/stats_esp_llr.php, https://www.primegrid.com/primes/primes.php?project=SOB&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.primegrid.com/primes/primes.php?project=PSP&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.primegrid.com/primes/primes.php?project=ESP&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://web.archive.org/web/20160405211049/http://www.seventeenorbust.com/, https://en.wikipedia.org/wiki/Sierpi%C5%84ski_number, https://t5k.org/glossary/xpage/SierpinskiNumber.html, https://www.rieselprime.de/ziki/Sierpi%C5%84ski_number, https://www.rieselprime.de/ziki/Sierpi%C5%84ski_problem, https://www.rieselprime.de/ziki/Proth_2_Sierpinski, https://www.rieselprime.de/ziki/Proth_2_Count-0, https://mathworld.wolfram.com/SierpinskiNumberoftheSecondKind.html, https://en.wikipedia.org/wiki/Seventeen_or_Bust, https://www.rieselprime.de/ziki/Seventeen_or_Bust, https://www.rieselprime.de/ziki/PrimeGrid_Seventeen_or_Bust, https://www.rieselprime.de/ziki/PrimeGrid_Prime_Sierpi%C5%84ski_Problem, https://web.archive.org/web/20190929190947/https://primes.utm.edu/glossary/xpage/ColbertNumber.html, https://mathworld.wolfram.com/ColbertNumber.html, http://www.numericana.com/answer/primes.htm#sierpinski, http://www.bitman.name/math/article/204 (in Italian), http://jpenne.free.fr/Sierpeven/, https://www.ams.org/journals/mcom/1983-40-161/S0025-5718-1983-0679453-8/S0025-5718-1983-0679453-8.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_40.pdf), https://www.fq.math.ca/Scanned/33-3/izotov.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_46.pdf), http://www.digizeitschriften.de/download/PPN378850199_0015/PPN378850199_0015___log24.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_213.pdf), https://www.ams.org/journals/mcom/1981-37-155/S0025-5718-1981-0616376-2/S0025-5718-1981-0616376-2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_214.pdf), https://www.ams.org/journals/mcom/1983-41-164/S0025-5718-1983-0717710-7/S0025-5718-1983-0717710-7.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_215.pdf), http://www.iakovlev.org/zip/riesel2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_8.pdf), https://doi.org/10.1016/j.jnt.2008.02.004 (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_47.pdf), https://cs.uwaterloo.ca/journals/JIS/VOL16/Ismailescu/ismailescu3.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_51.pdf), https://cs.uwaterloo.ca/journals/JIS/VOL18/Baczkowski/bacz2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_61.pdf), https://arxiv.org/pdf/1110.4671.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_62.pdf), https://oeis.org/A123159, https://oeis.org/A076336, https://oeis.org/A078680, https://oeis.org/A078683, https://oeis.org/A033809, https://oeis.org/A040076, https://oeis.org/A225721, https://oeis.org/A050921, https://oeis.org/A046067, https://oeis.org/A057025, https://oeis.org/A057192, https://oeis.org/A057247) (only six k left: 21181 and 22699 and 24737 and 55459 and 65536 and 67607 (k = 42362 = 21181×2 will have the same prime as k = 21181, k = 45398 = 22699×2 will have the same prime as k = 22699, k = 49474 = 24737×2 will have the same prime as k = 24737), searched to n = 41200000, and the largest known prime is 10223×2^31172165+1)
509203 is the smallest Riesel number (i.e. numbers k such that k×2ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base2-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base2.zip, http://www.bitman.name/math/article/2005 (in Italian), http://www.prothsearch.com/rieselprob.html, https://www.primegrid.com/forum_thread.php?id=1731, https://www.primegrid.com/stats_trp_llr.php, https://www.primegrid.com/primes/primes.php?project=TRP&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://web.archive.org/web/20061021145019/http://rieselsieve.com/, https://web.archive.org/web/20061021153313/http://stats.rieselsieve.com//queue.php, https://en.wikipedia.org/wiki/Riesel_number, https://t5k.org/glossary/xpage/RieselNumber.html, https://www.rieselprime.de/ziki/Riesel_number, https://www.rieselprime.de/ziki/Riesel_problem_1, https://www.rieselprime.de/ziki/Riesel_problem_2, https://www.rieselprime.de/ziki/Riesel_problem_3, https://www.rieselprime.de/ziki/Riesel_problem_4, https://www.rieselprime.de/ziki/Riesel_2_Riesel, https://www.rieselprime.de/ziki/Riesel_2_Count-0, https://mathworld.wolfram.com/RieselNumber.html, https://en.wikipedia.org/wiki/Riesel_Sieve, https://www.rieselprime.de/ziki/Riesel_Sieve, https://www.rieselprime.de/ziki/PrimeGrid_The_Riesel_Problem, http://www.bitman.name/math/article/203 (in Italian), http://www.iakovlev.org/zip/riesel2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_8.pdf), https://doi.org/10.1016/j.jnt.2008.02.004 (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_47.pdf), https://cs.uwaterloo.ca/journals/JIS/VOL16/Ismailescu/ismailescu3.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_51.pdf), https://cs.uwaterloo.ca/journals/JIS/VOL18/Baczkowski/bacz2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_61.pdf), https://arxiv.org/pdf/1110.4671.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_62.pdf), https://oeis.org/A273987, https://oeis.org/A076337, https://oeis.org/A101036, https://oeis.org/A050412, https://oeis.org/A052333, https://oeis.org/A108129, https://oeis.org/A040081, https://oeis.org/A038699, https://oeis.org/A046069, https://oeis.org/A057026, https://oeis.org/A128979, https://oeis.org/A101050)
271129 is the second-smallest Sierpinski number (i.e. numbers k such that k×2ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base2-2nd-conj.zip, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), http://www.prothsearch.com/sierp.html, https://www.primegrid.com/forum_thread.php?id=1647, https://www.primegrid.com/forum_thread.php?id=972, https://www.primegrid.com/forum_thread.php?id=1750, https://www.primegrid.com/forum_thread.php?id=5758, https://www.primegrid.com/stats_sob_llr.php, https://www.primegrid.com/stats_psp_llr.php, https://www.primegrid.com/stats_esp_llr.php, https://www.primegrid.com/primes/primes.php?project=SOB&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.primegrid.com/primes/primes.php?project=PSP&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.primegrid.com/primes/primes.php?project=ESP&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://web.archive.org/web/20160405211049/http://www.seventeenorbust.com/, https://en.wikipedia.org/wiki/Sierpi%C5%84ski_number, https://t5k.org/glossary/xpage/SierpinskiNumber.html, https://www.rieselprime.de/ziki/Sierpi%C5%84ski_number, https://www.rieselprime.de/ziki/Sierpi%C5%84ski_problem, https://www.rieselprime.de/ziki/Proth_2_Sierpinski, https://www.rieselprime.de/ziki/Proth_2_Count-0, https://mathworld.wolfram.com/SierpinskiNumberoftheSecondKind.html, https://en.wikipedia.org/wiki/Seventeen_or_Bust, https://www.rieselprime.de/ziki/Seventeen_or_Bust, https://www.rieselprime.de/ziki/PrimeGrid_Seventeen_or_Bust, https://www.rieselprime.de/ziki/PrimeGrid_Prime_Sierpi%C5%84ski_Problem, https://web.archive.org/web/20190929190947/https://primes.utm.edu/glossary/xpage/ColbertNumber.html, https://mathworld.wolfram.com/ColbertNumber.html, http://www.numericana.com/answer/primes.htm#sierpinski, http://www.bitman.name/math/article/204 (in Italian), http://jpenne.free.fr/Sierpeven/, https://www.ams.org/journals/mcom/1983-40-161/S0025-5718-1983-0679453-8/S0025-5718-1983-0679453-8.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_40.pdf), https://www.fq.math.ca/Scanned/33-3/izotov.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_46.pdf), http://www.digizeitschriften.de/download/PPN378850199_0015/PPN378850199_0015___log24.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_213.pdf), https://www.ams.org/journals/mcom/1981-37-155/S0025-5718-1981-0616376-2/S0025-5718-1981-0616376-2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_214.pdf), https://www.ams.org/journals/mcom/1983-41-164/S0025-5718-1983-0717710-7/S0025-5718-1983-0717710-7.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_215.pdf), http://www.iakovlev.org/zip/riesel2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_8.pdf), https://doi.org/10.1016/j.jnt.2008.02.004 (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_47.pdf), https://cs.uwaterloo.ca/journals/JIS/VOL16/Ismailescu/ismailescu3.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_51.pdf), https://cs.uwaterloo.ca/journals/JIS/VOL18/Baczkowski/bacz2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_61.pdf), https://arxiv.org/pdf/1110.4671.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_62.pdf), https://oeis.org/A123159, https://oeis.org/A076336, https://oeis.org/A078680, https://oeis.org/A078683, https://oeis.org/A033809, https://oeis.org/A040076, https://oeis.org/A225721, https://oeis.org/A050921, https://oeis.org/A046067, https://oeis.org/A057025, https://oeis.org/A057192, https://oeis.org/A057247) other than 157114 = 78557×2
762701 is the second-smallest Riesel number (i.e. numbers k such that k×2ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base2-2nd-conj.zip, http://www.bitman.name/math/article/2005 (in Italian), http://www.prothsearch.com/rieselprob.html, https://www.primegrid.com/forum_thread.php?id=1731, https://www.primegrid.com/stats_trp_llr.php, https://www.primegrid.com/primes/primes.php?project=TRP&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://web.archive.org/web/20061021145019/http://rieselsieve.com/, https://web.archive.org/web/20061021153313/http://stats.rieselsieve.com//queue.php, https://en.wikipedia.org/wiki/Riesel_number, https://t5k.org/glossary/xpage/RieselNumber.html, https://www.rieselprime.de/ziki/Riesel_number, https://www.rieselprime.de/ziki/Riesel_problem_1, https://www.rieselprime.de/ziki/Riesel_problem_2, https://www.rieselprime.de/ziki/Riesel_problem_3, https://www.rieselprime.de/ziki/Riesel_problem_4, https://www.rieselprime.de/ziki/Riesel_2_Riesel, https://www.rieselprime.de/ziki/Riesel_2_Count-0, https://mathworld.wolfram.com/RieselNumber.html, https://en.wikipedia.org/wiki/Riesel_Sieve, https://www.rieselprime.de/ziki/Riesel_Sieve, https://www.rieselprime.de/ziki/PrimeGrid_The_Riesel_Problem, http://www.bitman.name/math/article/203 (in Italian), http://www.iakovlev.org/zip/riesel2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_8.pdf), https://doi.org/10.1016/j.jnt.2008.02.004 (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_47.pdf), https://cs.uwaterloo.ca/journals/JIS/VOL16/Ismailescu/ismailescu3.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_51.pdf), https://cs.uwaterloo.ca/journals/JIS/VOL18/Baczkowski/bacz2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_61.pdf), https://arxiv.org/pdf/1110.4671.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_62.pdf), https://oeis.org/A273987, https://oeis.org/A076337, https://oeis.org/A101036, https://oeis.org/A050412, https://oeis.org/A052333, https://oeis.org/A108129, https://oeis.org/A040081, https://oeis.org/A038699, https://oeis.org/A046069, https://oeis.org/A057026, https://oeis.org/A128979, https://oeis.org/A101050)
125050976086 is the smallest generalized Sierpinski number to base 3 (i.e. numbers k such that gcd(k+1, 3−1) = 1 and k×3ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base3-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base3-10M.zip, http://www.noprimeleftbehind.net/crus/prime-sierp-base3-gt-25K.zip, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159, https://oeis.org/A291437, https://oeis.org/A291438)
63064644938 is the smallest generalized Riesel number to base 3 (i.e. numbers k such that gcd(k−1, 3−1) = 1 and k×3ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base3-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base3-10M.zip, http://www.noprimeleftbehind.net/crus/prime-riesel-base3-gt-25K.zip, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987, https://oeis.org/A343914)
66741 is the smallest generalized Sierpinski number to base 4 (i.e. numbers k such that gcd(k+1, 4−1) = 1 and k×4ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base4.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://www.rieselprime.de/ziki/Liskovets-Gallot_conjectures, https://www.rieselprime.de/ziki/CRUS_Liskovets-Gallot, https://www.rieselprime.de/Related/LiskovetsGallot.htm, http://www.bitman.name/math/article/1124, http://www.primepuzzles.net/problems/prob_036.htm, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base2-evenn.txt, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base2-oddn.txt, https://oeis.org/A123159, https://oeis.org/A251057, https://oeis.org/A256002) (only seven k left: 18534 and 21181 and 22699 and 49474 and 55459 and 64494 and 65536, searched to n = 5000000, and the largest known prime is 20446×4^15586082+1)
39939 is the smallest non-square generalized Riesel number to base 4 (i.e. numbers k such that gcd(k−1, 4−1) = 1 and k×4ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base4.txt, http://www.bitman.name/math/article/2005 (in Italian), https://www.rieselprime.de/ziki/Liskovets-Gallot_conjectures, https://www.rieselprime.de/ziki/CRUS_Liskovets-Gallot, https://www.rieselprime.de/Related/LiskovetsGallot.htm, http://www.bitman.name/math/article/1124, http://www.primepuzzles.net/problems/prob_036.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base2-evenn.txt, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base2-oddn.txt, https://oeis.org/A273987, https://oeis.org/A251757) (only five k left: 9519 and 14361 and 19464 and 23669 and 31859 (k = 38076 = 9519×4 will have the same prime as k = 9519), searched to n = 5000000, and the largest known prime is 4586×4^6459215−1, note: it is still not known whether 6459215 is the smallest n such that 4586×4ⁿ−1 is prime, since the search limit for 4586×4ⁿ−1 is only n = 5767403)
159986 is the smallest generalized Sierpinski number to base 5 (i.e. numbers k such that gcd(k+1, 5−1) = 1 and k×5ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base5-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base5.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://www.primegrid.com/forum_thread.php?id=5087, https://www.primegrid.com/stats_sr5_llr.php, https://www.primegrid.com/primes/primes.php?project=SR5&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.rieselprime.de/ziki/Sierpi%C5%84ski-Riesel_Base_5, https://www.rieselprime.de/ziki/Sierpi%C5%84ski_number_base_5, https://www.rieselprime.de/ziki/PrimeGrid_Sierpi%C5%84ski_base_5, https://web.archive.org/web/20131016004333/http://www.sr5.psp-project.de/, https://web.archive.org/web/20111018190410/http://www.sr5.psp-project.de/s5stats.html, https://oeis.org/A123159, https://oeis.org/A345698)
346802 is the smallest generalized Riesel number to base 5 (i.e. numbers k such that gcd(k−1, 5−1) = 1 and k×5ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base5-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base5.zip, http://www.bitman.name/math/article/2005 (in Italian), https://www.primegrid.com/forum_thread.php?id=5087, https://www.primegrid.com/stats_sr5_llr.php, https://www.primegrid.com/primes/primes.php?project=SR5&factors=XGF&only=ALL&announcements=ALL&sortby=size&dc=yes&search=, https://www.rieselprime.de/ziki/Sierpi%C5%84ski-Riesel_Base_5, https://www.rieselprime.de/ziki/Riesel_number_base_5, https://www.rieselprime.de/ziki/PrimeGrid_Riesel_base_5, https://web.archive.org/web/20131016004333/http://www.sr5.psp-project.de/, https://web.archive.org/web/20111018190339/http://www.sr5.psp-project.de/r5stats.html, https://oeis.org/A273987, https://oeis.org/A345403)
174308 is the smallest generalized Sierpinski number to base 6 (i.e. numbers k such that gcd(k+1, 6−1) = 1 and k×6ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base6.zip, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159, https://oeis.org/A244549, https://oeis.org/A250204)
84687 is the smallest generalized Riesel number to base 6 (i.e. numbers k such that gcd(k−1, 6−1) = 1 and k×6ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base6.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987, https://oeis.org/A244351, https://oeis.org/A250205) (only one k left: 1597 (k = 9582 = 1597×6 and 57492 = 1597×6² will have the same prime as k = 1597), searched to n = 7000000, and the largest known prime is 36772×6^1723287−1)
1112646039348 is the smallest generalized Sierpinski number to base 7 (i.e. numbers k such that gcd(k+1, 7−1) = 1 and k×7ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base7-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base7-10M.zip, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base7-prime.htm, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159)
408034255082 is the smallest generalized Riesel number to base 7 (i.e. numbers k such that gcd(k−1, 7−1) = 1 and k×7ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base7-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base7-10M.zip, http://www.noprimeleftbehind.net/crus/prime-riesel-base7-gt-25K.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987)
47 is the smallest non-cube generalized Sierpinski number to base 8 (i.e. numbers k such that gcd(k+1, 8−1) = 1 and k×8ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base8.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 31×8²⁰+1)
14 is the smallest non-cube generalized Riesel number to base 8 (i.e. numbers k such that gcd(k−1, 8−1) = 1 and k×8ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base8.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 11×8¹⁸−1)
2344 is the smallest generalized Sierpinski number to base 9 (i.e. numbers k such that gcd(k+1, 9−1) = 1 and k×9ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base9.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 2036×9^5004596+1, note: it is still not known whether 5004596 is the smallest n such that 2036×9ⁿ+1 is prime, since the search limit for 2036×9ⁿ+1 is only n = 5000000))**
74 is the smallest non-square generalized Riesel number to base 9 (i.e. numbers k such that gcd(k−1, 9−1) = 1 and k×9ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base9.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 24×9⁸−1)
9175 is the smallest generalized Sierpinski number to base 10 (i.e. numbers k such that gcd(k+1, 10−1) = 1 and k×10ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base10.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159, https://oeis.org/A243969) (only two k left: 100 and 7666 (k = 1000 will have the same prime as k = 100), searched to n = 5000000, and the largest known prime is 5028×10⁸³⁹⁸²+1)
10176 is the smallest generalized Riesel number to base 10 (i.e. numbers k such that gcd(k−1, 10−1) = 1 and k×10ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base10.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987, https://oeis.org/A243974) (only one k left: 4421, searched to n = 4100000, and the largest known prime is 7019×10⁸⁸¹³⁰⁹−1)
1490 is the smallest generalized Sierpinski number to base 11 (i.e. numbers k such that gcd(k+1, 11−1) = 1 and k×11ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base11.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 958×11³⁰⁰⁵⁴⁴+1)
862 is the smallest generalized Riesel number to base 11 (i.e. numbers k such that gcd(k−1, 11−1) = 1 and k×11ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base11.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 62×11²⁶²⁰²−1)
521 is the smallest generalized Sierpinski number to base 12 (i.e. numbers k such that gcd(k+1, 12−1) = 1 and k×12ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base12.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (only one k left: 12 (k = 144 will have the same prime as k = 12), searched to n = 33554430, and the largest known prime is 404×12⁷¹⁴⁵⁵⁸+1)
376 is the smallest non-(m² with m == 5, 8 mod 13 or 3×m² with m == 3, 10 mod 13) generalized Riesel number to base 12 (i.e. numbers k such that gcd(k−1, 12−1) = 1 and k×12ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base12.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 157×12²⁸⁵−1)
132 is the smallest generalized Sierpinski number to base 13 (i.e. numbers k such that gcd(k+1, 13−1) = 1 and k×13ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base13.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 48×13⁶²⁶⁷+1)
302 is the smallest generalized Riesel number to base 13 (i.e. numbers k such that gcd(k−1, 13−1) = 1 and k×13ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base13.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 288×13¹⁰⁹²¹⁷−1)
4 is the smallest generalized Sierpinski number to base 14 (i.e. numbers k such that gcd(k+1, 14−1) = 1 and k×14ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base14.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 1×14²+1)
4 is the smallest generalized Riesel number to base 14 (i.e. numbers k such that gcd(k−1, 14−1) = 1 and k×14ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base14.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 2×14⁴−1)
91218919470156 is the smallest generalized Sierpinski number to base 15 (i.e. numbers k such that gcd(k+1, 15−1) = 1 and k×15ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base15-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base15-10M.zip, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base15-prime.htm, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159)
36370321851498 is the smallest generalized Riesel number to base 15 (i.e. numbers k such that gcd(k−1, 15−1) = 1 and k×15ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base15-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base15-10M.zip, http://www.bitman.name/math/article/2005 (in Italian), http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base15-prime.htm, https://oeis.org/A273987)
66741 is the smallest non-(4×m⁴) generalized Sierpinski number to base 16 (i.e. numbers k such that gcd(k+1, 16−1) = 1 and k×16ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base16.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159)
33965 is the smallest non-square generalized Riesel number to base 16 (i.e. numbers k such that gcd(k−1, 16−1) = 1 and k×16ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base16.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987)
278 is the smallest generalized Sierpinski number to base 17 (i.e. numbers k such that gcd(k+1, 17−1) = 1 and k×17ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base17.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (only one k left: 244, searched to n = 5000000, and the largest known prime is 262×17¹⁸⁶⁷⁶⁸+1)
86 is the smallest generalized Riesel number to base 17 (i.e. numbers k such that gcd(k−1, 17−1) = 1 and k×17ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base17.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 44×17⁶⁴⁸⁸−1)
398 is the smallest generalized Sierpinski number to base 18 (i.e. numbers k such that gcd(k+1, 18−1) = 1 and k×18ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base18.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (only one k left: 18 (k = 324 will have the same prime as k = 18), searched to n = 33554430, and the largest known prime is 122×18²⁹²³¹⁸+1)
246 is the smallest generalized Riesel number to base 18 (i.e. numbers k such that gcd(k−1, 18−1) = 1 and k×18ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base18.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 151×18⁴¹⁸−1)
765174 is the smallest generalized Sierpinski number to base 19 (i.e. numbers k such that gcd(k+1, 19−1) = 1 and k×19ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base19-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base19.zip, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159)
1119866 is the smallest non-(m² with m == 2, 3 mod 5 or 19×m² with m == 2, 3 mod 13) generalized Riesel number to base 19 (i.e. numbers k such that gcd(k−1, 19−1) = 1 and k×19ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base19-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base19.zip, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987)
8 is the smallest generalized Sierpinski number to base 20 (i.e. numbers k such that gcd(k+1, 20−1) = 1 and k×20ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base20.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 6×20¹⁵+1)
8 is the smallest generalized Riesel number to base 20 (i.e. numbers k such that gcd(k−1, 20−1) = 1 and k×20ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base20.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 2×20¹⁰−1)
1002 is the smallest generalized Sierpinski number to base 21 (i.e. numbers k such that gcd(k+1, 21−1) = 1 and k×21ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base21.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 118×21¹⁹⁸⁴⁹+1)
560 is the smallest generalized Riesel number to base 21 (i.e. numbers k such that gcd(k−1, 21−1) = 1 and k×21ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base21.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 64×21²⁸⁶⁷−1)
6694 is the smallest generalized Sierpinski number to base 22 (i.e. numbers k such that gcd(k+1, 22−1) = 1 and k×22ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base22.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (only two k left: 22 and 5128 (k = 484 will have the same prime as k = 22), searched to n = 2000000, and the largest known prime is 1611×22⁷³⁸⁹⁸⁸+1)
4461 is the smallest generalized Riesel number to base 22 (i.e. numbers k such that gcd(k−1, 22−1) = 1 and k×22ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base22.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (only one k left: 3656, searched to n = 5000000, and the largest known prime is 3104×22¹⁶¹¹⁸⁸−1)
182 is the smallest generalized Sierpinski number to base 23 (i.e. numbers k such that gcd(k+1, 23−1) = 1 and k×23ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base23.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 68×23³⁶⁵²³⁹+1)
476 is the smallest generalized Riesel number to base 23 (i.e. numbers k such that gcd(k−1, 23−1) = 1 and k×23ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base23.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (only one k left: 404, searched to n = 2550000, and the largest known prime is 194×23²¹¹¹⁴⁰−1)
30651 is the smallest generalized Sierpinski number to base 24 (i.e. numbers k such that gcd(k+1, 24−1) = 1 and k×24ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base24-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base24.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159)
32336 is the smallest non-(m² with m == 2, 3 mod 5 or 6×m² with m == 1, 4 mod 5) generalized Riesel number to base 24 (i.e. numbers k such that gcd(k−1, 24−1) = 1 and k×24ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base24-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base24.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987)
262638 is the smallest generalized Sierpinski number to base 25 (i.e. numbers k such that gcd(k+1, 25−1) = 1 and k×25ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base25-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base25.zip, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159)
346802 is the smallest non-square generalized Riesel number to base 25 (i.e. numbers k such that gcd(k−1, 25−1) = 1 and k×25ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base25-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base25.zip, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987)
221 is the smallest generalized Sierpinski number to base 26 (i.e. numbers k such that gcd(k+1, 26−1) = 1 and k×26ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base26.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (only two k left: 65 and 155, searched to n = 2000000, and the largest known prime is 32×26³¹⁸⁰⁷¹+1)
149 is the smallest generalized Riesel number to base 26 (i.e. numbers k such that gcd(k−1, 26−1) = 1 and k×26ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base26.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 115×26⁵²⁰²⁷⁷−1)
538 is the smallest non-cube generalized Sierpinski number to base 27 (i.e. numbers k such that gcd(k+1, 27−1) = 1 and k×27ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base27.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (only one k left: 398, searched to n = 2000000, and the largest known prime is 342×27³⁶²⁹¹+1)
804 is the smallest non-cube generalized Riesel number to base 27 (i.e. numbers k such that gcd(k−1, 27−1) = 1 and k×27ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base27.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (only one k left: 706, searched to n = 5000000, and the largest known prime is 258×27⁶⁹⁹⁴²−1)
4554 is the smallest generalized Sierpinski number to base 28 (i.e. numbers k such that gcd(k+1, 28−1) = 1 and k×28ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base28.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (only two k left: 871 and 4552, searched to n = 1000000, and the largest known prime is 3394×28⁴²⁷²⁶²+1)
9078 is the smallest generalized Riesel number to base 28 (i.e. numbers k such that gcd(k−1, 28−1) = 1 and k×28ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base28.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (only four k left: 233 and 1422 and 4322 and 4871 (k = 6524 = 233×28 will have the same prime as k = 233), searched to n = 1000000, and the largest known prime is 6207×28⁴³⁰⁸⁰³−1)
4 is the smallest generalized Sierpinski number to base 29 (i.e. numbers k such that gcd(k+1, 29−1) = 1 and k×29ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base29.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 2×29¹+1)
4 is the smallest generalized Riesel number to base 29 (i.e. numbers k such that gcd(k−1, 29−1) = 1 and k×29ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base29.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 2×29¹³⁶−1)
867 is the smallest generalized Sierpinski number to base 30 (i.e. numbers k such that gcd(k+1, 30−1) = 1 and k×30ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base30.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (only two k left: 278 and 588, searched to n = 1000000, and the largest known prime is 699×30¹¹⁸³⁷+1)
4928 is the smallest generalized Riesel number to base 30 (i.e. numbers k such that gcd(k−1, 30−1) = 1 and k×30ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base30.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) other than 1369 = 37² (only seven k left: 659 and 1024 and 1580 and 1936 and 2293 and 2916 and 4897, searched to n = 1000000, and the largest known prime is 3719×30⁹⁵⁶⁰⁴⁴−1)
6360528 is the smallest generalized Sierpinski number to base 31 (i.e. numbers k such that gcd(k+1, 31−1) = 1 and k×31ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base31-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base31.zip, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159)
134718 is the smallest generalized Riesel number to base 31 (i.e. numbers k such that gcd(k−1, 31−1) = 1 and k×31ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base31.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (only one k left: 55758, searched to n = 3000000, and the largest known prime is 6962×31^2863120−1)
10 is the smallest non-5th-power generalized Sierpinski number to base 32 (i.e. numbers k such that gcd(k+1, 32−1) = 1 and k×32ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base32.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (only one k left: 4, searched to n = 1717986917, and the largest known prime is 9×32¹³+1)
10 is the smallest non-5th-power generalized Riesel number to base 32 (i.e. numbers k such that gcd(k−1, 32−1) = 1 and k×32ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base32.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 3×32¹¹−1)
1854 is the smallest generalized Sierpinski number to base 33 (i.e. numbers k such that gcd(k+1, 33−1) = 1 and k×33ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base33.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 766×33⁶¹⁰⁴¹²+1)
764 is the smallest non-(m² with m == 4, 13 mod 17 or 33×m² with m == 4, 13 mod 17) generalized Riesel number to base 33 (i.e. numbers k such that gcd(k−1, 33−1) = 1 and k×33ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base33.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 732×33¹⁹⁰¹¹−1)
6 is the smallest generalized Sierpinski number to base 34 (i.e. numbers k such that gcd(k+1, 34−1) = 1 and k×34ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base34.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (solved, largest prime is 1×34⁴+1)
6 is the smallest non-(m² with m == 2, 3 mod 5 or 34×m² with m == 2, 3 mod 5) generalized Riesel number to base 34 (i.e. numbers k such that gcd(k−1, 34−1) = 1 and k×34ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base34.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987) (solved, largest prime is 5×34²−1)
214018 is the smallest generalized Sierpinski number to base 35 (i.e. numbers k such that gcd(k+1, 35−1) = 1 and k×35ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base35-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base35.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159)
287860 is the smallest generalized Riesel number to base 35 (i.e. numbers k such that gcd(k−1, 35−1) = 1 and k×35ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base35-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base35.zip, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987)
1886 is the smallest generalized Sierpinski number to base 36 (i.e. numbers k such that gcd(k+1, 36−1) = 1 and k×36ⁿ+1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, https://web.archive.org/web/20230928115832/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17598&d=1516910519, https://web.archive.org/web/20221230035429/https://sites.google.com/site/robertgerbicz/sierpinski.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4557&d=1263456866, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/all-ks-sierp-base36.txt, https://web.archive.org/web/20231011144408/https://www.utm.edu/staff/caldwell/preprints/2to100.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_3.pdf), http://www.bitman.name/math/article/1259 (in Italian), https://oeis.org/A123159) (only one k left: 1296, searched to n = 134217725, and the largest known prime is 960×36¹⁵⁷¹+1)
116364 is the smallest non-square generalized Riesel number to base 36 (i.e. numbers k such that gcd(k−1, 36−1) = 1 and k×36ⁿ−1 is composite for all n ≥ 1) (http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm, https://web.archive.org/web/20230928115850/http://www.noprimeleftbehind.net/crus/vstats_new/all_ck_riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=17597&d=1516910519, https://web.archive.org/web/20221230035558/https://sites.google.com/site/robertgerbicz/riesel.txt, https://www.mersenneforum.org/attachment.php?attachmentid=4558&d=1263456995, https://www.mersenneforum.org/attachment.php?attachmentid=4415&d=1260969652, https://www.mersenneforum.org/showthread.php?t=10910, https://www.mersenneforum.org/showthread.php?t=25177, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base36-reserve.htm, http://www.noprimeleftbehind.net/crus/all-ks-riesel-base36.txt, http://www.bitman.name/math/article/2005 (in Italian), https://oeis.org/A273987)
78557 is the smallest dual Sierpinski number (i.e. odd numbers k such that 2ⁿ+k is composite for all n ≥ 1) (http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_1.pdf), https://www.rechenkraft.net/wiki/Five_or_Bust, https://oeis.org/A076336/a076336c.html, http://www.mit.edu/~kenta/three/prime/dual-sierpinski/ezgxggdm/dualsierp-excerpt.txt, http://mit.edu/kenta/www/three/prime/dual-sierpinski/ezgxggdm/dualsierp.txt.gz, http://www.bitman.name/math/article/1126, https://www.mersenneforum.org/showthread.php?t=10761, https://oeis.org/A067760, https://oeis.org/A123252, https://oeis.org/A094076, https://oeis.org/A139758) (solved if we allow probable primes, largest (probable) prime is 2^9092392+40291)
509203 is the smallest dual Riesel number (i.e. odd numbers k such that 2ⁿ−k is composite for all n ≥ 1 such that 2ⁿ > k) (http://www.bitman.name/math/article/1125, https://www.mersenneforum.org/showthread.php?t=6545, https://oeis.org/A096502, https://oeis.org/A096822, https://oeis.org/A101462)
271129 is the second-smallest dual Sierpinski number (i.e. odd numbers k such that 2ⁿ+k is composite for all n ≥ 1) (http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_1.pdf), https://www.rechenkraft.net/wiki/Five_or_Bust, https://oeis.org/A076336/a076336c.html, http://www.mit.edu/~kenta/three/prime/dual-sierpinski/ezgxggdm/dualsierp-excerpt.txt, http://mit.edu/kenta/www/three/prime/dual-sierpinski/ezgxggdm/dualsierp.txt.gz, http://www.bitman.name/math/article/1126, https://www.mersenneforum.org/showthread.php?t=10761, https://oeis.org/A067760, https://oeis.org/A123252, https://oeis.org/A094076, https://oeis.org/A139758)
762701 is the second-smallest dual Riesel number (i.e. odd numbers k such that 2ⁿ−k is composite for all n ≥ 1 such that 2ⁿ > k) (http://www.bitman.name/math/article/1125, https://www.mersenneforum.org/showthread.php?t=6545, https://oeis.org/A096502, https://oeis.org/A096822, https://oeis.org/A101462)
125050976086 is the smallest generalized dual Sierpinski number to base 3 (i.e. numbers k such that gcd(k, 3) = 1 and gcd(k+1, 3−1) = 1 and 3ⁿ+k is composite for all n ≥ 1)
63064644938 is the smallest generalized dual Riesel number to base 3 (i.e. numbers k such that gcd(k, 3) = 1 and gcd(k−1, 3−1) = 1 and 3ⁿ−k is composite for all n ≥ 1 such that 3ⁿ > k)
159986 is the smallest generalized dual Sierpinski number to base 5 (i.e. numbers k such that gcd(k, 5) = 1 and gcd(k+1, 5−1) = 1 and 5ⁿ+k is composite for all n ≥ 1)
346802 is the smallest generalized dual Riesel number to base 5 (i.e. numbers k such that gcd(k, 5) = 1 and gcd(k−1, 5−1) = 1 and 5ⁿ−k is composite for all n ≥ 1 such that 5ⁿ > k)
1112646039348 is the smallest generalized dual Sierpinski number to base 7 (i.e. numbers k such that gcd(k, 7) = 1 and gcd(k+1, 7−1) = 1 and 7ⁿ+k is composite for all n ≥ 1)
408034255082 is the smallest generalized dual Riesel number to base 7 (i.e. numbers k such that gcd(k, 7) = 1 and gcd(k−1, 7−1) = 1 and 7ⁿ−k is composite for all n ≥ 1 such that 7ⁿ > k)
1490 is the smallest generalized dual Sierpinski number to base 11 (i.e. numbers k such that gcd(k, 11) = 1 and gcd(k+1, 11−1) = 1 and 11ⁿ+k is composite for all n ≥ 1) (only one k left: 430, searched to n = 15000, and the largest known prime is 11⁴¹⁹⁴+1228)
862 is the smallest generalized dual Riesel number to base 11 (i.e. numbers k such that gcd(k, 11) = 1 and gcd(k−1, 11−1) = 1 and 11ⁿ−k is composite for all n ≥ 1 such that 11ⁿ > k) (only two k left: 184 and 324, searched to n = 10000, and the largest known prime is 11²⁴⁷⁹−514)
132 is the smallest generalized dual Sierpinski number to base 13 (i.e. numbers k such that gcd(k, 13) = 1 and gcd(k+1, 13−1) = 1 and 13ⁿ+k is composite for all n ≥ 1) (solved, largest prime is 13⁴¹⁶+120)
302 is the smallest generalized dual Riesel number to base 13 (i.e. numbers k such that gcd(k, 13) = 1 and gcd(k−1, 13−1) = 1 and 13ⁿ−k is composite for all n ≥ 1 such that 13ⁿ > k) (solved if we allow probable primes, largest (probable) prime is 13¹⁰⁶³³−50, it is definitely prime, but 13⁵⁷⁰²−216 is only probable prime)
278 is the smallest generalized dual Sierpinski number to base 17 (i.e. numbers k such that gcd(k, 17) = 1 and gcd(k+1, 17−1) = 1 and 17ⁿ+k is composite for all n ≥ 1) (only one k left: 218, searched to n = 14000, and the largest known prime is 17⁹⁰²¹+32)
86 is the smallest generalized dual Riesel number to base 17 (i.e. numbers k such that gcd(k, 17) = 1 and gcd(k−1, 17−1) = 1 and 17ⁿ−k is composite for all n ≥ 1 such that 17ⁿ > k) (solved, largest prime is 17¹⁸−80)
765174 is the smallest generalized dual Sierpinski number to base 19 (i.e. numbers k such that gcd(k, 19) = 1 and gcd(k+1, 19−1) = 1 and 19ⁿ+k is composite for all n ≥ 1)
1119866 is the smallest non-(m² with m == 2, 3 mod 5 or 19×m² with m == 2, 3 mod 13) generalized dual Riesel number to base 19 (i.e. numbers k such that gcd(k, 19) = 1 and gcd(k−1, 19−1) = 1 and 19ⁿ−k is composite for all n ≥ 1 such that 19ⁿ > k)
182 is the smallest generalized dual Sierpinski number to base 23 (i.e. numbers k such that gcd(k, 23) = 1 and gcd(k+1, 23−1) = 1 and 23ⁿ+k is composite for all n ≥ 1) (solved, largest prime is 23¹⁹²⁶+82)
476 is the smallest generalized dual Riesel number to base 23 (i.e. numbers k such that gcd(k, 23) = 1 and gcd(k−1, 23−1) = 1 and 23ⁿ−k is composite for all n ≥ 1 such that 23ⁿ > k) (only three k left: 224 and 238 and 394, searched to n = 11000, and the largest known (probable) prime is 23³⁴⁰⁹−112)
4 is the smallest generalized dual Sierpinski number to base 29 (i.e. numbers k such that gcd(k, 29) = 1 and gcd(k+1, 29−1) = 1 and 29ⁿ+k is composite for all n ≥ 1) (solved, largest prime is 29¹+2)
4 is the smallest generalized dual Riesel number to base 29 (i.e. numbers k such that gcd(k, 29) = 1 and gcd(k−1, 29−1) = 1 and 29ⁿ−k is composite for all n ≥ 1 such that 29ⁿ > k) (solved, largest prime is 29²−2)
6360528 is the smallest generalized dual Sierpinski number to base 31 (i.e. numbers k such that gcd(k, 31) = 1 and gcd(k+1, 31−1) = 1 and 31ⁿ+k is composite for all n ≥ 1)
134718 is the smallest generalized dual Riesel number to base 31 (i.e. numbers k such that gcd(k, 31) = 1 and gcd(k−1, 31−1) = 1 and 31ⁿ−k is composite for all n ≥ 1 such that 31ⁿ > k)
201446503145165177 is the smallest reverse Sierpinski base to k = 2 (i.e. bases b such that gcd(2+1, b−1) = 1 and 2×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354, https://oeis.org/A119624, https://oeis.org/A253178, https://oeis.org/A098872)
There are no reverse Riesel bases to k = 2 (i.e. bases b such that gcd(2−1, b−1) = 1 and 2×bⁿ−1 is composite for all n ≥ 1) (https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&d=1567314217, https://oeis.org/A119591, https://oeis.org/A098873, https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354)
There are no reverse Sierpinski bases to k = 3 (i.e. bases b such that gcd(3+1, b−1) = 1 and 3×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354, https://oeis.org/A098877)
There are no reverse Riesel bases to k = 3 (i.e. bases b such that gcd(3−1, b−1) = 1 and 3×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354, https://oeis.org/A098876)
14 is the smallest reverse Sierpinski base to k = 4 (i.e. bases b such that gcd(4+1, b−1) = 1 and 4×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 4×12²+1)
14 is the smallest non-square reverse Riesel base to k = 4 (i.e. bases b such that gcd(4−1, b−1) = 1 and 4×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 4×12¹−1)
140324348 is the smallest reverse Sierpinski base to k = 5 (i.e. bases b such that gcd(5+1, b−1) = 1 and 5×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354)
There are no reverse Riesel bases to k = 5 (i.e. bases b such that gcd(5−1, b−1) = 1 and 5×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354)
34 is the smallest reverse Sierpinski base to k = 6 (i.e. bases b such that gcd(6+1, b−1) = 1 and 6×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 6×20¹⁵+1)
34 is the smallest non-(6×m² with m == 2, 3 mod 5) reverse Riesel base to k = 6 (i.e. bases b such that gcd(6−1, b−1) = 1 and 6×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 6×27²−1)
There are no reverse Sierpinski bases to k = 7 (i.e. bases b such that gcd(7+1, b−1) = 1 and 7×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354)
9162668342 is the smallest reverse Riesel base to k = 7 (i.e. bases b such that gcd(7−1, b−1) = 1 and 7×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354)
20 is the smallest non-cube reverse Sierpinski base to k = 8 (i.e. bases b such that gcd(8+1, b−1) = 1 and 8×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 8×6⁴+1)
20 is the smallest non-cube reverse Riesel base to k = 8 (i.e. bases b such that gcd(8−1, b−1) = 1 and 8×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 8×7⁴−1)
177744 is the smallest reverse Sierpinski base to k = 9 (i.e. bases b such that gcd(9+1, b−1) = 1 and 9×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354)
There are no reverse Riesel bases to k = 9 (i.e. bases b such that gcd(9−1, b−1) = 1 and 9×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) except the even square bases b and the bases b == 4 mod 10
32 is the smallest reverse Sierpinski base to k = 10 (i.e. bases b such that gcd(10+1, b−1) = 1 and 10×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 10×17¹³⁵⁶+1)
32 is the smallest reverse Riesel base to k = 10 (i.e. bases b such that gcd(10−1, b−1) = 1 and 10×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 10×17¹¹⁷−1)
14 is the smallest reverse Sierpinski base to k = 11 (i.e. bases b such that gcd(11+1, b−1) = 1 and 11×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 11×12³+1)
14 is the smallest reverse Riesel base to k = 11 (i.e. bases b such that gcd(11−1, b−1) = 1 and 11×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 11×8¹⁸−1)
142 is the smallest reverse Sierpinski base to k = 12 (i.e. bases b such that gcd(12+1, b−1) = 1 and 12×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (only one base left: 12, searched to n = 33554430, and the largest known prime is 12×68⁶⁵⁶⁹²¹+1)
142 is the smallest reverse Riesel base to k = 12 (i.e. bases b such that gcd(12−1, b−1) = 1 and 12×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 12×98³⁵⁹⁹−1)
20 is the smallest reverse Sierpinski base to k = 13 (i.e. bases b such that gcd(13+1, b−1) = 1 and 13×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 13×18¹⁰+1)
20 is the smallest reverse Riesel base to k = 13 (i.e. bases b such that gcd(13−1, b−1) = 1 and 13×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 13×12²−1)
38 is the smallest reverse Sierpinski base to k = 14 (i.e. bases b such that gcd(14+1, b−1) = 1 and 14×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 14×23⁵+1)
8 is the smallest reverse Riesel base to k = 14 (i.e. bases b such that gcd(14−1, b−1) = 1 and 14×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (solved, largest prime is 14×5²−1)
There are no reverse Sierpinski bases to k = 15 (i.e. bases b such that gcd(15+1, b−1) = 1 and 15×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354)
8241218 is the smallest reverse Riesel base to k = 15 (i.e. bases b such that gcd(15−1, b−1) = 1 and 15×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354)
38 is the smallest reverse Sierpinski base to k = 16 (i.e. bases b such that gcd(16+1, b−1) = 1 and 16×bⁿ+1 is composite for all n ≥ 1) (https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1165&context=rhumj (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_2.pdf), https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) (only one base left: 32, searched to n = 3435973835, and the largest known prime is 16×33⁹+1)
50 is the smallest non-square reverse Riesel base to k = 16 (i.e. bases b such that gcd(16−1, b−1) = 1 and 16×bⁿ−1 is composite for all n ≥ 1) (https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n, https://www.mersenneforum.org/showthread.php?t=10354) other than 33 (solved, largest prime is 16×39³⁵−1)
201446503145165177 is the smallest dual reverse Sierpinski base to k = 2 (i.e. bases b such that gcd(2, b) = 1 and gcd(2+1, b−1) = 1 and bⁿ+2 is composite for all n ≥ 1) (https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067)
There are no dual reverse Riesel bases to k = 2 (i.e. bases b such that gcd(2, b) = 1 and gcd(2−1, b−1) = 1 and bⁿ−2 is composite for all n ≥ 1 such that bⁿ > 2) (https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A255707, https://oeis.org/A084714, https://oeis.org/A250200, https://oeis.org/A292201)
There are no dual reverse Sierpinski bases to k = 3 (i.e. bases b such that gcd(3, b) = 1 and gcd(3+1, b−1) = 1 and bⁿ+3 is composite for all n ≥ 1)
There are no dual reverse Riesel bases to k = 3 (i.e. bases b such that gcd(3, b) = 1 and gcd(3−1, b−1) = 1 and bⁿ−3 is composite for all n ≥ 1 such that bⁿ > 3)
140324348 is the smallest dual reverse Sierpinski base to k = 5 (i.e. bases b such that gcd(5, b) = 1 and gcd(5+1, b−1) = 1 and bⁿ+5 is composite for all n ≥ 1)
There are no dual reverse Riesel bases to k = 5 (i.e. bases b such that gcd(5, b) = 1 and gcd(5−1, b−1) = 1 and bⁿ−5 is composite for all n ≥ 1 such that bⁿ > 5)
There are no dual reverse Sierpinski bases to k = 7 (i.e. bases b such that gcd(7, b) = 1 and gcd(7+1, b−1) = 1 and bⁿ+7 is composite for all n ≥ 1)
9162668342 is the smallest dual reverse Riesel base to k = 7 (i.e. bases b such that gcd(7, b) = 1 and gcd(7−1, b−1) = 1 and bⁿ−7 is composite for all n ≥ 1 such that bⁿ > 7)
14 is the smallest dual reverse Sierpinski base to k = 11 (i.e. bases b such that gcd(11, b) = 1 and gcd(11+1, b−1) = 1 and bⁿ+11 is composite for all n ≥ 1) (solved, largest prime is 12¹+11)
74 is the smallest dual reverse Riesel base to k = 11 (i.e. bases b such that gcd(11, b) = 1 and gcd(11−1, b−1) = 1 and bⁿ−11 is composite for all n ≥ 1 such that bⁿ > 11) (solved, largest prime is 68⁶−11) (note that for b = 14, the only one prime of the form 14ⁿ−11 with n ≥ 1 is 14¹−11 = 3)
20 is the smallest dual reverse Sierpinski base to k = 13 (i.e. bases b such that gcd(13, b) = 1 and gcd(13+1, b−1) = 1 and bⁿ+13 is composite for all n ≥ 1) (solved, largest prime is 14¹⁶+13)
38 is the smallest dual reverse Riesel base to k = 13 (i.e. bases b such that gcd(13, b) = 1 and gcd(13−1, b−1) = 1 and bⁿ−13 is composite for all n ≥ 1 such that bⁿ > 13) (solved, largest prime is 14³−13) (note that for b = 20, the only one prime of the form 20ⁿ−13 with n ≥ 1 is 20¹−13 = 7)

We call families of the form x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b) "linear" families, and we reduce these families by removing all trailing digits y from x, and removing all leading digits y from z, to make the families be easier, e.g. family 12333{3}33345 in base b is reduced to family 12{3}45 in base b, since they are in fact the same family. Our algorithm then proceeds as follows:

1. M := {minimal primes in base b of length 2 or 3}, L := union of all x{Y}z (where x and z are strings (may be empty) of digits in base b) such that x ≠ 0 and gcd(z, b) = 1 and Y is the set of digits y in base b such that xyz has no subsequence in M.
1. While L contains nonlinear families (families which are not linear families): Explore each family of L, and update L. Examine each family of L by:
2.1. Let w be the shortest string in the family. If w has a subsequence in M, then remove the family from L. If w represents a prime, then add w to M and remove the family from L.
2.2. If possible, simplify the family.
2.3. Using the techniques below (covering congruence, algebraic factorization, or combine of them), check if the family can be proven to only contain composites (only count the numbers > b), and if so then remove the family from L.
1. Update L, after each split examine the new families as in step 2.

e.g. in decimal (base b = 10):

M := {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991}

L := {2{0,2}1, 2{0,8}7, 3{0,3,6,9}3, 3{0,3,6,9}9, 4{6}9, 5{0,5,8}1, 5{0,2}7, 6{0,3,6,9}3, 6{0,3,4,6,9}9, 7{0,7}7, 8{0,5}1, 8{0}7, 9{0,2,5,8}1, 9{0,3,6,9}3, 9{0,3,4,6,9}9}

and since 2221 is prime, it follows that the family 2{0,2}1 splits into the families 2{0}1 and 2{0}2{0}1

and since the family 2{0}1 can be proven to contain no primes > base (since all numbers in this family are divisible by 3), it can be removed

and since 20201 is prime, it follows that the family 2{0}2{0}1 splits into the families 2{0}21 and 22{0}1

221 and 2021 are composites, but 20021 is prime, thus add 20021 to L

none of 221, 2201, 22001, 220001, 2200001 are primes, but 22000001 is prime, thus add 22000001 to L

and since the family 3{0,3,6,9}3 can be proven to contain no primes > base (since all numbers in this family are divisible by 3), it can be removed

etc.

The process of exploring/examining/splitting a nonlinear family can be concisely expressed in a tree (https://en.wikipedia.org/wiki/Tree_(graph_theory), https://mathworld.wolfram.com/Tree.html) of decompositions, for an example of a tree of decompositions for a nonlinear family (for the family 1{0,1,6}1 in base b = 9) see figure 1 of https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_17.pdf) and figure 1 of https://cs.uwaterloo.ca/~shallit/Papers/br10.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_18.pdf) and figure 1 of https://doi.org/10.1080/10586458.2015.1064048 (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_20.pdf). (in fact, for the main problem in this project, we should consider the family 1{0,1,6,7}1 (in base b = 9) instead of 1{0,1,6}1 (in base b = 9), but these three articles are for the original minimal prime problem (i.e. prime > b is not required))

Shrinking the family x{Y}z (where x and z are strings (may be empty) of digits in base b, Y is a set of digits in base b)

If y ∈ Y and the string xyyz represents a prime > b in base b (in this case, add this prime to the list) or has a subsequence which represents a prime > b in base b, then x{Y}z can be replaced with x{Y \ y}z ∪ x{Y \ y}y{Y \ y}z.
If y₁ ∈ Y and y₂ ∈ Y and y₁ ≠ y₂ and the string xy₁y₂z represents a prime > b in base b (in this case, add this prime to the list) or has a subsequence which represents a prime > b in base b, then x{Y}z can be replaced with x{Y \ y₁}{Y \ y₂}z.
If y₁ ∈ Y and y₂ ∈ Y and y₁ ≠ y₂ and both the strings xy₁y₂z and xy₂y₁z represent a prime > b in base b (in this case, add this prime to the list) or have a subsequence which represents a prime > b in base b, then x{Y}z can be replaced with x{Y \ y₁}z ∪ x{Y \ y₂}z.

e.g. in decimal (base b = 10):

2221 is a prime > 10, thus the family 2{0,2}1 splits into the two families 2{0}1 and 2{0}2{0}1.
227 is a prime > 10, and it is a subsequence of 5227, thus the family 5{0,2}7 splits into the two families 5{0}7 and 5{0}2{0}7.
449 is a prime > 10, and it is a subsequence of 6449, thus the family 6{0,3,4,6,9}9 splits into the two families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9.
Both 5051 and 5501 are primes > 10, thus the family 5{0,5}1 splits into the two families 5{0}1 and 5{5}1 = {5}1.
8501 is a prime > 10, thus the family 8{0,5}1 splits into the family 8{0}{5}1.
887 is a prime > 10, and it is a subsequence of 2887, also 2087 is a prime > 10, thus the family 2{0,8}7 splits into the two families 2{0}7 and 28{0}7.
349 and 449 are primes > 10, and they are subsequences of 9349 and 9449, respectively, also 9049, 9649, 9949 are primes > 10, thus the family 9{0,3,4,6,9}9 splits into the two families 9{0,3,6,9}9 and 94{0,3,6,9}9.
251, 281, 521, 821, 881 are primes > 10, and they are subsequences of 9251, 9281, 9521, 9821, 9881, respectively, also 9001, 9221, 9551, 9851 are primes > 10, thus the family 9{0,2,5,8}1 splits into the numbers {91, 901, 921, 951, 981, 9021, 9051, 9081, 9201, 9501, 9581, 9801, 90581, 95081, 95801}.

If the methods we have discussed cannot be used to rule out or shrink x{Y}z where Y = {y₁, y₂, ..., y_n}, then we can replace x{Y}z by xy₁{Y}z ∪ xy₂{Y}z ∪ ... ∪ xy_n{Y}z and re-run the methods on this new language.

If all remain families are linear families (i.e. of the form x{y}z), then we search the smallest (probable) primes in these families and add these primes to the list.

e.g. in decimal (base b = 10):

The smallest prime in the family 5{0}27 is 5000000000000000000000000000027.
The smallest prime in the family {5}1 is 555555555551.
The smallest prime in the family 8{5}1 is 8555555555555555555551, but 8555555555555555555551 is not minimal prime since 555555555551 is a subsequence of 8555555555555555555551.

There is no guarantee that the techniques discussed will ever terminate, but in practice they often do. They are able to determine the minimal primes in base b for 2 ≤ b ≤ 16 and b = 18, 20, 22, 24, 30. The bases b = 17, 19, 21, 23, 25 ≤ b ≤ 29, 31 ≤ b ≤ 36 are solved with the exception of 793+? families of the form x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b).

(for the examples of nonlinear families, see https://web.archive.org/web/20240305201337/https://stdkmd.net/nrr/prime/primecount3.htm and https://web.archive.org/web/20240305201316/https://stdkmd.net/nrr/prime/primecount3.txt (only base 10 families), nonlinear families usually have small primes if they cannot be ruled out as only containing composites by covering congruence, see the section above)

range of bases b	the factors of bⁿ±1 with 1 ≤ n ≤ 100	the factors of bⁿ±1 with 101 ≤ n ≤ 200	the factors of bⁿ±1 with 201 ≤ n ≤ 300	the factors of bⁿ±1 with 301 ≤ n ≤ 400	the first holes of bⁿ±1 and their known prime factors
2 ≤ b ≤ 100	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=2&TBase=100&FExp=1&TExp=100&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=2&TBase=100&FExp=1&TExp=100&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=2&TBase=100&FExp=1&TExp=100&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=2&TBase=100&FExp=101&TExp=200&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=2&TBase=100&FExp=101&TExp=200&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=2&TBase=100&FExp=101&TExp=200&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=2&TBase=100&FExp=201&TExp=300&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=2&TBase=100&FExp=201&TExp=300&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=2&TBase=100&FExp=201&TExp=300&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=2&TBase=100&FExp=301&TExp=400&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=2&TBase=100&FExp=301&TExp=400&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=2&TBase=100&FExp=301&TExp=400&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFH?FBase=2&TBase=100&c0=&Expanded=, http://myfactorcollection.mooo.com:8090/cgi-bin/showCRHoles?BaseRangeList=A (bases 13 ≤ b ≤ 100 instead of 2 ≤ b ≤ 100, also list known prime factors only for bⁿ < 10²⁵⁵), http://maths-people.anu.edu.au/~brent/ftp/factors/holes.txt (bases 13 ≤ b ≤ 100 instead of 2 ≤ b ≤ 100, also list known prime factors only for bⁿ < 10²⁵⁵)
101 ≤ b ≤ 200	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=101&TBase=200&FExp=1&TExp=100&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=101&TBase=200&FExp=1&TExp=100&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=101&TBase=200&FExp=1&TExp=100&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=101&TBase=200&FExp=101&TExp=200&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=101&TBase=200&FExp=101&TExp=200&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=101&TBase=200&FExp=101&TExp=200&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=101&TBase=200&FExp=201&TExp=300&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=101&TBase=200&FExp=201&TExp=300&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=101&TBase=200&FExp=201&TExp=300&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=101&TBase=200&FExp=301&TExp=400&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=101&TBase=200&FExp=301&TExp=400&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=101&TBase=200&FExp=301&TExp=400&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFH?FBase=101&TBase=200&c0=&Expanded=, http://myfactorcollection.mooo.com:8090/cgi-bin/showCRHoles?BaseRangeList=B (bases 101 ≤ b ≤ 199 instead of 101 ≤ b ≤ 200, also list known prime factors only for bⁿ < 10²⁵⁵)
201 ≤ b ≤ 300	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=201&TBase=300&FExp=1&TExp=100&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=201&TBase=300&FExp=1&TExp=100&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=201&TBase=300&FExp=1&TExp=100&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=201&TBase=300&FExp=101&TExp=200&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=201&TBase=300&FExp=101&TExp=200&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=201&TBase=300&FExp=101&TExp=200&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=201&TBase=300&FExp=201&TExp=300&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=201&TBase=300&FExp=201&TExp=300&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=201&TBase=300&FExp=201&TExp=300&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=201&TBase=300&FExp=301&TExp=400&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=201&TBase=300&FExp=301&TExp=400&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=201&TBase=300&FExp=301&TExp=400&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFH?FBase=201&TBase=300&c0=&Expanded=, http://myfactorcollection.mooo.com:8090/cgi-bin/showCRHoles?BaseRangeList=C (bases 200 ≤ b ≤ 299 instead of 201 ≤ b ≤ 300, also list known prime factors only for bⁿ < 10²⁵⁵)
301 ≤ b ≤ 400	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=301&TBase=400&FExp=1&TExp=100&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=301&TBase=400&FExp=1&TExp=100&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=301&TBase=400&FExp=1&TExp=100&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=301&TBase=400&FExp=101&TExp=200&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=301&TBase=400&FExp=101&TExp=200&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=301&TBase=400&FExp=101&TExp=200&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=301&TBase=400&FExp=201&TExp=300&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=301&TBase=400&FExp=201&TExp=300&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=301&TBase=400&FExp=201&TExp=300&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=301&TBase=400&FExp=301&TExp=400&c0=&EN=&LM= (all factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showPrimFactors?FBase=301&TBase=400&FExp=301&TExp=400&c0=&LM= (only primitive factors) and http://myfactorcollection.mooo.com:8090/cgi-bin/showComps?FBase=301&TBase=400&FExp=301&TExp=400&FDigits=&TDigits=&FTL=&TTL=&c0=&MaxCount=&LabelList=E&SortList=A&CompExp= (remaining composites)	http://myfactorcollection.mooo.com:8090/cgi-bin/showFH?FBase=301&TBase=400&c0=&Expanded=, http://myfactorcollection.mooo.com:8090/cgi-bin/showCRHoles?BaseRangeList=D (bases 300 ≤ b ≤ 400 instead of 301 ≤ b ≤ 400, also list known prime factors only for bⁿ < 10²⁵⁵)

The above section only includes the multiplicative order (https://en.wikipedia.org/wiki/Multiplicative_order, https://t5k.org/glossary/xpage/Order.html, https://mathworld.wolfram.com/MultiplicativeOrder.html, http://www.numbertheory.org/php/order.html, https://oeis.org/A250211, https://oeis.org/A139366, https://oeis.org/A323376, https://oeis.org/A057593, https://oeis.org/A086145) of the base (b) mod the primes (i.e. ord_p(b) with prime p), if you want to calculate the multiplicative order of the base (b) mod a composite number c coprime (https://en.wikipedia.org/wiki/Coprime_integers, https://t5k.org/glossary/xpage/RelativelyPrime.html, https://www.rieselprime.de/ziki/Coprime, https://mathworld.wolfram.com/RelativelyPrime.html, http://www.numericana.com/answer/primes.htm#coprime) to b, factor (https://en.wikipedia.org/wiki/Integer_factorization, https://www.rieselprime.de/ziki/Factorization, https://mathworld.wolfram.com/PrimeFactorization.html, https://mathworld.wolfram.com/PrimeFactorizationAlgorithms.html, http://www.numericana.com/answer/factoring.htm) c to product of distinct prime powers (https://oeis.org/A246655, https://en.wikipedia.org/wiki/Prime_power, https://mathworld.wolfram.com/PrimePower.html), and calculate the multiplicative order of b mod p^e (i.e. ord_p^e(b)) for all these prime powers p^e, and ord_p^e(b) = p^{max(e−r(b,p),0)}×ord_p(b), where r(b,p) is the largest integer s such that p^s divides b^p−1−1, the primes p such that r(b,p) > 1 are called generalized Wieferich prime (https://en.wikipedia.org/wiki/Wieferich_prime, https://t5k.org/glossary/xpage/WieferichPrime.html, https://mathworld.wolfram.com/WieferichPrime.html, https://www.primegrid.com/forum_thread.php?id=9436, https://www.primegrid.com/stats_ww.php, https://oeis.org/A001220) base b.

This is a list for all known generalized Wieferich primes in bases 2 ≤ b ≤ 36 (r(b,p) = 2 for the generalized Wieferich primes p in base b with no orders listed (for these generalized Wieferich primes p, the orders are 1), and r(b,p) = (the order listed) + 1 for the generalized Wieferich primes p in base b with orders listed): (references: http://www.fermatquotient.com/FermatQuotienten/FermQ_Sort.txt, http://www.fermatquotient.com/FermatQuotienten/FermQ_Sorg.txt, http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math11/fer_quo.htm, http://download2.polytechnic.edu.na/pub4/sourceforge/w/wi/wieferich/results/table.txt (although this page is not available in the web and unfortunately has no archive page in the wayback machine), https://web.archive.org/web/20140809030451/http://www1.uni-hamburg.de/RRZ/W.Keller/FermatQuotient.html (prime bases b), https://web.archive.org/web/20140810051836/http://www.cecm.sfu.ca/~mjm/WieferichBarker/WPBS1.html (prime bases b), http://www.bitman.name/math/table/489 (in Italian), http://www.urticator.net/essay/6/624.html, http://go.helms-net.de/math/expdioph/fermatquot_ge2_table1.htm, http://wayback.cecm.sfu.ca/~mjm/WieferichBarker/, https://web.archive.org/web/20160417130531/http://home.earthlink.net/~oddperfect/FermatQuotients.html (prime bases b), https://web.archive.org/web/20060925172546/http://www.lrz-muenchen.de/~hr/tmp/A039951.txt, http://www.primepuzzles.net/puzzles/puzz_762.htm, http://www.sci.kobe-u.ac.jp/old/seminar/pdf/2008_yamazaki.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_63.pdf), https://kconrad.math.uconn.edu/blurbs/gradnumthy/integersradical.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_183.pdf), https://www.ams.org/journals/mcom/1993-61-203/S0025-5718-1993-1182246-5/S0025-5718-1993-1182246-5.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_185.pdf), https://www.ams.org/journals/mcom/2005-74-250/S0025-5718-04-01666-7/S0025-5718-04-01666-7.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_246.pdf), https://www.maa.org/sites/default/files/321929430448.pdf.bannered.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_248.pdf), https://www.maa.org/sites/default/files/321929430448.pdf.bannered.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_249.pdf), http://go.helms-net.de/math/expdioph/fermatquotients.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_64.pdf))

(Also OEIS sequences for the smallest generalized Wieferich primes p in base b: https://oeis.org/A039951, https://oeis.org/A174422 (prime b), https://oeis.org/A268352 (2nd smallest prime), https://oeis.org/A178871 (2nd smallest prime, prime b), https://oeis.org/A096082 (p = 2 not allowed), https://oeis.org/A255838 (p > b required, prime b), https://oeis.org/A247072 (p > sqrt(b) required))

b	generalized Wieferich primes in base b (written in base 10)	search limit	OEIS sequence
2	1093, 3511, ...	6×10¹⁷	https://oeis.org/A001220
3	11, 1006003, ...	1.2×10¹⁵	https://oeis.org/A014127
4	1093, 3511, ...	6×10¹⁷	the same as https://oeis.org/A001220
5	2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801, ...	1.2×10¹⁵	https://oeis.org/A123692
6	66161, 534851, 3152573, ...	1.816×10¹⁴	https://oeis.org/A212583
7	5, 491531, ...	1.2×10¹⁵	https://oeis.org/A123693
8	3, 1093, 3511, ...	6×10¹⁷	the same as https://oeis.org/A001220 plus the prime 3
9	2 (order 2), 11, 1006003, ...	1.2×10¹⁵	the same as https://oeis.org/A014127 plus the prime 2
10	3, 487, 56598313, ...	1.816×10¹⁴	https://oeis.org/A045616
11	71, ...	1.816×10¹⁴	–
12	2693, 123653, ...	1.816×10¹⁴	https://oeis.org/A111027
13	2, 863, 1747591, ...	1.816×10¹⁴	https://oeis.org/A128667
14	29, 353, 7596952219, ...	1.816×10¹⁴	https://oeis.org/A234810
15	29131, 119327070011, ...	1.816×10¹⁴	https://oeis.org/A242741
16	1093, 3511, ...	6×10¹⁷	the same as https://oeis.org/A001220
17	2 (order 3), 3, 46021, 48947, 478225523351, ...	1.816×10¹⁴	https://oeis.org/A128668
18	5, 7 (order 2), 37, 331, 33923, 1284043, ...	1.816×10¹⁴	https://oeis.org/A244260
19	3, 7 (order 2), 13, 43, 137, 63061489, ...	1.816×10¹⁴	https://oeis.org/A090968
20	281, 46457, 9377747, 122959073, ...	1.816×10¹⁴	https://oeis.org/A242982
21	2, ...	1.816×10¹⁴	–
22	13, 673, 1595813, 492366587, 9809862296159, ...	1.816×10¹⁴	https://oeis.org/A298951
23	13, 2481757, 13703077, 15546404183, 2549536629329, ...	1.816×10¹⁴	https://oeis.org/A128669
24	5, 25633, ...	1.816×10¹⁴	–
25	2 (order 2), 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801, ...	1.2×10¹⁵	the same as https://oeis.org/A123692
26	3 (order 2), 5, 71, 486999673, 6695256707, ...	1.816×10¹⁴	https://oeis.org/A306255
27	11, 1006003, ...	1.2×10¹⁵	the same as https://oeis.org/A014127
28	3 (order 2), 19, 23, ...	1.816×10¹⁴	–
29	2, ...	1.816×10¹⁴	–
30	7, 160541, 94727075783, ...	1.816×10¹⁴	https://oeis.org/A306256
31	7, 79, 6451, 2806861, ...	1.816×10¹⁴	https://oeis.org/A331424
32	5, 1093, 3511, ...	6×10¹⁷	the same as https://oeis.org/A001220 plus the prime 5
33	2 (order 4), 233, 47441, 9639595369, ...	1.816×10¹⁴	–
34	46145917691, ...	1.816×10¹⁴	–
35	3, 1613, 3571, ...	1.816×10¹⁴	–
36	66161, 534851, 3152573, ...	1.816×10¹⁴	the same as https://oeis.org/A212583

(a×bⁿ+c)/gcd(a+c,b−1) (with a ≥ 1, b ≥ 2, c ≠ 0, gcd(a,c) = 1, gcd(b,c) = 1) has algebraic factorization if and only if either "there is an integer r > 1 such that a×bⁿ and −c are both rth powers" (in this case, (a×bⁿ+c)/gcd(a+c,b−1) has sum-of-two-rth-powers factorization if c > 0, or difference-of-two-rth-powers factorization if c < 0, although there is no "sum-of-two-rth-powers factorization" for even r, but no such situation (i.e. c > 0 and r is even) exists, since if c > 0 then −c < 0, but negative numbers cannot be squares, however, if r is even then all rth powers are squares (since if s divides r, then all rth powers are sth powers), thus, −c cannot be an rth power if c > 0 and r is even) or "one of a×bⁿ and c is a 4th power, and the other is of the form 4×m⁴" (in this case, (a×bⁿ+c)/gcd(a+c,b−1) has Aurifeuillean factorization of x⁴+4×y⁴), thus, if |c| (the absolute value (https://en.wikipedia.org/wiki/Absolute_value, https://www.rieselprime.de/ziki/Absolute_value, https://mathworld.wolfram.com/AbsoluteValue.html) of c) is not a perfect power (https://oeis.org/A001597, https://en.wikipedia.org/wiki/Perfect_power, https://mathworld.wolfram.com/PerfectPower.html, https://www.numbersaplenty.com/set/perfect_power/), then there is no n such that (a×bⁿ+c)/gcd(a+c,b−1) has algebraic factorization, also, if there is no n such that a×bⁿ is a perfect power (https://oeis.org/A001597, https://en.wikipedia.org/wiki/Perfect_power, https://mathworld.wolfram.com/PerfectPower.html, https://www.numbersaplenty.com/set/perfect_power/), then there is no n such that (a×bⁿ+c)/gcd(a+c,b−1) has algebraic factorization.

We can show that: For the case of covering congruence, the numbers in the family are not equal to any element in S, if n makes the numbers > b, thus these factorizations are nontrivial (https://en.wikipedia.org/wiki/Triviality_(mathematics), https://mathworld.wolfram.com/Trivial.html); for the case of algebraic factorization (if the numbers are factored as F × G / d), both F and G are > d, if n makes the numbers > b, thus these factorizations are nontrivial (the exceptions are the base 9 family {1} and the base 25 family {1} and the base 27 family 9{G} and the base 32 family {1}. For the base 9 family {1}, the algebraic form is (9ⁿ−1)/8 with n ≥ 2, and can be factored to (3ⁿ−1) × (3ⁿ+1) / 8, if n ≥ 3, then both 3ⁿ−1 and 3ⁿ+1 are > 8, thus these factorizations are nontrivial, it only remains to check the case n = 2, but the number with n = 2 is 10 = 2 × 5 is not prime; for the base 25 family {1}, the algebraic form is (25ⁿ−1)/24 with n ≥ 2, and can be factored to (5ⁿ−1) × (5ⁿ+1) / 24, if n ≥ 3, then both 5ⁿ−1 and 5ⁿ+1 are > 24, thus these factorizations are nontrivial, it only remains to check the case n = 2, but the number with n = 2 is 26 = 2 × 13 is not prime; for the base 27 family 9{G}, the algebraic form is (125×27ⁿ−8)/13 with n ≥ 1, and can be factored to (5×3ⁿ−2) × (25×9ⁿ+10×3ⁿ+4) / 13, if n ≥ 2, then both 5×3ⁿ−2 and 25×9ⁿ+10×3ⁿ+4 are > 13, thus these factorizations are nontrivial, it only remains to check the case n = 1, but the number with n = 1 is 259 = 7 × 37 is not prime; for the base 32 family {1}, the algebraic form is (32ⁿ−1)/31 with n ≥ 2, and can be factored to (2ⁿ−1) × (16ⁿ+8ⁿ+4ⁿ+2ⁿ+1) / 31, if n ≥ 6, then both 2ⁿ−1 and 16ⁿ+8ⁿ+4ⁿ+2ⁿ+1 are > 31, thus these factorizations are nontrivial, it only remains to check the cases n = 2, 3, 4, 5, but the numbers with n = 2, 3, 4, 5 are 33 = 3 × 11, 1057 = 7 × 151, 33825 = 3 × 5² × 11 × 41, 1082401 = 601 × 1801 are not primes); for the case of combine of covering congruence and algebraic factorization (if the numbers are factored as F × G / d), the numbers in the family are not equal to any element in S and both F and G are > d, if n makes the numbers > b, thus these factorizations are nontrivial.

type for a family can be ruled out as only containing composites (only count the numbers > b)	possible bases b	such bases 2 ≤ b ≤ 36
covering congruence with 1 prime	any base b (however, all such families in base b = 2 end with 0 and thus have trailing zeros (https://en.wikipedia.org/wiki/Trailing_zero) and thus not counted)	(2), 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36
covering congruence with 2 primes	b such that b+1 is not a prime power (https://oeis.org/A246655, https://en.wikipedia.org/wiki/Prime_power, https://mathworld.wolfram.com/PrimePower.html) (however, the case b = 5 has only four such families: {1}3, {1}4, 3{1}, 4{1}, all of them are covered by the prime 111 (31 in decimal), thus the smallest base b with families which have covering congruence with 2 primes is b = 9)	(5), 9, 11, 13, 14, 17, 19, 20, 21, 23, 25, 27, 29, 32, 33, 34, 35
covering congruence with 3 primes and period 3	b such that omega(b²+b+1) ≥ 3 (where omega is the omega function (https://en.wikipedia.org/wiki/Prime_omega_function, https://oeis.org/A001221), the number of distinct primes dividing n)	16, 25
covering congruence with 3 primes and period 4	b such that b+1 is not a power of 2 (https://oeis.org/A000079, https://en.wikipedia.org/wiki/Power_of_two) and b²+1 is not a prime power (https://oeis.org/A246655, https://en.wikipedia.org/wiki/Prime_power, https://mathworld.wolfram.com/PrimePower.html) (however, bases b = 5, 8, 9, 11, 12, 18 has no such families, base 8 family 6{4}7 is covered by the prime 4₂₂₀7)	(5), (8), (9), (11), (12), 13, 17, (18), 19, 21, 22, 23, 25, 27, 28, 29, 30, 32, 33, 34, 35
algebraic factorization with difference of two squares	b such that b is square (https://oeis.org/A000290, https://en.wikipedia.org/wiki/Square_number, https://www.rieselprime.de/ziki/Square_number, https://mathworld.wolfram.com/SquareNumber.html, https://www.numbersaplenty.com/set/square_number/) (however, base b = 4 has no such families, the family {1} has the prime 11 (5 in decimal))	(4), 9, 16, 25, 36
algebraic factorization with sum/difference of two cubes	b such that b is cube (https://oeis.org/A000578, https://en.wikipedia.org/wiki/Cube_(algebra), https://mathworld.wolfram.com/CubicNumber.html, https://www.numbersaplenty.com/set/cubic_number/) (however, base b = 8 has no such families which have algebraic factorization with difference of two cubes, the family {1} has the prime 111 (73 in decimal), base b = 8 only have families which have algebraic factorization with sum of two cubes)	8, 27
algebraic factorization with sum/difference of two 5th powers	b such that b is 5th power (https://oeis.org/A000584, https://en.wikipedia.org/wiki/Fifth_power_(algebra))	32
algebraic factorization with x⁴+4×y⁴	b such that b is 4th power (https://oeis.org/A000583, https://en.wikipedia.org/wiki/Fourth_power, https://mathworld.wolfram.com/BiquadraticNumber.html)	16
combine of covering congruence with 1 prime and algebraic factorization with difference of two squares	b such that b is not square (https://oeis.org/A000290, https://en.wikipedia.org/wiki/Square_number, https://www.rieselprime.de/ziki/Square_number, https://mathworld.wolfram.com/SquareNumber.html, https://www.numbersaplenty.com/set/square_number/) and b+1 has a prime factor p == 1 mod 4	12, 14, 19, 24, 28, 29, 33, 34

The algebraic form of 9_nD (in base b = 21) is (9×21ⁿ⁺¹+71)/20, and 71 is not a perfect power, thus the family 9_nD (in base b = 21) has no algebraic factorization for any n
9_nD (in base b = 21) is divisible by 2 if and only if n == 1 mod 2
9_nD (in base b = 21) is divisible by 43 if and only if n == 2 mod 7
9_nD (in base b = 21) is divisible by 97 if and only if n == 2 mod 96
9_nD (in base b = 21) is divisible by 5 if and only if n == 3 mod 5
9_nD (in base b = 21) is divisible by 547 if and only if n == 3 mod 39
9_nD (in base b = 21) is divisible by 13 if and only if n == 0 mod 4
9_nD (in base b = 21) is divisible by 109 if and only if n == 4 mod 27
9_nD (in base b = 21) is divisible by 1297 if and only if n == 4 mod 648
9_nD (in base b = 21) is divisible by 23 if and only if n == 6 mod 22
9_nD (in base b = 21) is divisible by 37 if and only if n == 6 mod 18
9_nD (in base b = 21) is divisible by 138679 if and only if n == 10 mod 69339
9_nD (in base b = 21) is divisible by 31 if and only if n == 14 mod 30
9_nD (in base b = 21) is divisible by 957158401 if and only if n == 22 mod 957158400
9_nD (in base b = 21) is divisible by 113 if and only if n == 26 mod 112
9_nD (in base b = 21) is divisible by 149 if and only if n == 26 mod 148
9_nD (in base b = 21) is divisible by 83 if and only if n == 34 mod 41
9_nD (in base b = 21) is divisible by 151 if and only if n == 34 mod 75
9_nD (in base b = 21) is divisible by 317 if and only if n == 34 mod 316
9_nD (in base b = 21) is divisible by 571 if and only if n == 46 mod 285

etc.

and it does not appear to be any covering set (of either primes or algebraic factors, or both), thus this form cannot be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them), and its Nash weight (or difficulty) is positive, and it has prime candidate, and hence there must be a prime at some point.

Also, you can see the prime factorizations (https://en.wikipedia.org/wiki/Integer_factorization, https://www.rieselprime.de/ziki/Factorization, https://mathworld.wolfram.com/PrimeFactorization.html, https://mathworld.wolfram.com/PrimeFactorizationAlgorithms.html, http://www.numericana.com/answer/factoring.htm) of the numbers in the family 9_nD in base b = 21: (for more information, see http://factordb.com/index.php?query=%289*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

n	currently known prime factorization of the number 9_nD in base b = 21
1	2 × 101
2	43 × 97
3	2⁵ × 5 × 547
4	13 × 109 × 1297
5	2 × 19297379
6	23 × 37 × 952397
7	2² × 19 × 3491 × 64151
8	5 × 13 × 373 × 14742257
10	138679 × 1136616757
14	31 × 20605229 × 47991331061
18	5 × 44600683 × 127256483 × 210081439
22	957158401 × 1211357903339029702951
26	113 × 149 × 293877403 × 45572469859265068620757
34	83 × 151 × 317 × 116959 × 1833983 × 10007937292019458273806456107
46	571 × 172443379 × (51-digit prime)
54	64514074883 × 1952284707517 × (50-digit prime)
62	1987 × 2179 × 4491749 × 31018210441926961332833324941 × (42-digit prime)
66	10169 × 669662569903 × (73-digit prime)
70	2107831759082832524772111929 × 194079650340743929919158086605141 × 8297867485221151080164383803051187

and it does not appear to be any covering congruence of primes, since if there is a covering congruence of primes for the family {9}D in base b = 21, then the period must be at least lcm(2, ord₄₃(21), ord₁₃(21), ord₂₃(21), ord₁₃₈₆₇₉(21), ord₃₁(21), 5, ord_957158401(21), ord₁₁₃(21), ord₈₃(21), ord₅₇₁(21), ord_64514074883(21), ord₁₉₈₇(21), ord₁₀₁₆₉(21), ord_{2107831759082832524772111929}(21)) (note: since the primes p = 2 and p = 5 divides b−1 = 21−1 = 20, and for these two primes, ord_p(21) = 1, thus the smallest n such that R_n(21) (where "R_n(b)" means the repunit in base b with length n, i.e. R_n(b) = (bⁿ−1)/(b−1) (see https://stdkmd.net/nrr/repunit/repunitnote.htm#repunit_factorization)) is divisible by p is the primes p themselves instead of ord_p(21) = 1, thus their period is the primes p themselves instead of ord_p(21) = 1, their situation is like the prime p = 3 in decimal (b = 10)) (where lcm is the least common multiple (https://en.wikipedia.org/wiki/Least_common_multiple, https://mathworld.wolfram.com/LeastCommonMultiple.html, http://www.numericana.com/answer/numbers.htm#lcm), ord_n(b) is the multiplicative order (https://en.wikipedia.org/wiki/Multiplicative_order, https://t5k.org/glossary/xpage/Order.html, https://mathworld.wolfram.com/MultiplicativeOrder.html, http://www.numbertheory.org/php/order.html, https://oeis.org/A250211, https://oeis.org/A139366, https://oeis.org/A323376, https://oeis.org/A057593, https://oeis.org/A086145) of b mod n) = lcm(2, 7, 4, 22, 69339, 30, 5, 957158400, 112, 41, 285, 32257037441, 662, 2542, 2107831759082832524772111928) = 7191035432210805538926222608335822284250318907919283200 > 7.19103 × 10⁵⁴, which is very impossible, and since 71 is not a perfect power, thus the family 9_nD (in base b = 21) = (9×21ⁿ⁺¹+71)/20 has no algebraic factorization for any n, thus the possbility that the family {9}D in base b = 21 can be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them) is very small (< 1/(7.19103 × 10⁵⁴)), thus we can almost sure that there is a prime > b in the family {9}D in base b = 21, in fact, we can almost sure that there are infinitely many primes > b in the family {9}D in base b = 21.

For an example of an unsolved family in bases 2 ≤ b ≤ 36 with a very low (but still positive) Nash weight (https://www.rieselprime.de/ziki/Nash_weight, http://irvinemclean.com/maths/nash.htm, http://www.brennen.net/primes/ProthWeight.html, https://www.mersenneforum.org/showthread.php?t=11844, https://www.mersenneforum.org/showthread.php?t=2645, https://www.mersenneforum.org/showthread.php?t=7213, https://www.mersenneforum.org/showthread.php?t=18818, https://www.mersenneforum.org/showpost.php?p=50442&postcount=1, https://www.mersenneforum.org/showpost.php?p=50444&postcount=1, https://www.mersenneforum.org/showpost.php?p=201642&postcount=1, https://www.mersenneforum.org/attachment.php?attachmentid=13663&d=1451910741, https://github.com/happy5214/nash, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/allnash, https://www.rieselprime.de/ziki/Riesel_2_Low-weight, https://www.rieselprime.de/ziki/Proth_2_Low-weight, https://www.rieselprime.de/ziki/Category:Riesel_2_Low-weight, https://www.rieselprime.de/ziki/Category:Proth_2_Low-weight, https://www.rieselprime.de/ziki/Category:Riesel_5_Low-weight, https://www.rieselprime.de/ziki/Category:Proth_5_Low-weight, https://web.archive.org/web/20230928115952/http://www.noprimeleftbehind.net/crus/vstats_new/riesel_weights.txt, https://web.archive.org/web/20230928120009/http://www.noprimeleftbehind.net/crus/vstats_new/sierpinski_weights.txt, https://arxiv.org/pdf/2307.07894.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_203.pdf), https://web.archive.org/web/20231002020455/http://yves.gallot.pagesperso-orange.fr/papers/weight.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_216.pdf)) (or difficulty (https://stdkmd.net/nrr/prime/prime_difficulty.htm, https://stdkmd.net/nrr/prime/prime_difficulty.txt, https://web.archive.org/web/20240305201107/https://stdkmd.net/nrr/prime/primedifficulty.htm, https://web.archive.org/web/20240305201027/https://stdkmd.net/nrr/prime/primedifficulty.txt, http://www.noprimeleftbehind.net/crus/vstats_new/crus-unproven.htm, https://web.archive.org/web/20230928120025/http://www.noprimeleftbehind.net/crus/vstats_new/riesel_difficulty.txt, https://web.archive.org/web/20230928120047/http://www.noprimeleftbehind.net/crus/vstats_new/sierpinski_difficulty.txt)), the family 5{H}5 in base b = 19: (its algebraic form is (107×19ⁿ⁺¹−233)/18, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%28107*19%5E%28n%2B1%29-233%29%2F18&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

5H_n5 (in base b = 19) is divisible by 2 if and only if n == 0 mod 2 (and to this step, only n == 1 mod 2 gives possible candidates for prime numbers!)
5H_n5 (in base b = 19) is divisible by 3 if and only if n == 1 mod 3 (and to this step, only n == 3, 5 mod 6 gives possible candidates for prime numbers!)
5H_n5 (in base b = 19) is divisible by 7 if and only if n == 5 mod 6 (and to this step, only n == 3 mod 6 gives possible candidates for prime numbers!)
5H_n5 (in base b = 19) is divisible by 13 if and only if n == 9 mod 12 (and to this step, only n == 3 mod 12 gives possible candidates for prime numbers!)
5H_n5 (in base b = 19) is divisible by 17 if and only if n == 3 mod 8 (and to this step, only n == 15 mod 24 gives possible candidates for prime numbers!)

Thus the only interesting cases to search for possible primes are when n == 15 mod 24 (and thus the Nash weight (or difficulty) of this family is less than 1/24), and the least prime factor (http://mathworld.wolfram.com/LeastPrimeFactor.html, https://oeis.org/A020639) of 5H_n5 (in base b = 19) is ≤ 17 if n is not == 15 mod 24, and 5H_n5 (in base b = 19) is not 19-rough number (https://en.wikipedia.org/wiki/Rough_number, https://mathworld.wolfram.com/RoughNumber.html, https://oeis.org/A007310, https://oeis.org/A007775, https://oeis.org/A008364, https://oeis.org/A008365, https://oeis.org/A008366, https://oeis.org/A166061, https://oeis.org/A166063) if n is not == 15 mod 24, and thus if we sieve (https://www.rieselprime.de/ziki/Sieving, https://www.rieselprime.de/ziki/Sieving_a_range_of_sequences, https://mathworld.wolfram.com/Sieve.html, http://www.rechenkraft.net/yoyo/y_status_sieve.php, https://www.primegrid.com/stats_psp_sieve.php, https://www.primegrid.com/stats_pps_sieve.php, https://www.primegrid.com/stats_sr5_sieve.php, https://www.primegrid.com/stats_cw_sieve.php, https://www.primegrid.com/sieving/rsp/) the family 5H_n5 (in base b = 19) with primes ≤ 17, then all n not == 15 mod 24 will be removed.

And for n == 15 mod 24, we have: (all "composites without known proper factor > 1" in the list below have been trial factored (https://en.wikipedia.org/wiki/Trial_division, https://t5k.org/glossary/xpage/TrialDivision.html, https://www.rieselprime.de/ziki/Trial_factoring, https://mathworld.wolfram.com/TrialDivision.html, http://www.numericana.com/answer/factoring.htm#trial, https://www.mersenne.ca/tf1G/, https://www.mersenne.ca/tfmissed.php, https://oeis.org/A189172) to 10¹², also none of these composites have algebraic factors)

n	currently known prime factorization of the number 5H_n5 in base b = 19
15	11 × 29 × 47 × 71 × 439 × 15287 × 240013247
39	281 × 9833 × 99133 × 281717 × 390527 × 278727989572543299217912827703
63	11063830209439375789 × (64-digit prime)
87	3889 × 21599 × 5720809 × 832699912393 × (87-digit composite without known proper factor > 1, this composite has already checked with P−1 to B1 = 50000 and 3 times P+1 to B1 = 150000 and 10 times ECM to B1 = 250000 (these can be checked for composites < 10³⁰⁰), see http://factordb.com/sequences.php?se=1&aq=%2810719%5E88-233%29%2F18&action=last20&fr=0&to=100, the "Check for factors" box shows "Already checked", this is the ECM* effort t-level (https://oeis.org/wiki/OEIS_sequences_needing_factors#T-levels, https://stdkmd.net/nrr/wanted.htm (the "ECM" column of the three tables), https://stdkmd.net/nrr/c.cgi?q=37771_259#ecm, https://stdkmd.net/nrr/c.cgi?q=23333_233#ecm, http://myfactorcollection.mooo.com:8090/lists.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the lists in the boxes), http://myfactorcollection.mooo.com:8090/dbio.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the DB inputs/outputs in the boxes), https://github.com/brubsby/t-level, https://www.mersenneforum.org/showthread.php?t=29615) t30 (see http://www.loria.fr/~zimmerma/records/ecm/params.html and https://www.rieselprime.de/ziki/Elliptic_curve_method#Choosing_the_best_parameters_for_ECM), i.e. the prime factors of this composite number are probably > 10³⁰)
111	89 × (143-digit composite without known proper factor > 1, this composite has already checked with P−1 to B1 = 50000 and 3 times P+1 to B1 = 150000 and 10 times ECM to B1 = 250000 (these can be checked for composites < 10³⁰⁰), see http://factordb.com/sequences.php?se=1&aq=%2810719%5E112-233%29%2F18&action=last20&fr=0&to=100, the "Check for factors" box shows "Already checked", this is the ECM* effort t-level (https://oeis.org/wiki/OEIS_sequences_needing_factors#T-levels, https://stdkmd.net/nrr/wanted.htm (the "ECM" column of the three tables), https://stdkmd.net/nrr/c.cgi?q=37771_259#ecm, https://stdkmd.net/nrr/c.cgi?q=23333_233#ecm, http://myfactorcollection.mooo.com:8090/lists.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the lists in the boxes), http://myfactorcollection.mooo.com:8090/dbio.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the DB inputs/outputs in the boxes), https://github.com/brubsby/t-level, https://www.mersenneforum.org/showthread.php?t=29615) t30 (see http://www.loria.fr/~zimmerma/records/ecm/params.html and https://www.rieselprime.de/ziki/Elliptic_curve_method#Choosing_the_best_parameters_for_ECM), i.e. the prime factors of this composite number are probably > 10³⁰)
135	11 × 75193 × (169-digit composite without known proper factor > 1, this composite has already checked with P−1 to B1 = 50000 and 3 times P+1 to B1 = 150000 and 10 times ECM to B1 = 250000 (these can be checked for composites < 10³⁰⁰), see http://factordb.com/sequences.php?se=1&aq=%2810719%5E136-233%29%2F18&action=last20&fr=0&to=100, the "Check for factors" box shows "Already checked", this is the ECM* effort t-level (https://oeis.org/wiki/OEIS_sequences_needing_factors#T-levels, https://stdkmd.net/nrr/wanted.htm (the "ECM" column of the three tables), https://stdkmd.net/nrr/c.cgi?q=37771_259#ecm, https://stdkmd.net/nrr/c.cgi?q=23333_233#ecm, http://myfactorcollection.mooo.com:8090/lists.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the lists in the boxes), http://myfactorcollection.mooo.com:8090/dbio.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the DB inputs/outputs in the boxes), https://github.com/brubsby/t-level, https://www.mersenneforum.org/showthread.php?t=29615) t30 (see http://www.loria.fr/~zimmerma/records/ecm/params.html and https://www.rieselprime.de/ziki/Elliptic_curve_method#Choosing_the_best_parameters_for_ECM), i.e. the prime factors of this composite number are probably > 10³⁰)
159	26021 × 1645306722881711 × (186-digit composite without known proper factor > 1, this composite has already checked with P−1 to B1 = 50000 and 3 times P+1 to B1 = 150000 and 10 times ECM to B1 = 250000 (these can be checked for composites < 10³⁰⁰), see http://factordb.com/sequences.php?se=1&aq=%2810719%5E160-233%29%2F18&action=last20&fr=0&to=100, the "Check for factors" box shows "Already checked", this is the ECM* effort t-level (https://oeis.org/wiki/OEIS_sequences_needing_factors#T-levels, https://stdkmd.net/nrr/wanted.htm (the "ECM" column of the three tables), https://stdkmd.net/nrr/c.cgi?q=37771_259#ecm, https://stdkmd.net/nrr/c.cgi?q=23333_233#ecm, http://myfactorcollection.mooo.com:8090/lists.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the lists in the boxes), http://myfactorcollection.mooo.com:8090/dbio.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the DB inputs/outputs in the boxes), https://github.com/brubsby/t-level, https://www.mersenneforum.org/showthread.php?t=29615) t30 (see http://www.loria.fr/~zimmerma/records/ecm/params.html and https://www.rieselprime.de/ziki/Elliptic_curve_method#Choosing_the_best_parameters_for_ECM), i.e. the prime factors of this composite number are probably > 10³⁰)
183	29 × (235-digit composite without known proper factor > 1, this composite has already checked with P−1 to B1 = 50000 and 3 times P+1 to B1 = 150000 and 10 times ECM to B1 = 250000 (these can be checked for composites < 10³⁰⁰), see http://factordb.com/sequences.php?se=1&aq=%2810719%5E184-233%29%2F18&action=last20&fr=0&to=100, the "Check for factors" box shows "Already checked", this is the ECM* effort t-level (https://oeis.org/wiki/OEIS_sequences_needing_factors#T-levels, https://stdkmd.net/nrr/wanted.htm (the "ECM" column of the three tables), https://stdkmd.net/nrr/c.cgi?q=37771_259#ecm, https://stdkmd.net/nrr/c.cgi?q=23333_233#ecm, http://myfactorcollection.mooo.com:8090/lists.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the lists in the boxes), http://myfactorcollection.mooo.com:8090/dbio.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the DB inputs/outputs in the boxes), https://github.com/brubsby/t-level, https://www.mersenneforum.org/showthread.php?t=29615) t30 (see http://www.loria.fr/~zimmerma/records/ecm/params.html and https://www.rieselprime.de/ziki/Elliptic_curve_method#Choosing_the_best_parameters_for_ECM), i.e. the prime factors of this composite number are probably > 10³⁰)

and it does not appear to be any covering congruence of primes, besides, since 233 is not a perfect power, thus the family 5H_n5 (in base b = 19) has no algebraic factorization for any n, thus its Nash weight (or difficulty) is positive (although very low), so there must be a prime at some point (and the corresponding n must be == 15 mod 24).

And for n == 15 mod 24, we have: (all "composites without known proper factor > 1" in the list below have been trial factored (https://en.wikipedia.org/wiki/Trial_division, https://t5k.org/glossary/xpage/TrialDivision.html, https://www.rieselprime.de/ziki/Trial_factoring, https://mathworld.wolfram.com/TrialDivision.html, http://www.numericana.com/answer/factoring.htm#trial, https://www.mersenne.ca/tf1G/, https://www.mersenne.ca/tfmissed.php, https://oeis.org/A189172) to 10⁹, also none of these composites have algebraic factors)

Also the family C{H}C in base b = 19: (its algebraic form is (233×19ⁿ⁺¹−107)/18, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%28233*19%5E%28n%2B1%29-107%29%2F18&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show) (in fact, it is the dual (http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_1.pdf), https://www.rechenkraft.net/wiki/Five_or_Bust, https://oeis.org/A076336/a076336c.html, http://www.mit.edu/~kenta/three/prime/dual-sierpinski/ezgxggdm/dualsierp-excerpt.txt, http://mit.edu/kenta/www/three/prime/dual-sierpinski/ezgxggdm/dualsierp.txt.gz, http://www.bitman.name/math/article/1126, http://www.bitman.name/math/article/1125, https://www.mersenneforum.org/showpost.php?p=144991&postcount=1, https://www.mersenneforum.org/showthread.php?t=10761, https://www.mersenneforum.org/showthread.php?t=6545) family of the family 5{H}5 in base b = 19, thus they have the same Nash weight (https://www.rieselprime.de/ziki/Nash_weight, http://irvinemclean.com/maths/nash.htm, http://www.brennen.net/primes/ProthWeight.html, https://www.mersenneforum.org/showthread.php?t=11844, https://www.mersenneforum.org/showthread.php?t=2645, https://www.mersenneforum.org/showthread.php?t=7213, https://www.mersenneforum.org/showthread.php?t=18818, https://www.mersenneforum.org/showpost.php?p=50442&postcount=1, https://www.mersenneforum.org/showpost.php?p=50444&postcount=1, https://www.mersenneforum.org/showpost.php?p=201642&postcount=1, https://www.mersenneforum.org/attachment.php?attachmentid=13663&d=1451910741, https://github.com/happy5214/nash, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/allnash, https://www.rieselprime.de/ziki/Riesel_2_Low-weight, https://www.rieselprime.de/ziki/Proth_2_Low-weight, https://www.rieselprime.de/ziki/Category:Riesel_2_Low-weight, https://www.rieselprime.de/ziki/Category:Proth_2_Low-weight, https://www.rieselprime.de/ziki/Category:Riesel_5_Low-weight, https://www.rieselprime.de/ziki/Category:Proth_5_Low-weight, https://web.archive.org/web/20230928115952/http://www.noprimeleftbehind.net/crus/vstats_new/riesel_weights.txt, https://web.archive.org/web/20230928120009/http://www.noprimeleftbehind.net/crus/vstats_new/sierpinski_weights.txt, https://arxiv.org/pdf/2307.07894.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_203.pdf), https://web.archive.org/web/20231002020455/http://yves.gallot.pagesperso-orange.fr/papers/weight.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_216.pdf)) (or difficulty (https://stdkmd.net/nrr/prime/prime_difficulty.htm, https://stdkmd.net/nrr/prime/prime_difficulty.txt, https://web.archive.org/web/20240305201107/https://stdkmd.net/nrr/prime/primedifficulty.htm, https://web.archive.org/web/20240305201027/https://stdkmd.net/nrr/prime/primedifficulty.txt, http://www.noprimeleftbehind.net/crus/vstats_new/crus-unproven.htm, https://web.archive.org/web/20230928120025/http://www.noprimeleftbehind.net/crus/vstats_new/riesel_difficulty.txt, https://web.archive.org/web/20230928120047/http://www.noprimeleftbehind.net/crus/vstats_new/sierpinski_difficulty.txt)), a family can be proven to only contain composites or only contain finitely many primes by covering congruence, algebraic factorization, or combine of them if and only if its dual family can also be proven to only contain composites or only contain finitely many primes by covering congruence, algebraic factorization, or combine of them (note: this is not true for all reasons for a family can be proven to only contain composites or only contain finitely many primes, e.g. 8×128ⁿ+1, 32×128ⁿ+1, 64×128ⁿ+1 can be proven to only contain composites, while their dual families (16×128ⁿ+1, 4×128ⁿ+1, 2×128ⁿ+1, respectively) cannot be proven to only contain composites or only contain finitely many primes, in fact, the latter two of them have known primes (4×128²+1 and 2×128¹+1, respectively), the reason for these three families is combine of sum-of-two-pth-powers factorization for the odd primes p which are not quadratic residues (https://en.wikipedia.org/wiki/Quadratic_residue, https://t5k.org/glossary/xpage/QuadraticResidue.html, https://www.rieselprime.de/ziki/Quadratic_residue, https://mathworld.wolfram.com/QuadraticResidue.html) mod 7 (i.e. the odd primes p == 3, 5, 6 mod 7) (i.e. the odd primes p in https://oeis.org/A003625), and by the Dirichlet's theorem (https://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions, https://t5k.org/glossary/xpage/DirichletsTheorem.html, https://mathworld.wolfram.com/DirichletsTheorem.html, http://www.numericana.com/answer/primes.htm#dirichlet), there are infinitely many such odd primes p, thus, the reason for these three families is combine of sum-of-two-pth-powers factorization for infinitely many odd primes p (and the period is also infinite), and such infinite-cover does not apply to this), every family has a corresponding dual family (although the dual family may not corresponding to minimal primes), (assuming a ≥ 1, b ≥ 2 (b is the base), c ≠ 0, gcd(a,c) = 1, gcd(b,c) = 1) if gcd(a,b) = 1, then the dual family of a×bⁿ+1 is bⁿ+a, and the dual family of a×bⁿ−1 is bⁿ−a, more generally, if gcd(a,b) = 1 and c > 0, then the dual family of (a×bⁿ+c)/gcd(a+c,b−1) is (c×bⁿ+a)/gcd(a+c,b−1), and the dual family of (a×bⁿ−c)/gcd(a+c,b−1) is (c×bⁿ−a)/gcd(a+c,b−1), however, when gcd(a,b) > 1, some dual families may not be easy to be observe, e.g. the dual family of 5×10ⁿ+27 (the family 5{0}27 in decimal (base b = 10), the family corresponding to the largest minimal prime in decimal (base b = 10), i.e. 5×10²⁸+27, or 50₂₈27) is 54×10ⁿ+1 (the family 54{0}1 in decimal (base b = 10), which does not correspond to any minimal prime), and the dual family of (5×10ⁿ−41)/9 (the family {5}1 in decimal (base b = 10), the family corresponding to the second-largest minimal prime in decimal (base b = 10), i.e. (5×10¹²−41)/9, or 5₁₁1) is (82×10ⁿ−1)/9 (the family 9{1} in decimal (base b = 10), which does not correspond to any minimal prime), besides, only families of the form bⁿ+1 (with even b), (bⁿ+1)/2 (with odd b), (bⁿ−1)/(b−1), (sqrt(b)×bⁿ−1)/(sqrt(b)−1) (with square b), (sqrt(b)×bⁿ+1)/(sqrt(b)+1) (with square b) are self-dual)

CH_nC (in base b = 19) is divisible by 2 if and only if n == 0 mod 2 (and to this step, only n == 1 mod 2 gives possible candidates for prime numbers!)
CH_nC (in base b = 19) is divisible by 3 if and only if n == 0 mod 3 (and to this step, only n == 1, 5 mod 6 gives possible candidates for prime numbers!)
CH_nC (in base b = 19) is divisible by 7 if and only if n == 5 mod 6 (and to this step, only n == 1 mod 6 gives possible candidates for prime numbers!)
CH_nC (in base b = 19) is divisible by 13 if and only if n == 1 mod 12 (and to this step, only n == 7 mod 12 gives possible candidates for prime numbers!)
CH_nC (in base b = 19) is divisible by 17 if and only if n == 3 mod 8 (and to this step, only n == 7 mod 24 gives possible candidates for prime numbers!)

And for n == 7 mod 24, we have: (all "composites without known proper factor > 1" in the list below have been trial factored (https://en.wikipedia.org/wiki/Trial_division, https://t5k.org/glossary/xpage/TrialDivision.html, https://www.rieselprime.de/ziki/Trial_factoring, https://mathworld.wolfram.com/TrialDivision.html, http://www.numericana.com/answer/factoring.htm#trial, https://www.mersenne.ca/tf1G/, https://www.mersenne.ca/tfmissed.php, https://oeis.org/A189172) to 10¹², also none of these composites have algebraic factors)

n	currently known prime factorization of the number CH_nC in base b = 19
7	2347 × 4937 × 18973
31	951820073 × 682709071131761 × 1657326648944531039
55	5039891 × 5312207 × 44999186966208286552983113 × 4379094008236471173214119625150027
79	409 × 709 × 11467 × 37699 × 10660810089661 × 1282461768425116416287 × 76403952268139600660997011 × 197365776416390077077003257867
103	11² × 1049 × 6997 × (126-digit prime)
127	83 × 127498425829 × (152-digit composite without known proper factor > 1, this composite has already checked with P−1 to B1 = 50000 and 3 times P+1 to B1 = 150000 and 10 times ECM to B1 = 250000 (these can be checked for composites < 10³⁰⁰), see http://factordb.com/sequences.php?se=1&aq=%2823319%5E128-107%29%2F18&action=last20&fr=0&to=100, the "Check for factors" box shows "Already checked", this is the ECM* effort t-level (https://oeis.org/wiki/OEIS_sequences_needing_factors#T-levels, https://stdkmd.net/nrr/wanted.htm (the "ECM" column of the three tables), https://stdkmd.net/nrr/c.cgi?q=37771_259#ecm, https://stdkmd.net/nrr/c.cgi?q=23333_233#ecm, http://myfactorcollection.mooo.com:8090/lists.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the lists in the boxes), http://myfactorcollection.mooo.com:8090/dbio.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the DB inputs/outputs in the boxes), https://github.com/brubsby/t-level, https://www.mersenneforum.org/showthread.php?t=29615) t30 (see http://www.loria.fr/~zimmerma/records/ecm/params.html and https://www.rieselprime.de/ziki/Elliptic_curve_method#Choosing_the_best_parameters_for_ECM), i.e. the prime factors of this composite number are probably > 10³⁰)
151	29 × 89 × 1896473 × 5672167 × (180-digit composite without known proper factor > 1, this composite has already checked with P−1 to B1 = 50000 and 3 times P+1 to B1 = 150000 and 10 times ECM to B1 = 250000 (these can be checked for composites < 10³⁰⁰), see http://factordb.com/sequences.php?se=1&aq=%2823319%5E152-107%29%2F18&action=last20&fr=0&to=100, the "Check for factors" box shows "Already checked", this is the ECM* effort t-level (https://oeis.org/wiki/OEIS_sequences_needing_factors#T-levels, https://stdkmd.net/nrr/wanted.htm (the "ECM" column of the three tables), https://stdkmd.net/nrr/c.cgi?q=37771_259#ecm, https://stdkmd.net/nrr/c.cgi?q=23333_233#ecm, http://myfactorcollection.mooo.com:8090/lists.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the lists in the boxes), http://myfactorcollection.mooo.com:8090/dbio.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the DB inputs/outputs in the boxes), https://github.com/brubsby/t-level, https://www.mersenneforum.org/showthread.php?t=29615) t30 (see http://www.loria.fr/~zimmerma/records/ecm/params.html and https://www.rieselprime.de/ziki/Elliptic_curve_method#Choosing_the_best_parameters_for_ECM), i.e. the prime factors of this composite number are probably > 10³⁰)
175	(227-digit composite without known proper factor > 1, this composite has already checked with P−1 to B1 = 50000 and 3 times P+1 to B1 = 150000 and 10 times ECM to B1 = 250000 (these can be checked for composites < 10³⁰⁰), see http://factordb.com/sequences.php?se=1&aq=%2823319%5E176-107%29%2F18&action=last20&fr=0&to=100, the "Check for factors" box shows "Already checked", this is the ECM* effort t-level (https://oeis.org/wiki/OEIS_sequences_needing_factors#T-levels, https://stdkmd.net/nrr/wanted.htm (the "ECM" column of the three tables), https://stdkmd.net/nrr/c.cgi?q=37771_259#ecm, https://stdkmd.net/nrr/c.cgi?q=23333_233#ecm, http://myfactorcollection.mooo.com:8090/lists.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the lists in the boxes), http://myfactorcollection.mooo.com:8090/dbio.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the DB inputs/outputs in the boxes), https://github.com/brubsby/t-level, https://www.mersenneforum.org/showthread.php?t=29615) t30 (see http://www.loria.fr/~zimmerma/records/ecm/params.html and https://www.rieselprime.de/ziki/Elliptic_curve_method#Choosing_the_best_parameters_for_ECM), i.e. the prime factors of this composite number are probably > 10³⁰)
199	1830029658442819 × (242-digit composite without known proper factor > 1, this composite has already checked with P−1 to B1 = 50000 and 3 times P+1 to B1 = 150000 and 10 times ECM to B1 = 250000 (these can be checked for composites < 10³⁰⁰), see http://factordb.com/sequences.php?se=1&aq=%2823319%5E200-107%29%2F18&action=last20&fr=0&to=100, the "Check for factors" box shows "Already checked", this is the ECM* effort t-level (https://oeis.org/wiki/OEIS_sequences_needing_factors#T-levels, https://stdkmd.net/nrr/wanted.htm (the "ECM" column of the three tables), https://stdkmd.net/nrr/c.cgi?q=37771_259#ecm, https://stdkmd.net/nrr/c.cgi?q=23333_233#ecm, http://myfactorcollection.mooo.com:8090/lists.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the lists in the boxes), http://myfactorcollection.mooo.com:8090/dbio.html (the labels "Brent Format with t-level" and "Wagstaff Format with t-level" of the DB inputs/outputs in the boxes), https://github.com/brubsby/t-level, https://www.mersenneforum.org/showthread.php?t=29615) t30 (see http://www.loria.fr/~zimmerma/records/ecm/params.html and https://www.rieselprime.de/ziki/Elliptic_curve_method#Choosing_the_best_parameters_for_ECM), i.e. the prime factors of this composite number are probably > 10³⁰)

and it does not appear to be any covering congruence of primes, besides, since 107 is not a perfect power, thus the family CH_nC (in base b = 19) has no algebraic factorization for any n, thus its Nash weight (or difficulty) is positive (although very low), so there must be a prime at some point (and the corresponding n must be == 7 mod 24).

And for n == 7 mod 24, we have: (all "composites without known proper factor > 1" in the list below have been trial factored (https://en.wikipedia.org/wiki/Trial_division, https://t5k.org/glossary/xpage/TrialDivision.html, https://www.rieselprime.de/ziki/Trial_factoring, https://mathworld.wolfram.com/TrialDivision.html, http://www.numericana.com/answer/factoring.htm#trial, https://www.mersenne.ca/tf1G/, https://www.mersenne.ca/tfmissed.php, https://oeis.org/A189172) to 10⁹, also none of these composites have algebraic factors)

Another example of a family and its dual family are both unsolved families is the base b = 25 family FB{0}H (its algebraic form is 386×25ⁿ⁺¹+17, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=386*25%5E%28n%2B1%29%2B17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show) and the base b = 25 family H{0}FB (its algebraic form is 17×25ⁿ⁺²+386, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=17*25%5E%28n%2B2%29%2B386&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show).

Also two examples of a family and its dual family both have known (probable) primes (and these two (probable) primes are both minimal primes (assuming their primality)) but both have no easy primes (i.e. lengths ≤ 1000 in base b) are (the base b = 17 families 109{0}D and D{0}109 are dual families, and the base b = 21 families 1{0}5D and 5D{0}1 are also dual families):

b (2 ≤ b ≤ 36)	family	algebraic form	base-b form of the smallest (probable) prime in this family (write "d_n" if there are 5 or more (n) consecutive same digits d)	length of the smallest (probable) prime in this family	length of the smallest (probable) prime in this family in decimal	algebraic ((a×bⁿ+c)/gcd(a+c,b−1)) form of the smallest (probable) prime in this family	factordb entry of the smallest (probable) prime in this family	the smallest (probable) prime in this family written in base b (use lower case letters instead of upper case letters)	the smallest (probable) prime in this family written in decimal	factorization of the first 200 numbers in corresponding family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0))
17	109{0}D	298×17ⁿ⁺¹+13	1090₆₃₈₇D	6391	7863	298×17⁶³⁸⁸+13	http://factordb.com/index.php?id=1100000003782940751&open=prime	http://factordb.com/index.php?showid=1100000003782940751&base=17	http://factordb.com/index.php?showid=1100000003782940751	http://factordb.com/index.php?query=298*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	D{0}109	13×17ⁿ⁺³+298	D0₁₁₆₉109	1173	1444	13×17¹¹⁷²+298	http://factordb.com/index.php?id=1100000003782940735&open=prime	http://factordb.com/index.php?showid=1100000003782940735&base=17	http://factordb.com/index.php?showid=1100000003782940735	http://factordb.com/index.php?query=13*17%5E%28n%2B3%29%2B298&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	1{0}5D	21ⁿ⁺²+118	10₁₁₃₉₅5D	11398	15070	21¹¹³⁹⁷+118	http://factordb.com/index.php?id=1100000003815090811&open=prime	http://factordb.com/index.php?showid=1100000003815090811&base=21	http://factordb.com/index.php?showid=1100000003815090811	http://factordb.com/index.php?query=21%5E%28n%2B2%29%2B118&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	5D{0}1	118×21ⁿ⁺¹+1	5D0₁₉₈₄₈1	19851	26247	118×21¹⁹⁸⁴⁹+1	http://factordb.com/index.php?id=1100000000777265872&open=prime	http://factordb.com/index.php?showid=1100000000777265872&base=21	http://factordb.com/index.php?showid=1100000000777265872	http://factordb.com/index.php?query=118*21%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show

The same holds for all other unsolved families in bases 2 ≤ b ≤ 36, thus we can almost sure that all unsolved families in bases 2 ≤ b ≤ 36 have a prime, in fact, we can almost sure that all unsolved families in bases 2 ≤ b ≤ 36 have infinitely many primes. (if the family has algebraic factorization for some n, then we should only consider the n such that this family does not have algebraic factorization and check whether there is a covering congruence for these n, e.g. the unsolved family 2EB_n is base b = 23, whose algebraic form is (121×23ⁿ−1)/2, which has a difference-of-two-squares factorization if n is even (factored to (11×23^n/2−1) × (11×23^n/2+1) / 2), thus we should only consider the odd n and check whether there is a covering congruence for the odd n)

Also, there are unsolved families in bases 2 ≤ b ≤ 36 which are impossible to be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them), note the difference of the unsolved families in bases 2 ≤ b ≤ 36 which are very unlikely to be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them), the latter still has a possibility, such as the three families above (family {9}D in base b = 21 and family 5{H}5 in base b = 19 and family C{H}C in base b = 19), the former has no possibility, such as the three examples below:

Family 1{7} in base b = 17: (its algebraic form is (23×17ⁿ−7)/16, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%2823*17%5En-7%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

Since 7 is not a perfect power, thus the family 17_n (in base b = 17) has no algebraic factorization for any n, thus if this family can be ruled out as only containing composites, then it must have a covering congruence, and if the period of its covering congruence is m, consider the prime factor p dividing (23×17ⁿ−7)/16 for all n == 0 mod m, p must divide (23×17⁰−7)/16 = −1, which is a contradiction.

Family 9{6}M in base b = 25: (its algebraic form is (37×25ⁿ⁺¹+63)/4, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%2837*25%5E%28n%2B1%29%2B63%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

Since 63 is not a perfect power, thus the family 96_nM (in base b = 25) has no algebraic factorization for any n, thus if this family can be ruled out as only containing composites, then it must have a covering congruence, and if the period of its covering congruence is m, consider the prime factor p dividing (37×25ⁿ⁺¹+63)/4 for all n == −1 mod m, p must divide (37×25⁽⁻¹⁾⁺¹+63)/4 = 25, and thus p must be 5 (since 5 is the only prime factor of 25), but no numbers in the family 9{6}M (in base b = 25) are divisible by 5 (since all numbers in this family are == 22 mod 25, thus are == 2 mod 5), which is a contradiction.

Family E{D} in base b = 25: (its algebraic form is (349×25ⁿ−13)/24, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%28349*25%5En-13%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

Since 13 is not a perfect power, thus the family ED_n (in base b = 25) has no algebraic factorization for any n, thus if this family can be ruled out as only containing composites, then it must have a covering congruence, and if the period of its covering congruence is m, consider the prime factor p dividing (349×25ⁿ−13)/24 for all n == −1 mod m, p must divide the numerator of (349×25⁻¹−13)/24 = 1/25, i.e. p divides 1, which is a contradiction.

Family 1{F}5 in base b = 27: (its algebraic form is (41×27ⁿ⁺¹−275)/26, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%2841*27%5E%28n%2B1%29-275%29%2F26&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

Since 275 is not a perfect power, thus the family 1F_n5 (in base b = 27) has no algebraic factorization for any n, thus if this family can be ruled out as only containing composites, then it must have a covering congruence, and if the period of its covering congruence is m, consider the prime factor p dividing (41×27ⁿ⁺¹−275)/26 for all n == −1 mod m, p must divide (41×27⁽⁻¹⁾⁺¹−275)/26 = −9, and thus p must be 3 (since 3 is the only prime factor of −9), but no numbers in the family 1{F}5 (in base b = 27) are divisible by 3 (since all numbers in this family are == 5 mod 27, thus are == 2 mod 3), which is a contradiction.

In fact, the corresponding families for the largest minimal primes in bases b = 7, 10, 14, 22, 30 are such families, since:

Family {3}1 in base b = 7: (its algebraic form is (7ⁿ⁺¹−5)/2, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%287%5E%28n%2B1%29-5%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

Since 5 is not a perfect power, thus the family 3_n1 (in base b = 7) has no algebraic factorization for any n, thus if this family can be ruled out as only containing composites, then it must have a covering congruence, and if the period of its covering congruence is m, consider the prime factor p dividing (7ⁿ⁺¹−5)/2 for all n == 0 mod m, p must divide (7⁰⁺¹−5)/2 = 1, which is a contradiction.

Family 5{0}27 in base b = 10: (its algebraic form is 5×10ⁿ⁺²+27, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=5*10%5E%28n%2B2%29%2B27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

Since 27 is a cube, thus 5×10ⁿ⁺²+27 has sum-of-two-cubes factorization if 5×10ⁿ⁺² is a cube (if not, then it has no algebraic factorization), but 5×10ⁿ⁺² cannot be a perfect power, since the prime factorization of 5×10ⁿ⁺² is 2ⁿ⁺² × 5ⁿ⁺³, but n+2 and n+3 must be coprime, thus 2ⁿ⁺² × 5ⁿ⁺³ cannot be a perfect power, thus the family 50_n27 (in base b = 10) has no algebraic factorization for any n, thus if this family can be ruled out as only containing composites, then it must have a covering congruence, and if the period of its covering congruence is m, consider the prime factor p dividing 5×10ⁿ⁺²+27 for all n == −2 mod m, p must divide 5×10⁽⁻²⁾⁺²+27 = 32, and thus p must be 2 (since 2 is the only prime factor of 32), but no numbers in the family 5{0}27 (in base b = 10) are divisible by 2 (since all numbers in this family are == 7 mod 10, thus are == 1 mod 2), which is a contradiction.

Family 4{D} in base b = 14: (its algebraic form is 5×14ⁿ−1, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=5*14%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

Since 1 is an rth power for all r, thus 5×14ⁿ−1 has difference-of-two-rth-powers factorization if 5×14ⁿ is an rth power (if not, then it has no algebraic factorization), but 5×14ⁿ cannot be a perfect power, after all, 5×14ⁿ is divisible by 5 but not 5², thus the family 4D_n (in base b = 14) has no algebraic factorization for any n, thus if this family can be ruled out as only containing composites, then it must have a covering congruence, and if the period of its covering congruence is m, consider the prime factor p dividing 5×14ⁿ−1 for all n == 0 mod m, p must divide 5×14⁰−1 = 4, and thus p must be 2 (since 2 is the only prime factor of 4), but no numbers in the family 4{D} (in base b = 14) are divisible by 2 (since all numbers in this family are == 13 mod 14, thus are == 1 mod 2), which is a contradiction.

Family B{K}5 in base b = 22: (its algebraic form is (251×22ⁿ⁺¹−335)/21, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%28251*22%5E%28n%2B1%29-335%29%2F21&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

Since 335 is not a perfect power, thus the family BK_n5 (in base b = 22) has no algebraic factorization for any n, thus if this family can be ruled out as only containing composites, then it must have a covering congruence, and if the period of its covering congruence is m, consider the prime factor p dividing (251×22ⁿ⁺¹−335)/21 for all n == −1 mod m, p must divide (251×22⁽⁻¹⁾⁺¹−335)/21 = −4, and thus p must be 2 (since 2 is the only prime factor of −4), but no numbers in the family B{K}5 (in base b = 22) are divisible by 2 (since all numbers in this family are == 5 mod 22, thus are == 1 mod 2), which is a contradiction.

Family O{T} in base b = 30: (its algebraic form is 25×30ⁿ−1, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=25*30%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

Since 1 is an rth power for all r, thus 25×30ⁿ−1 has difference-of-two-rth-powers factorization if 25×30ⁿ is an rth power (if not, then it has no algebraic factorization), and indeed 25×30ⁿ is a square if n == 0 mod 2, but 25×30ⁿ cannot be a perfect power if n == 1 mod 2, since the prime factorization of 25×30ⁿ is 2ⁿ × 3ⁿ × 5ⁿ⁺², but n and n+2 must be coprime if n == 1 mod 2, thus 2ⁿ × 3ⁿ × 5ⁿ⁺² cannot be a perfect power if n == 1 mod 2, thus the family OT_n (in base b = 30) has no algebraic factorization for any n == 1 mod 2, thus if this family can be ruled out as only containing composites, then it must have a covering congruence on the n == 1 mod 2, and if the period of its covering congruence is m, consider the prime factor p dividing 25×30ⁿ−1 for all n == −1 mod 2×m (such n must be == 1 mod 2), p must divide the numerator of 25×30⁻¹−1 = −1/6, i.e. p divides 1, which is a contradiction.

e.g. (only list the families which all numbers do not contain "prime > b" subsequence) (for the case of covering congruence, we can show that the corresponding numbers are > all elements in the sets if the corresponding numbers are > b, thus these factorizations are nontrivial; and for the case of algebraic factorization, we can show that both factors are > 1 if the corresponding numbers are > b, thus these factorizations are nontrivial; for the case of combine of them, we can show that for the part of covering congruence, the corresponding numbers are > all elements in the sets if the corresponding numbers are > b, and for the part of algebraic factorization, both factors are > 1 if the corresponding numbers are > b, thus these factorizations are nontrivial)

For the factor patterns of some families: (list the first 20 numbers in these families, start with the smallest number > b in these families) (all numbers are written in base b, and these factorizations are nontrivial (https://en.wikipedia.org/wiki/Triviality_(mathematics), https://mathworld.wolfram.com/Trivial.html), i.e. both of these two factors are > 1, of course, one or two of these two factors may be composite)

Example 1, family 4{6}9 in base b = 10: (the period of the factor pattern is 1, and its algebraic form is (14×10ⁿ⁺¹+7)/3, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%2814*10%5E%28n%2B1%29%2B7%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

49 = 7 × 7
469 = 7 × 67
4669 = 7 × 667
46669 = 7 × 6667
466669 = 7 × 66667
4666669 = 7 × 666667
46666669 = 7 × 6666667
466666669 = 7 × 66666667
4666666669 = 7 × 666666667
46666666669 = 7 × 6666666667
466666666669 = 7 × 66666666667
4666666666669 = 7 × 666666666667
46666666666669 = 7 × 6666666666667
466666666666669 = 7 × 66666666666667
4666666666666669 = 7 × 666666666666667
46666666666666669 = 7 × 6666666666666667
466666666666666669 = 7 × 66666666666666667
4666666666666666669 = 7 × 666666666666666667
46666666666666666669 = 7 × 6666666666666666667
466666666666666666669 = 7 × 66666666666666666667

Example 2, family 28{0}7 in base b = 10: (the period of the factor pattern is 1, and its algebraic form is 28×10ⁿ⁺¹+7, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=28*10%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

287 = 7 × 41
2807 = 7 × 401
28007 = 7 × 4001
280007 = 7 × 40001
2800007 = 7 × 400001
28000007 = 7 × 4000001
280000007 = 7 × 40000001
2800000007 = 7 × 400000001
28000000007 = 7 × 4000000001
2800000000007 = 7 × 4000000001
28000000000007 = 7 × 40000000001
280000000000007 = 7 × 400000000001
2800000000000007 = 7 × 4000000000001
28000000000000007 = 7 × 40000000000001
280000000000000007 = 7 × 400000000000001
2800000000000000007 = 7 × 4000000000000001
28000000000000000007 = 7 × 40000000000000001
280000000000000000007 = 7 × 400000000000000001
2800000000000000000007 = 7 × 4000000000000000001
28000000000000000000007 = 7 × 40000000000000000001

Example 3, family {1} in base b = 9: (the period of the factor pattern is 2, and its algebraic form is (9ⁿ−1)/8, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%289%5En-1%29%2F8&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

11 = 2 × 5
111 = 7 × 14
1111 = 22 × 45
11111 = 67 × 144
111111 = 222 × 445
1111111 = 667 × 1444
11111111 = 2222 × 4445
111111111 = 6667 × 14444
1111111111 = 22222 × 44445
11111111111 = 66667 × 144444
111111111111 = 222222 × 444445
1111111111111 = 666667 × 1444444
11111111111111 = 2222222 × 4444445
111111111111111 = 6666667 × 14444444
1111111111111111 = 22222222 × 44444445
11111111111111111 = 66666667 × 144444444
111111111111111111 = 222222222 × 444444445
1111111111111111111 = 666666667 × 1444444444
11111111111111111111 = 2222222222 × 4444444445
111111111111111111111 = 6666666667 × 14444444444

Example 4, family 3{8} in base b = 9: (the period of the factor pattern is 2, and its algebraic form is 4×9ⁿ−1, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=4*9%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

38 = 5 × 7
388 = 18 × 21
3888 = 58 × 61
38888 = 188 × 201
388888 = 588 × 601
3888888 = 1888 × 2001
38888888 = 5888 × 6001
388888888 = 18888 × 20001
3888888888 = 58888 × 60001
38888888888 = 188888 × 200001
388888888888 = 588888 × 600001
3888888888888 = 1888888 × 2000001
38888888888888 = 5888888 × 6000001
388888888888888 = 18888888 × 20000001
3888888888888888 = 58888888 × 60000001
38888888888888888 = 188888888 × 200000001
388888888888888888 = 588888888 × 600000001
3888888888888888888 = 1888888888 × 2000000001
38888888888888888888 = 5888888888 × 6000000001
388888888888888888888 = 18888888888 × 20000000001

Example 5, family 1{0}1 in base b = 8: (the period of the factor pattern is 3, and its algebraic form is 8ⁿ⁺¹+1, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=8%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

11 = 3 × 3
101 = 5 × 15
1001 = 11 × 71
10001 = 21 × 361
100001 = 41 × 1741
1000001 = 101 × 7701
10000001 = 201 × 37601
100000001 = 401 × 177401
1000000001 = 1001 × 777001
10000000001 = 2001 × 3776001
100000000001 = 4001 × 17774001
1000000000001 = 10001 × 77770001
10000000000001 = 20001 × 377760001
100000000000001 = 40001 × 1777740001
1000000000000001 = 100001 × 7777700001
10000000000000001 = 200001 × 37777600001
100000000000000001 = 400001 × 177777400001
1000000000000000001 = 1000001 × 777777000001
10000000000000000001 = 2000001 × 3777776000001
100000000000000000001 = 4000001 × 17777774000001

Example 6, family {8}5 in base b = 9: (the period of the factor pattern is 2, and its algebraic form is 9ⁿ⁺¹−4, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=9%5E%28n%2B1%29-4&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

85 = 7 × 12
885 = 27 × 32
8885 = 87 × 102
88885 = 287 × 302
888885 = 887 × 1002
8888885 = 2887 × 3002
88888885 = 8887 × 10002
888888885 = 28887 × 30002
8888888885 = 88887 × 100002
88888888885 = 288887 × 300002
888888888885 = 888887 × 1000002
8888888888885 = 2888887 × 3000002
88888888888885 = 8888887 × 10000002
888888888888885 = 28888887 × 30000002
8888888888888885 = 88888887 × 100000002
88888888888888885 = 288888887 × 300000002
888888888888888885 = 888888887 × 1000000002
8888888888888888885 = 2888888887 × 3000000002
88888888888888888885 = 8888888887 × 10000000002

Example 7, family {2}5 in base b = 11: (the period of the factor pattern is 2, and its algebraic form is (5×11ⁿ−1)/2, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%285*11%5En-1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

25 = 3 × 9
255 = 2 × 128
2555 = 3 × 919
25555 = 2 × 12828
255555 = 3 × 91919
2555555 = 2 × 1282828
25555555 = 3 × 9191919
255555555 = 2 × 128282828
2555555555 = 3 × 919191919
25555555555 = 2 × 12828282828
255555555555 = 3 × 91919191919
2555555555555 = 2 × 1282828282828
25555555555555 = 3 × 9191919191919
255555555555555 = 2 × 128282828282828
2555555555555555 = 3 × 919191919191919
25555555555555555 = 2 × 12828282828282828
255555555555555555 = 3 × 91919191919191919
2555555555555555555 = 2 × 1282828282828282828
25555555555555555555 = 3 × 9191919191919191919
255555555555555555555 = 2 × 128282828282828282828

Example 8, family {B}9B in base b = 12: (the period of the factor pattern is 2, and its algebraic form is 12ⁿ⁺²−25, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=12%5E%28n%2B2%29-25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

9B = 7 × 15
B9B = 11 × AB
BB9B = B7 × 105
BBB9B = 11 × B0AB
BBBB9B = BB7 × 1005
BBBBB9B = 11 × B0B0AB
BBBBBB9B = BBB7 × 10005
BBBBBBB9B = 11 × B0B0B0AB
BBBBBBBB9B = BBBB7 × 100005
BBBBBBBBB9B = 11 × B0B0B0B0AB
BBBBBBBBBB9B = BBBBB7 × 1000005
BBBBBBBBBBB9B = 11 × B0B0B0B0B0AB
BBBBBBBBBBBB9B = BBBBBB7 × 10000005
BBBBBBBBBBBBB9B = 11 × B0B0B0B0B0B0AB
BBBBBBBBBBBBBB9B = BBBBBBB7 × 100000005
BBBBBBBBBBBBBBB9B = 11 × B0B0B0B0B0B0B0AB
BBBBBBBBBBBBBBBB9B = BBBBBBBB7 × 1000000005
BBBBBBBBBBBBBBBBB9B = 11 × B0B0B0B0B0B0B0B0AB
BBBBBBBBBBBBBBBBBB9B = BBBBBBBBB7 × 10000000005
BBBBBBBBBBBBBBBBBBB9B = 11 × B0B0B0B0B0B0B0B0B0AB

Example 9, family B{0}1 in base b = 14: (the period of the factor pattern is 2, and its algebraic form is 11×14ⁿ⁺¹+1, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=11*14%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

B1 = 5 × 23
B01 = 3 × 395
B001 = 5 × 22B3
B0001 = 3 × 39495
B00001 = 5 × 22B2B3
B000001 = 3 × 3949495
B0000001 = 5 × 22B2B2B3
B00000001 = 3 × 394949495
B000000001 = 5 × 22B2B2B2B3
B0000000001 = 3 × 39494949495
B00000000001 = 5 × 22B2B2B2B2B3
B000000000001 = 3 × 3949494949495
B0000000000001 = 5 × 22B2B2B2B2B2B3
B00000000000001 = 3 × 394949494949495
B000000000000001 = 5 × 22B2B2B2B2B2B2B3
B0000000000000001 = 3 × 39494949494949495
B00000000000000001 = 5 × 22B2B2B2B2B2B2B2B3
B000000000000000001 = 3 × 3949494949494949495
B0000000000000000001 = 5 × 22B2B2B2B2B2B2B2B2B3
B00000000000000000001 = 3 × 394949494949494949495

Example 10, family 3{0}95 in base b = 13: (the period of the factor pattern is 4, and its algebraic form is 3×13ⁿ⁺²+122, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=3*13%5E%28n%2B2%29%2B122&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

395 = 14 × 2B
3095 = 7 × 58A
30095 = 5 × 7A71
300095 = 7 × 5758A
3000095 = 14 × 23A92B
30000095 = 7 × 575758A
300000095 = 5 × 7A527A71
3000000095 = 7 × 57575758A
30000000095 = 14 × 23A923A92B
300000000095 = 7 × 5757575758A
3000000000095 = 5 × 7A527A527A71
30000000000095 = 7 × 575757575758A
300000000000095 = 14 × 23A923A923A92B
3000000000000095 = 7 × 57575757575758A
30000000000000095 = 5 × 7A527A527A527A71
300000000000000095 = 7 × 5757575757575758A
3000000000000000095 = 14 × 23A923A923A923A92B
30000000000000000095 = 7 × 575757575757575758A
300000000000000000095 = 5 × 7A527A527A527A527A71
3000000000000000000095 = 7 × 57575757575757575758A

Example 11, family {4}D in base b = 16: (the period of the factor pattern is 3, and its algebraic form is (4×16ⁿ⁺¹+131)/15, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%284*16%5E%28n%2B1%29%2B131%29%2F15&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

4D = 7 × B
44D = 3 × 16F
444D = D × 541
4444D = 7 × 9C0B
44444D = 3 × 16C16F
444444D = D × 540541
4444444D = 7 × 9C09C0B
44444444D = 3 × 16C16C16F
444444444D = D × 540540541
4444444444D = 7 × 9C09C09C0B
44444444444D = 3 × 16C16C16C16F
444444444444D = D × 540540540541
4444444444444D = 7 × 9C09C09C09C0B
44444444444444D = 3 × 16C16C16C16C16F
444444444444444D = D × 540540540540541
4444444444444444D = 7 × 9C09C09C09C09C0B
44444444444444444D = 3 × 16C16C16C16C16C16F
444444444444444444D = D × 540540540540540541
4444444444444444444D = 7 × 9C09C09C09C09C09C0B
44444444444444444444D = 3 × 16C16C16C16C16C16C16F

Example 12, family {C}D in base b = 16: (the period of the factor pattern is 4, and its algebraic form is (4×16ⁿ⁺¹+1)/5, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%284*16%5E%28n%2B1%29%2B1%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

CD = 5 × 29
CCD = 1D × 71
CCCD = 6D × 1E1
CCCCD = 18D × 841
CCCCCD = 64D × 2081
CCCCCCD = 19CD × 7F01
CCCCCCCD = 66CD × 1FE01
CCCCCCCCD = 198CD × 80401
CCCCCCCCCD = 664CD × 200801
CCCCCCCCCCD = 199CCD × 7FF001
CCCCCCCCCCCD = 666CCD × 1FFE001
CCCCCCCCCCCCD = 1998CCD × 8004001
CCCCCCCCCCCCCD = 6664CCD × 20008001
CCCCCCCCCCCCCCD = 1999CCCD × 7FFF0001
CCCCCCCCCCCCCCCD = 6666CCCD × 1FFFE0001
CCCCCCCCCCCCCCCCD = 19998CCCD × 800040001
CCCCCCCCCCCCCCCCCD = 66664CCCD × 2000080001
CCCCCCCCCCCCCCCCCCD = 19999CCCCD × 7FFFF00001
CCCCCCCCCCCCCCCCCCCD = 66666CCCCD × 1FFFFE00001
CCCCCCCCCCCCCCCCCCCCD = 199998CCCCD × 80000400001

Example 13, family 1{9} in base b = 17: (the period of the factor pattern is 2, and its algebraic form is (25×17ⁿ−9)/16, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%2825*17%5En-9%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

19 = 2 × D
199 = B × 27
1999 = 2 × D4D
19999 = AB × 287
199999 = 2 × D4D4D
1999999 = AAB × 2887
19999999 = 2 × D4D4D4D
199999999 = AAAB × 28887
1999999999 = 2 × D4D4D4D4D
19999999999 = AAAAB × 288887
199999999999 = 2 × D4D4D4D4D4D
1999999999999 = AAAAAB × 2888887
19999999999999 = 2 × D4D4D4D4D4D4D
199999999999999 = AAAAAAB × 28888887
1999999999999999 = 2 × D4D4D4D4D4D4D4D
19999999999999999 = AAAAAAAB × 288888887
199999999999999999 = 2 × D4D4D4D4D4D4D4D4D
1999999999999999999 = AAAAAAAAB × 2888888887
19999999999999999999 = 2 × D4D4D4D4D4D4D4D4D4D
199999999999999999999 = AAAAAAAAAB × 28888888887

Example 14, family 1{6} in base b = 19: (the period of the factor pattern is 2, and its algebraic form is (4×19ⁿ−1)/3, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%284*19%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

16 = 5 × 5
166 = D × 1I
1666 = 5 × 515
16666 = CD × 1II
166666 = 5 × 51515
1666666 = CCD × 1III
16666666 = 5 × 5151515
166666666 = CCCD × 1IIII
1666666666 = 5 × 515151515
16666666666 = CCCCD × 1IIIII
166666666666 = 5 × 51515151515
1666666666666 = CCCCCD × 1IIIIII
16666666666666 = 5 × 5151515151515
166666666666666 = CCCCCCD × 1IIIIIII
1666666666666666 = 5 × 515151515151515
16666666666666666 = CCCCCCCD × 1IIIIIIII
166666666666666666 = 5 × 51515151515151515
1666666666666666666 = CCCCCCCCD × 1IIIIIIIII
16666666666666666666 = 5 × 5151515151515151515
166666666666666666666 = CCCCCCCCCD × 1IIIIIIIIII

Example 15, family {D}GA in base b = 23: (the period of the factor pattern is 12, and its algebraic form is (13×23ⁿ⁺²+1439)/22, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%2813*23%5E%28n%2B2%29%2B1439%29%2F22&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

GA = 6 × 2H
DGA = 5 × 2H2
DDGA = 6 × 262H
DDDGA = 7 × 1LF28
DDDDGA = 6 × 26262H
DDDDDGA = 3A × 3M03M1
DDDDDDGA = 6 × 2626262H
DDDDDDDGA = 1E × 8A74GC44
DDDDDDDDGA = 6 × 262626262H
DDDDDDDDDGA = 7 × 1LF1LF1LF28
DDDDDDDDDDGA = 6 × 26262626262H
DDDDDDDDDDDGA = 3A × 3M03M03M03M1
DDDDDDDDDDDDGA = 6 × 2626262626262H
DDDDDDDDDDDDDGA = 5 × 2GBL2GBL2GBL2H2
DDDDDDDDDDDDDDGA = 6 × 262626262626262H
DDDDDDDDDDDDDDDGA = 7 × 1LF1LF1LF1LF1LF28
DDDDDDDDDDDDDDDDGA = 6 × 26262626262626262H
DDDDDDDDDDDDDDDDDGA = 3A × 3M03M03M03M03M03M1
DDDDDDDDDDDDDDDDDDGA = 6 × 2626262626262626262H
DDDDDDDDDDDDDDDDDDDGA = 1E × 8A74GC4257J08A74GC44

Example 16, family 2{1} in base b = 25: (the period of the factor pattern is 2, and its algebraic form is (49×25ⁿ−1)/24, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%2849*25%5En-1%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

21 = 3 × H
211 = 14 × 1J
2111 = 2N × HC
21111 = 144 × 1IJ
211111 = 2MN × HCC
2111111 = 1444 × 1IIJ
21111111 = 2MMN × HCCC
211111111 = 14444 × 1IIIJ
2111111111 = 2MMMN × HCCCC
21111111111 = 144444 × 1IIIIJ
211111111111 = 2MMMMN × HCCCCC
2111111111111 = 1444444 × 1IIIIIJ
21111111111111 = 2MMMMMN × HCCCCCC
211111111111111 = 14444444 × 1IIIIIIJ
2111111111111111 = 2MMMMMMN × HCCCCCCC
21111111111111111 = 144444444 × 1IIIIIIIJ
211111111111111111 = 2MMMMMMMN × HCCCCCCCC
2111111111111111111 = 1444444444 × 1IIIIIIIIJ
21111111111111111111 = 2MMMMMMMMN × HCCCCCCCCC
211111111111111111111 = 14444444444 × 1IIIIIIIIIJ

Example 17, family 7{Q} in base b = 27: (the period of the factor pattern is 3, and its algebraic form is 8×27ⁿ−1, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=8*27%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

7Q = 5 × 1G
7QQ = H × CJ
7QQQ = 1Q × 421
7QQQQ = 5Q × 1961
7QQQQQ = HQ × C0I1
7QQQQQQ = 1QQ × 40201
7QQQQQQQ = 5QQ × 190601
7QQQQQQQQ = HQQ × C00I01
7QQQQQQQQQ = 1QQQ × 4002001
7QQQQQQQQQQ = 5QQQ × 19006001
7QQQQQQQQQQQ = HQQQ × C000I001
7QQQQQQQQQQQQ = 1QQQQ × 400020001
7QQQQQQQQQQQQQ = 5QQQQ × 1900060001
7QQQQQQQQQQQQQQ = HQQQQ × C0000I0001
7QQQQQQQQQQQQQQQ = 1QQQQQ × 40000200001
7QQQQQQQQQQQQQQQQ = 5QQQQQ × 190000600001
7QQQQQQQQQQQQQQQQQ = HQQQQQ × C00000I00001
7QQQQQQQQQQQQQQQQQQ = 1QQQQQQ × 4000002000001
7QQQQQQQQQQQQQQQQQQQ = 5QQQQQQ × 19000006000001
7QQQQQQQQQQQQQQQQQQQQ = HQQQQQQ × C000000I000001

Example 18, family A{0}9J in base b = 30: (the period of the factor pattern is 6, and its algebraic form is 10×30ⁿ⁺²+289, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=10*30%5E%28n%2B2%29%2B289&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

A9J = 7 × 1E7
A09J = 11 × 9KJ
A009J = J × FNL1
A0009J = 11 × 9K9KJ
A00009J = D × N296SD
A000009J = 11 × 9K9K9KJ
A0000009J = 7 × 1CPLCPLE7
A00000009J = 11 × 9K9K9K9KJ
A000000009J = J × FNKFNKFNL1
A0000000009J = 11 × 9K9K9K9K9KJ
A00000000009J = D × N296RKN296SD
A000000000009J = 11 × 9K9K9K9K9K9KJ
A0000000000009J = 7 × 1CPLCPLCPLCPLE7
A00000000000009J = 11 × 9K9K9K9K9K9K9KJ
A000000000000009J = J × FNKFNKFNKFNKFNL1
A0000000000000009J = 11 × 9K9K9K9K9K9K9K9KJ
A00000000000000009J = D × N296RKN296RKN296SD
A000000000000000009J = 11 × 9K9K9K9K9K9K9K9K9KJ
A0000000000000000009J = 7 × 1CPLCPLCPLCPLCPLCPLE7
A00000000000000000009J = 11 × 9K9K9K9K9K9K9K9K9K9KJ

Example 19, family {1} in base b = 32: (the period of the factor pattern is 5, and its algebraic form is (32ⁿ−1)/31, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%2832%5En-1%29%2F31&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

11 = 3 × B
111 = 7 × 4N
1111 = F × 26F
11111 = IP × 1O9
111111 = 1V × GOSV
1111111 = 3V × 8AAQV
11111111 = 7V × 44KMMV
111111111 = FV × 2266EEV
1111111111 = IP × 1O9001O9
11111111111 = 1VV × GGOOSSUV
111111111111 = 3VV × 88AAAQQUV
1111111111111 = 7VV × 444KKMMMUV
11111111111111 = FVV × 222666EEEUV
111111111111111 = IP × 1O9001O9001O9
1111111111111111 = 1VVV × GGGOOOSSSUV
11111111111111111 = 3VVV × 888AAAAQQQUUV
111111111111111111 = 7VVV × 4444KKKMMMMUUV
1111111111111111111 = FVVV × 22226666EEEEUUV
11111111111111111111 = IP × 1O9001O9001O9001O9

Example 20, family 3{7} in base b = 36: (the period of the factor pattern is 2, and its algebraic form is (16×36ⁿ−1)/5, and for the factorization of the numbers in the family (n is the number of digits in the "{}", start with the smallest n making the number > b) see http://factordb.com/index.php?query=%2816*36%5En-1%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show)

37 = 5 × N
377 = T × 3Z
3777 = 4T × NZ
37777 = ST × 3ZZ
377777 = 4ST × NZZ
3777777 = SST × 3ZZZ
37777777 = 4SST × NZZZ
377777777 = SSST × 3ZZZZ
3777777777 = 4SSST × NZZZZ
37777777777 = SSSST × 3ZZZZZ
377777777777 = 4SSSST × NZZZZZ
3777777777777 = SSSSST × 3ZZZZZZ
37777777777777 = 4SSSSST × NZZZZZZ
377777777777777 = SSSSSST × 3ZZZZZZZ
3777777777777777 = 4SSSSSST × NZZZZZZZ
37777777777777777 = SSSSSSST × 3ZZZZZZZZ
377777777777777777 = 4SSSSSSST × NZZZZZZZZ
3777777777777777777 = SSSSSSSST × 3ZZZZZZZZZ
37777777777777777777 = 4SSSSSSSST × NZZZZZZZZZ
377777777777777777777 = SSSSSSSSST × 3ZZZZZZZZZZ

(only list the families which can be proven to be not covered by any prime > b (this would include all such families of the form x{0}y and all such families of the form x{y} (unless y = 1) and all such families of the form {x}y (unless x = 1)), the only exceptions are the base 21 family B0{H}6H (which is covered by the smallest prime in the family B{H}6H in base 21 (if such prime exists)) and the base 8 family 6{4}7 (which is covered by the prime 4₂₂₀7 in base 8))

(Note: There are families with more that one covering congruence, for more such examples see https://oeis.org/A263391 and https://oeis.org/A263392, also the case "444...44407" in https://sites.google.com/view/smallest-quasi-repdigit-primes, also the cases "936Rn" and "1222Rn" and "2739Rn" in https://web.archive.org/web/20070220134129/http://www.users.globalnet.co.uk/~perry/maths/wildeprimes/wildeprimes.htm)

(Note: Some of these families not only can be proven to contain no primes (only count the numbers > b), even can be proven to contain no semiprimes (https://en.wikipedia.org/wiki/Semiprime, https://t5k.org/glossary/xpage/Semiprime.html, https://mathworld.wolfram.com/Semiprime.html, https://www.numbersaplenty.com/set/semiprime/, https://oeis.org/A001358) (i.e. the product of two primes (not necessary distinct)) (only count the numbers > b), see the table below, but this is out of the main problem in this project)

(this table is sorted by: single trivial prime factor (2{0}1 in base b = 10 through D{6}R in base b = 28) → covering congruence with 2 primes ({1}5 in base b = 9 through {X}5 in base b = 34) → covering congruence with ≥ 3 primes (6{4}7 in base b = 8 through {G}L in base b = 32) → algebraic factorization ({1} in base b = 9 through 9{S}IJ in base b = 36) → combine of covering congruence and algebraic factorization (8{D} in base b = 14 through {X}P in base b = 34))

b (2 ≤ b ≤ 36)	family	algebraic ((a×bⁿ+c)/d) form of this family (n is the number of digits in the "{}", also the lower bound of n to make the numbers > b) (note: d divides gcd(a+c,b−1), but d need not be gcd(a+c,b−1), d = gcd(a+c,b−1) if and only if the numbers in the family are not divisible by some prime factor of b−1, i.e. the numbers in the family are coprime to b−1, in fact, d = gcd(a+c,b−1)/gcd(a+c,b−1,(largest trivial factor of the family)))	why this family contain no primes > b	factorization of the first 200 numbers in this family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0)) (only for linear families)
10	2{0}1	2×10ⁿ⁺¹+1 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=2*10%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
10	2{0}7	2×10ⁿ⁺¹+7 (n ≥ 0)	always divisible by 3 (in fact, always divisible by 9)	http://factordb.com/index.php?query=2*10%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
10	5{0}1	5×10ⁿ⁺¹+1 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=5*10%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
10	5{0}7	5×10ⁿ⁺¹+7 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=5*10%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
10	8{0}1	8×10ⁿ⁺¹+1 (n ≥ 0)	always divisible by 3 (in fact, always divisible by 9)	http://factordb.com/index.php?query=8*10%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
10	8{0}7	8×10ⁿ⁺¹+7 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=8*10%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
10	28{0}7	28×10ⁿ⁺¹+7 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=28*10%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
10	4{6}9	(14×10ⁿ⁺¹+7)/3 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%2814*10%5E%28n%2B1%29%2B7%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
10	families ending with 0, 2, 4, 6, or 8	–	always divisible by 2	–
10	families ending with 0 or 5	–	always divisible by 5	–
10	{0,3,6,9}	–	always divisible by 3 (nonlinear family)	–
10	{0,7}	–	always divisible by 7 (nonlinear family)	–
any base (b)	families ending with digits d which are not coprime to b	–	always divisible by gcd(d,b)	–
any base (b)	families whose digits all have a common factor d > 1	–	always divisible by d	–
3	1{0}1	3ⁿ⁺¹+1 (n ≥ 0)	always divisible by 2	http://factordb.com/index.php?query=3%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
4	2{0}1	2×4ⁿ⁺¹+1 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=2*4%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
5	1{0}1	5ⁿ⁺¹+1 (n ≥ 0)	always divisible by 2	http://factordb.com/index.php?query=5%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
5	1{0}3	5ⁿ⁺¹+3 (n ≥ 0)	always divisible by 2 (in fact, always divisible by 4)	http://factordb.com/index.php?query=5%5E%28n%2B1%29%2B3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
5	3{0}1	3×5ⁿ⁺¹+1 (n ≥ 0)	always divisible by 2 (in fact, always divisible by 4)	http://factordb.com/index.php?query=3*5%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
5	11{0}3	6×5ⁿ⁺¹+3 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=6*5%5E%28n%2B1%29%2B3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
5	3{0}11	3×5ⁿ⁺²+6 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=3*5%5E%28n%2B2%29%2B6&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
6	4{0}1	4×6ⁿ⁺¹+1 (n ≥ 0)	always divisible by 5	http://factordb.com/index.php?query=4*6%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	1{0}1	7ⁿ⁺¹+1 (n ≥ 0)	always divisible by 2	http://factordb.com/index.php?query=7%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	1{0}3	7ⁿ⁺¹+3 (n ≥ 0)	always divisible by 2	http://factordb.com/index.php?query=7%5E%28n%2B1%29%2B3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	1{0}5	7ⁿ⁺¹+5 (n ≥ 0)	always divisible by 2 (in fact, always divisible by 6)	http://factordb.com/index.php?query=7%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	3{0}1	3×7ⁿ⁺¹+1 (n ≥ 0)	always divisible by 2	http://factordb.com/index.php?query=3*7%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	3{0}5	3×7ⁿ⁺¹+5 (n ≥ 0)	always divisible by 2	http://factordb.com/index.php?query=3*7%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	5{0}1	5×7ⁿ⁺¹+1 (n ≥ 0)	always divisible by 2 (in fact, always divisible by 6)	http://factordb.com/index.php?query=5*7%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	5{0}3	5×7ⁿ⁺¹+3 (n ≥ 0)	always divisible by 2	http://factordb.com/index.php?query=5*7%5E%28n%2B1%29%2B3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	1{0}2	7ⁿ⁺¹+2 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=7%5E%28n%2B1%29%2B2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	2{0}1	2×7ⁿ⁺¹+1 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=2*7%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	4{0}5	4×7ⁿ⁺¹+5 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=4*7%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	5{0}4	5×7ⁿ⁺¹+4 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=5*7%5E%28n%2B1%29%2B4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
7	1{0}1{0}1	7^m+n+2+7ⁿ⁺¹+1 (m+n ≥ 0)	always divisible by 3 (nonlinear family)	–
7	1{0}3{0}5	7^m+n+2+3×7ⁿ⁺¹+5 (m+n ≥ 0)	always divisible by 3 (nonlinear family)	–
7	1{0}5{0}3	7^m+n+2+5×7ⁿ⁺¹+3 (m+n ≥ 0)	always divisible by 3 (nonlinear family)	–
7	3{0}1{0}5	3×7^m+n+2+7ⁿ⁺¹+5 (m+n ≥ 0)	always divisible by 3 (nonlinear family)	–
7	3{0}5{0}1	3×7^m+n+2+5×7ⁿ⁺¹+1 (m+n ≥ 0)	always divisible by 3 (nonlinear family)	–
7	5{0}1{0}3	5×7^m+n+2+7ⁿ⁺¹+3 (m+n ≥ 0)	always divisible by 3 (nonlinear family)	–
7	5{0}3{0}1	5×7^m+n+2+3×7ⁿ⁺¹+1 (m+n ≥ 0)	always divisible by 3 (nonlinear family)	–
7	1{0}1{0}1{0}1	7^r+m+n+3+7^m+n+2+7ⁿ⁺¹+1 (r+m+n ≥ 0)	always divisible by 2 (nonlinear family)	–
7	1{0}1{0}2	7^m+n+2+7ⁿ⁺¹+2 (m+n ≥ 0)	always divisible by 2 (nonlinear family)	–
7	1{0}2{0}1	7^m+n+2+2×7ⁿ⁺¹+1 (m+n ≥ 0)	always divisible by 2 (nonlinear family)	–
7	2{0}1{0}1	2×7^m+n+2+7ⁿ⁺¹+1 (m+n ≥ 0)	always divisible by 2 (nonlinear family)	–
7	4{0}5{0}5	4×7^m+n+2+5×7ⁿ⁺¹+5 (m+n ≥ 0)	always divisible by 2 (nonlinear family)	–
7	5{0}4{0}5	5×7^m+n+2+4×7ⁿ⁺¹+5 (m+n ≥ 0)	always divisible by 2 (nonlinear family)	–
7	5{0}5{0}4	5×7^m+n+2+5×7ⁿ⁺¹+4 (m+n ≥ 0)	always divisible by 2 (nonlinear family)	–
8	2{0}5	2×8ⁿ⁺¹+5 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=2*8%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
8	4{0}3	4×8ⁿ⁺¹+3 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=4*8%5E%28n%2B1%29%2B3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
8	6{0}1	6×8ⁿ⁺¹+1 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=6*8%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
8	44{0}3	36×8ⁿ⁺¹+3 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=36*8%5E%28n%2B1%29%2B3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
8	6{0}11	6×8ⁿ⁺²+9 (n ≥ 0)	always divisible by 3	http://factordb.com/index.php?query=6*8%5E%28n%2B2%29%2B9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
8	3{4}1	(25×8ⁿ⁺¹−25)/7 (n ≥ 0)	always divisible by 5 (in fact, always divisible by 25) (in fact, also difference-of-two-cubes factorization) (25×8ⁿ⁺¹−25)/7 = 25 × (2ⁿ−1) × (4ⁿ+2ⁿ+1) / 7 (special example, as the numbers with length ≥ 10 in this family contain "prime > b" subsequence, this prime is 4₈1)	http://factordb.com/index.php?query=%2825*8%5E%28n%2B1%29-25%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{7}62	(7×9ⁿ⁺²−119)/8 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%287*9%5E%28n%2B2%29-119%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	2{5}3	(5×11ⁿ⁺¹−5)/2 (n ≥ 0)	always divisible by 5 (in fact, always divisible by 25)	http://factordb.com/index.php?query=%285*11%5E%28n%2B1%29-5%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	3{5}2	(7×11ⁿ⁺¹−7)/2 (n ≥ 0)	always divisible by 5 (in fact, always divisible by 35)	http://factordb.com/index.php?query=%287*11%5E%28n%2B1%29-7%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	3{5}9	(7×11ⁿ⁺¹+7)/2 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%287*11%5E%28n%2B1%29%2B7%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	A{5}2	(21×11ⁿ⁺¹−7)/2 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%2821*11%5E%28n%2B1%29-7%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	A{5}9	(21×11ⁿ⁺¹+7)/2 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%2821*11%5E%28n%2B1%29%2B7%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
12	A{0}21	10×12ⁿ⁺²+25	always divisible by 5	http://factordb.com/index.php?query=10*12%5E%28n%2B2%29%2B25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3{6}A	(7×13ⁿ⁺¹+7)/2 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%287*13%5E%28n%2B1%29%2B7%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	5{A}C	(35×13ⁿ⁺¹+7)/6 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%2835*13%5E%28n%2B1%29%2B7%29%2F6&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	A{6}3	(21×13ⁿ⁺¹−7)/2 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%2821*13%5E%28n%2B1%29-7%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	C{A}5	(77×13ⁿ⁺¹−35)/6 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%2877*13%5E%28n%2B1%29-35%29%2F6&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	8{6}9	(110×14ⁿ⁺¹+33)/13 (n ≥ 0)	always divisible by 11	http://factordb.com/index.php?query=%28110*14%5E%28n%2B1%29%2B33%29%2F13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	40{4}9	(732×14ⁿ⁺¹+61)/13 (n ≥ 0)	always divisible by 61	http://factordb.com/index.php?query=%28732*14%5E%28n%2B1%29%2B61%29%2F13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
15	9{6}8	(66×15ⁿ⁺¹+11)/7 (n ≥ 0)	always divisible by 11	http://factordb.com/index.php?query=%2866*15%5E%28n%2B1%29%2B11%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2{C}3	(14×16ⁿ⁺¹−49)/5 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%2814*16%5E%28n%2B1%29-49%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	A{4}1	(154×16ⁿ⁺¹−49)/15 (n ≥ 0)	always divisible by 7	http://factordb.com/index.php?query=%28154*16%5E%28n%2B1%29-49%29%2F15&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	8{C}F	(44×16ⁿ⁺¹+11)/5 (n ≥ 0)	always divisible by 11 (in fact, also Aurifeuillean factorization of x⁴+4×y⁴ (44×16ⁿ⁺¹+11)/5 = 11 × (2×4ⁿ⁺¹−2×2ⁿ⁺¹+1) × (2×4ⁿ⁺¹+2×2ⁿ⁺¹+1) / 5	http://factordb.com/index.php?query=%2844*16%5E%28n%2B1%29%2B11%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	8{A}F	(26×16ⁿ⁺¹+13)/3 (n ≥ 0)	always divisible by 13	http://factordb.com/index.php?query=%2826*16%5E%28n%2B1%29%2B13%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	A{6}9	(52×16ⁿ⁺¹+13)/5 (n ≥ 0)	always divisible by 13 (in fact, also Aurifeuillean factorization of x⁴+4×y⁴ (52×16ⁿ⁺¹+13)/5 = 13 × (2×4ⁿ⁺¹−2×2ⁿ⁺¹+1) × (2×4ⁿ⁺¹+2×2ⁿ⁺¹+1) / 5	http://factordb.com/index.php?query=%2852*16%5E%28n%2B1%29%2B13%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	B0{H}6H	(4637×21ⁿ⁺²−4637)/20 (n ≥ 0)	always divisible by 4637	http://factordb.com/index.php?query=%284637*21%5E%28n%2B2%29-4637%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	4{O}9	(44×28ⁿ⁺¹−143)/9 (n ≥ 0)	always divisible by 11	http://factordb.com/index.php?query=%2844*28%5E%28n%2B1%29-143%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	N{6}R	(209×28ⁿ⁺¹+187)/9 (n ≥ 0)	always divisible by 11	http://factordb.com/index.php?query=%28209*28%5E%28n%2B1%29%2B187%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	D{6}R	(119×28ⁿ⁺¹+187)/9 (n ≥ 0)	always divisible by 17	http://factordb.com/index.php?query=%28119*28%5E%28n%2B1%29%2B187%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{1}5	(9ⁿ⁺¹+31)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%289%5E%28n%2B1%29%2B31%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{1}61	(9ⁿ⁺²+359)/8 (n ≥ 0)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%289%5E%28n%2B2%29%2B359%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	16{1}	(121×9ⁿ−1)/8 (n ≥ 0)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even (in fact, also difference-of-two-squares factorization) (121×9ⁿ−1)/8 = (11×3ⁿ−1) × (11×3ⁿ+1) / 8	http://factordb.com/index.php?query=%28121*9%5En-1%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	2{7}	(23×9ⁿ−7)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%2823*9%5En-7%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{3}5	(3×9ⁿ⁺¹+13)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%283*9%5E%28n%2B1%29%2B13%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{3}8	(3×9ⁿ⁺¹+37)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%283*9%5E%28n%2B1%29%2B37%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{3}05	(3×9ⁿ⁺²−203)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%283*9%5E%28n%2B2%29-203%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	5{1}	(41×9ⁿ−1)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%2841*9%5En-1%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	5{7}	(47×9ⁿ−7)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%2847*9%5En-7%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	6{1}	(49×9ⁿ−1)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is even, divisible by 5 if n is odd (in fact, also difference-of-two-squares factorization) (49×9ⁿ−1)/8 = (7×3ⁿ−1) × (7×3ⁿ+1) / 8	http://factordb.com/index.php?query=%2849*9%5En-1%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{7}2	(7×9ⁿ⁺¹−47)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%287*9%5E%28n%2B1%29-47%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{7}5	(7×9ⁿ⁺¹−23)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%287*9%5E%28n%2B1%29-23%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{7}05	(3×9ⁿ⁺²−527)/8 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%287*9%5E%28n%2B2%29-527%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{1}6{1}	(9^m+n+1+40×9ⁿ−1)/8 (m+n ≥ 1)	always divisible by some element of {2,5} (nonlinear family) divisible by 2 if m+n is even, divisible by 5 if m+n is odd	–
9	{7}2{7}	(7×9^m+n+1−40×9ⁿ−7)/8 (m+n ≥ 1)	always divisible by some element of {2,5} (nonlinear family) divisible by 2 if m+n is even, divisible by 5 if m+n is odd	–
9	5{0}{1}	(40×9^m+n+9ⁿ−1)/8 (m+n ≥ 1)	always divisible by some element of {2,5} (nonlinear family) divisible by 2 if n is odd, divisible by 5 if n is even	–
9	5{0}{7}	(40×9^m+n+7×9ⁿ−7)/8 (m+n ≥ 1)	always divisible by some element of {2,5} (nonlinear family) divisible by 2 if n is odd, divisible by 5 if n is even	–
9	{1}{0}5	(9^m+n+1−9ⁿ⁺¹+40)/8 (m+n ≥ 1)	always divisible by some element of {2,5} (nonlinear family) divisible by 2 if m is odd, divisible by 5 if m is even	–
9	{3}{0}5	(3×9^m+n+1−3×9ⁿ⁺¹+40)/8 (m+n ≥ 1)	always divisible by some element of {2,5} (nonlinear family) divisible by 2 if m is odd, divisible by 5 if m is even	–
9	{7}{0}5	(7×9^m+n+1−7×9ⁿ⁺¹+40)/8 (m+n ≥ 1)	always divisible by some element of {2,5} (nonlinear family) divisible by 2 if m is odd, divisible by 5 if m is even	–
11	2{5}	(5×11ⁿ−1)/2 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd	http://factordb.com/index.php?query=%285*11%5En-1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	3{1}	(31×11ⁿ−1)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even (special example, as the numbers with length ≥ 18 in this family contain "prime > b" subsequence, this prime is 1₁₇)	http://factordb.com/index.php?query=%2831*11%5En-1%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	3{5}	(7×11ⁿ−1)/2 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even	http://factordb.com/index.php?query=%287*11%5En-1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	3{7}	(37×11ⁿ−7)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is odd, divisible by 3 if n is even	http://factordb.com/index.php?query=%2837*11%5En-7%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	4{1}	(41×11ⁿ−1)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is even, divisible by 3 if n is odd (special example, as the numbers with length ≥ 18 in this family contain "prime > b" subsequence, this prime is 1₁₇)	http://factordb.com/index.php?query=%2841*11%5En-1%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	4{7}	(47×11ⁿ−7)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is even, divisible by 3 if n is odd	http://factordb.com/index.php?query=%2847*11%5En-7%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	8{5}	(17×11ⁿ−1)/2 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is even, divisible by 3 if n is odd	http://factordb.com/index.php?query=%2817*11%5En-1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	9{1}	(91×11ⁿ−1)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is odd, divisible by 3 if n is even (special example, as the numbers with length ≥ 18 in this family contain "prime > b" subsequence, this prime is 1₁₇)	http://factordb.com/index.php?query=%2891*11%5En-1%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	9{5}	(19×11ⁿ−1)/2 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is odd, divisible by 3 if n is even	http://factordb.com/index.php?query=%2819*11%5En-1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	9{7}	(97×11ⁿ−7)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even	http://factordb.com/index.php?query=%2897*11%5En-7%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	A{1}	(101×11ⁿ−1)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (special example, as the numbers with length ≥ 18 in this family contain "prime > b" subsequence, this prime is 1₁₇)	http://factordb.com/index.php?query=%28101*11%5En-1%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	A{7}	(107×11ⁿ−7)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd	http://factordb.com/index.php?query=%28107*11%5En-7%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{5}2	(11ⁿ⁺¹−7)/2 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd	http://factordb.com/index.php?query=%2811%5E%28n%2B1%29-7%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{1}3	(11ⁿ⁺¹+19)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even (special example, as the numbers with length ≥ 18 in this family contain "prime > b" subsequence, this prime is 1₁₇)	http://factordb.com/index.php?query=%2811%5E%28n%2B1%29%2B19%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{5}3	(11ⁿ⁺¹−5)/2 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even	http://factordb.com/index.php?query=%2811%5E%28n%2B1%29-5%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{7}3	(7×11ⁿ⁺¹−47)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is odd, divisible by 3 if n is even	http://factordb.com/index.php?query=%287*11%5E%28n%2B1%29-47%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{1}4	(11ⁿ⁺¹+29)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is even, divisible by 3 if n is odd (special example, as the numbers with length ≥ 18 in this family contain "prime > b" subsequence, this prime is 1₁₇)	http://factordb.com/index.php?query=%2811%5E%28n%2B1%29%2B29%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{7}4	(7×11ⁿ⁺¹−37)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is even, divisible by 3 if n is odd	http://factordb.com/index.php?query=%287*11%5E%28n%2B1%29-37%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{5}8	(11ⁿ⁺¹+5)/2 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is even, divisible by 3 if n is odd	http://factordb.com/index.php?query=%2811%5E%28n%2B1%29%2B5%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{1}9	(11ⁿ⁺¹+79)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is odd, divisible by 3 if n is even (special example, as the numbers with length ≥ 18 in this family contain "prime > b" subsequence, this prime is 1₁₇)	http://factordb.com/index.php?query=%2811%5E%28n%2B1%29%2B79%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{5}9	(11ⁿ⁺¹+7)/2 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even (in fact, always divisible by some element of {2²,3}) divisible by 2² if n is odd, divisible by 3 if n is even	http://factordb.com/index.php?query=%2811%5E%28n%2B1%29%2B7%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{7}9	(7×11ⁿ⁺¹+13)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even	http://factordb.com/index.php?query=%287*11%5E%28n%2B1%29%2B13%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{1}A	(11ⁿ⁺¹+89)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if the length is odd, divisible by 3 if the length is even (special example, as the numbers with length ≥ 18 in this family contain "prime > b" subsequence, this prime is 1₁₇)	http://factordb.com/index.php?query=%2811%5E%28n%2B1%29%2B89%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	{7}A	(7×11ⁿ⁺¹+23)/10 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if the length is odd, divisible by 3 if the length is even	http://factordb.com/index.php?query=%287*11%5E%28n%2B1%29%2B23%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	3{0}{5}	(6×11^m+n+11ⁿ−1)/2	always divisible by some element of {2,3} (nonlinear family) divisible by 2 if n is odd, divisible by 3 if n is even	–
11	{5}{0}3	(11^m+n+1−11ⁿ⁺¹+6)/2	always divisible by some element of {2,3} (nonlinear family) divisible by 2 if m is odd, divisible by 3 if m is even	–
14	4{0}1	4×14ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {3,5} divisible by 3 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=4*14%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	B{0}1	11×14ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {3,5} divisible by 3 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=11*14%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	3{D}	4×14ⁿ−1 (n ≥ 1)	always divisible by some element of {3,5} divisible by 3 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=4*14%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	A{D}	11×14ⁿ−1 (n ≥ 1)	always divisible by some element of {3,5} divisible by 3 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=11*14%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	1{0}B	14ⁿ⁺¹+11 (n ≥ 0)	always divisible by some element of {3,5} divisible by 3 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=14%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	{D}3	14ⁿ⁺¹−11 (n ≥ 1)	always divisible by some element of {3,5} divisible by 3 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=14%5E%28n%2B1%29-11&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	{4}9	(4×14ⁿ⁺¹+61)/13 (n ≥ 1)	always divisible by some element of {3,5} divisible by 3 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%284*14%5E%28n%2B1%29%2B61%29%2F13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	{8}5	(8×14ⁿ⁺¹−47)/13 (n ≥ 1)	always divisible by some element of {3,5} divisible by 3 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%288*14%5E%28n%2B1%29-47%29%2F13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	2{B}	(43×17ⁿ−11)/16 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, always divisible by some element of {2,3²}) divisible by 2 if n is even, divisible by 3² if n is odd	http://factordb.com/index.php?query=%2843*17%5En-11%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	9{B}	(155×17ⁿ−11)/16 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even (in fact, always divisible by some element of {2,3²}) divisible by 2 if n is odd, divisible by 3² if n is even	http://factordb.com/index.php?query=%28155*17%5En-11%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	{B}2	(11×17ⁿ⁺¹−155)/16 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, always divisible by some element of {2,3²}) divisible by 2 if n is even, divisible by 3² if n is odd	http://factordb.com/index.php?query=%2811*17%5E%28n%2B1%29-155%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	{B}9	(11×17ⁿ⁺¹−43)/16 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is odd, divisible by 3 if n is even (in fact, always divisible by some element of {2,3²}) divisible by 2 if n is odd, divisible by 3² if n is even	http://factordb.com/index.php?query=%2811*17%5E%28n%2B1%29-43%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
19	4{9}	(9×19ⁿ−1)/2 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is even, divisible by 5 if n is odd (in fact, always divisible by some element of {2²,5}) divisible by 2² if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%289*19%5En-1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
19	5{9}	(11×19ⁿ−1)/2 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even (in fact, always divisible by some element of {2²,5}) divisible by 2² if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%2811*19%5En-1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
19	{9}4	(19ⁿ⁺¹−11)/2 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is even, divisible by 5 if n is odd (in fact, always divisible by some element of {2²,5}) divisible by 2² if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%2819%5E%28n%2B1%29-11%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
19	{9}5	(19ⁿ⁺¹−9)/2 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even (in fact, always divisible by some element of {2²,5}) divisible by 2² if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%2819%5E%28n%2B1%29-9%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	8{0}1	8×20ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {3,7} divisible by 3 if n is odd, divisible by 7 if n is even	http://factordb.com/index.php?query=8*20%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	D{0}1	13×20ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {3,7} divisible by 3 if n is even, divisible by 7 if n is odd	http://factordb.com/index.php?query=13*20%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	7{J}	8×20ⁿ−1 (n ≥ 1)	always divisible by some element of {3,7} divisible by 3 if n is odd, divisible by 7 if n is even	http://factordb.com/index.php?query=8*20%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	C{J}	13×20ⁿ−1 (n ≥ 1)	always divisible by some element of {3,7} divisible by 3 if n is even, divisible by 7 if n is odd	http://factordb.com/index.php?query=13*20%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	1{0}D	20ⁿ⁺¹+13 (n ≥ 0)	always divisible by some element of {3,7} divisible by 3 if n is even, divisible by 7 if n is odd	http://factordb.com/index.php?query=20%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	{J}7	20ⁿ⁺¹−13 (n ≥ 1)	always divisible by some element of {3,7} divisible by 3 if n is odd, divisible by 7 if n is even	http://factordb.com/index.php?query=20%5E%28n%2B1%29-13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	D{1}	(313×25ⁿ−1)/24 (n ≥ 1)	always divisible by some element of {2,13} divisible by 2 if n is odd, divisible by 13 if n is even	http://factordb.com/index.php?query=%28313*25%5En-1%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	E{1}	(337×25ⁿ−1)/24 (n ≥ 1)	always divisible by some element of {2,13} divisible by 2 if n is even, divisible by 13 if n is odd	http://factordb.com/index.php?query=%28337*25%5En-1%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{1}D	(25ⁿ⁺¹+287)/24 (n ≥ 1)	always divisible by some element of {2,13} divisible by 2 if n is odd, divisible by 13 if n is even	http://factordb.com/index.php?query=%2825%5E%28n%2B1%29%2B287%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{1}E	(25ⁿ⁺¹+311)/24 (n ≥ 1)	always divisible by some element of {2,13} divisible by 2 if n is even, divisible by 13 if n is odd	http://factordb.com/index.php?query=%2825%5E%28n%2B1%29%2B311%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	1E{1}	(937×25ⁿ−1)/24 (n ≥ 0)	always divisible by some element of {2,13} divisible by 2 if n is odd, divisible by 13 if n is even	http://factordb.com/index.php?query=%28937*25%5En-1%29%2F24&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	1F{1}	(961×25ⁿ−1)/24 (n ≥ 0)	always divisible by some element of {2,13} divisible by 2 if n is even, divisible by 13 if n is odd (in fact, also difference-of-two-squares factorization) (961×25ⁿ−1)/24 = (31×5ⁿ−1) × (31×5ⁿ+1) / 24	http://factordb.com/index.php?query=%28961*25%5En-1%29%2F24&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	3G{3}	(729×25ⁿ−1)/8 (n ≥ 0)	always divisible by some element of {2,13} divisible by 2 if n is odd, divisible by 13 if n is even (in fact, also difference-of-two-squares factorization) (729×25ⁿ−1)/8 = (27×5ⁿ−1) × (27×5ⁿ+1) / 8	http://factordb.com/index.php?query=%28729*25%5En-1%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	D0{3}	(2601×25ⁿ−1)/8 (n ≥ 0)	always divisible by some element of {2,13} divisible by 2 if n is odd, divisible by 13 if n is even (in fact, also difference-of-two-squares factorization) (2601×25ⁿ−1)/8 = (51×5ⁿ−1) × (51×5ⁿ+1) / 8	http://factordb.com/index.php?query=%282601*25%5En-1%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	G6{3}	(3249×25ⁿ−1)/8 (n ≥ 0)	always divisible by some element of {2,13} divisible by 2 if n is even, divisible by 13 if n is odd (in fact, also difference-of-two-squares factorization) (3249×25ⁿ−1)/8 = (57×5ⁿ−1) × (57×5ⁿ+1) / 8	http://factordb.com/index.php?query=%283249*25%5En-1%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	4{0}1	4×29ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {3,5} divisible by 3 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=4*29%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	Q{0}1	26×29ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {3,5} divisible by 3 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=26*29%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	3{S}	4×29ⁿ−1 (n ≥ 1)	always divisible by some element of {3,5} divisible by 3 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=4*29%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	P{S}	26×29ⁿ−1 (n ≥ 1)	always divisible by some element of {3,5} divisible by 3 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=26*29%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	1{0}4	29ⁿ⁺¹+4 (n ≥ 0)	always divisible by some element of {3,5} divisible by 3 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=29%5E%28n%2B1%29%2B4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	1{0}Q	29ⁿ⁺¹+26 (n ≥ 0)	always divisible by some element of {3,5} divisible by 3 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=29%5E%28n%2B1%29%2B26&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	{S}P	29ⁿ⁺¹−4 (n ≥ 1)	always divisible by some element of {3,5} divisible by 3 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=29%5E%28n%2B1%29-4&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	{S}3	29ⁿ⁺¹−26 (n ≥ 1)	always divisible by some element of {3,5} divisible by 3 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=29%5E%28n%2B1%29-26&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	2{H}	(73×29ⁿ−17)/28 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, also always divisible by some element of {2,5}) divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%2873*29%5En-17%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	F{H}	(437×29ⁿ−17)/28 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, also always divisible by some element of {2,5}) divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%28437*29%5En-17%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	{H}2	(17×29ⁿ⁺¹−437)/28 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, also always divisible by some element of {2,5}) divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%2817*29%5E%28n%2B1%29-437%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	{H}F	(17×29ⁿ⁺¹−73)/28 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, also always divisible by some element of {2,5}) divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%2817*29%5E%28n%2B1%29-73%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	3{D}	(97×29ⁿ−13)/28 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, also always divisible by some element of {2,5}) divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%2897*29%5En-13%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	A{D}	(293×29ⁿ−13)/28 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, also always divisible by some element of {2,5}) divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%28293*29%5En-13%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	{D}3	(13×29ⁿ⁺¹−293)/28 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, also always divisible by some element of {2,5}) divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%2813*29%5E%28n%2B1%29-293%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	{D}A	(13×29ⁿ⁺¹−97)/28 (n ≥ 1)	always divisible by some element of {2,3} divisible by 2 if n is even, divisible by 3 if n is odd (in fact, also always divisible by some element of {2,5}) divisible by 2 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%2813*29%5E%28n%2B1%29-97%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	5{B}	(151×29ⁿ−11)/28 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even (in fact, also always divisible by some element of {3,5}) divisible by 3 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%28151*29%5En-11%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	6{B}	(179×29ⁿ−11)/28 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is even, divisible by 5 if n is odd (in fact, also always divisible by some element of {3,5}) divisible by 3 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%28179*29%5En-11%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	{B}5	(11×29ⁿ⁺¹−179)/28 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is odd, divisible by 5 if n is even (in fact, also always divisible by some element of {3,5}) divisible by 3 if n is odd, divisible by 5 if n is even	http://factordb.com/index.php?query=%2811*29%5E%28n%2B1%29-179%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	{B}6	(11×29ⁿ⁺¹−151)/28 (n ≥ 1)	always divisible by some element of {2,5} divisible by 2 if n is even, divisible by 5 if n is odd (in fact, also always divisible by some element of {3,5}) divisible by 3 if n is even, divisible by 5 if n is odd	http://factordb.com/index.php?query=%2811*29%5E%28n%2B1%29-151%29%2F28&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	A{0}1	10×32ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {3,11} divisible by 3 if n is even, divisible by 11 if n is odd	http://factordb.com/index.php?query=10*32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	N{0}1	23×32ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {3,11} divisible by 3 if n is odd, divisible by 11 if n is even	http://factordb.com/index.php?query=23*32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	9{V}	10×32ⁿ−1 (n ≥ 1)	always divisible by some element of {3,11} divisible by 3 if n is even, divisible by 11 if n is odd	http://factordb.com/index.php?query=10*32%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	M{V}	23×32ⁿ−1 (n ≥ 1)	always divisible by some element of {3,11} divisible by 3 if n is odd, divisible by 11 if n is even	http://factordb.com/index.php?query=23*32%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	1{0}N	32ⁿ⁺¹+23 (n ≥ 0)	always divisible by some element of {3,11} divisible by 3 if n is odd, divisible by 11 if n is even	http://factordb.com/index.php?query=32%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	{V}9	32ⁿ⁺¹−23 (n ≥ 1)	always divisible by some element of {3,11} divisible by 3 if n is even, divisible by 11 if n is odd	http://factordb.com/index.php?query=32%5E%28n%2B1%29-23&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	6{0}1	6×34ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {5,7} divisible by 5 if n is even, divisible by 7 if n is odd	http://factordb.com/index.php?query=6*34%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	5{X}	6×34ⁿ−1 (n ≥ 1)	always divisible by some element of {5,7} divisible by 5 if n is even, divisible by 7 if n is odd	http://factordb.com/index.php?query=6*34%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	S{X}	29×34ⁿ−1 (n ≥ 1)	always divisible by some element of {5,7} divisible by 5 if n is odd, divisible by 7 if n is even	http://factordb.com/index.php?query=29*34%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	{X}5	34ⁿ⁺¹−29 (n ≥ 1)	always divisible by some element of {5,7} divisible by 5 if n is even, divisible by 7 if n is odd	http://factordb.com/index.php?query=34%5E%28n%2B1%29-29&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
8	6{4}7	(46×8ⁿ⁺¹+17)/7 (n ≥ 0)	always divisible by some element of {3,5,13} divisible by 3 if the length is odd, divisible by 5 if the length is == 2 mod 4, divisible by 13 if the length is == 0 mod 4 (special example, as the numbers with length ≥ 222 in this family contain "prime > b" subsequence, this prime is 4₂₂₀7)	http://factordb.com/index.php?query=%2846*8%5E%28n%2B1%29%2B17%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	95{0}3	122×13ⁿ⁺¹+3 (n ≥ 0)	always divisible by some element of {5,7,17} divisible by 7 if n is even, divisible by 5 if n == 3 mod 4, divisible by 17 if n == 1 mod 4	http://factordb.com/index.php?query=122*13%5E%28n%2B1%29%2B3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3{0}95	3×13ⁿ⁺²+122 (n ≥ 0)	always divisible by some element of {5,7,17} divisible by 7 if n is odd, divisible by 5 if n == 2 mod 4, divisible by 17 if n == 0 mod 4	http://factordb.com/index.php?query=3*13%5E%28n%2B2%29%2B122&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{4}D	(4×16ⁿ⁺¹+131)/15 (n ≥ 1)	always divisible by some element of {3,7,13} divisible by 3 if n == 2 mod 3, divisible by 7 if n == 1 mod 3, divisible by 13 if n == 0 mod 3	http://factordb.com/index.php?query=%284*16%5E%28n%2B1%29%2B131%29%2F15&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{8}F	(8×16ⁿ⁺¹+97)/15 (n ≥ 1)	always divisible by some element of {3,7,13} divisible by 3 if n == 0 mod 3, divisible by 7 if n == 2 mod 3, divisible by 13 if n == 1 mod 3	http://factordb.com/index.php?query=%288*16%5E%28n%2B1%29%2B97%29%2F15&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	7F{0}D	134×17ⁿ⁺¹+13 (n ≥ 0)	always divisible by some element of {3,5,29} divisible by 3 if n is odd, divisible by 5 if n == 2 mod 4, divisible by 29 if n == 0 mod 4	http://factordb.com/index.php?query=134*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	D{0}7F	13×17ⁿ⁺²+134 (n ≥ 0)	always divisible by some element of {3,5,29} divisible by 3 if n is even, divisible by 5 if n == 3 mod 4, divisible by 29 if n == 1 mod 4	http://factordb.com/index.php?query=13*17%5E%28n%2B2%29%2B134&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	{7}D	(7×21ⁿ⁺¹+113)/20 (n ≥ 1)	always divisible by some element of {2,13,17} divisible by 2 if n is odd, divisible by 13 if n == 0 mod 4, divisible by 17 if n == 2 mod 4	http://factordb.com/index.php?query=%287*21%5E%28n%2B1%29%2B113%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	7{0}FJ	7×21ⁿ⁺²+334 (n ≥ 0)	always divisible by some element of {11,13,17} divisible by 11 if n is even, divisible by 13 if n == 3 mod 4, divisible by 17 if n == 1 mod 4	http://factordb.com/index.php?query=7*21%5E%28n%2B2%29%2B334&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
23	7L{0}1	182×23ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {3,5,53} divisible by 3 if n is odd, divisible by 5 if n == 2 mod 4, divisible by 53 if n == 0 mod 4	http://factordb.com/index.php?query=182*23%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
23	1{0}7L	23ⁿ⁺²+182 (n ≥ 0)	always divisible by some element of {3,5,53} divisible by 3 if n is even, divisible by 5 if n == 3 mod 4, divisible by 53 if n == 1 mod 4	http://factordb.com/index.php?query=23%5E%28n%2B2%29%2B182&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
23	{D}GA	(13×23ⁿ⁺²+1439)/22 (n ≥ 0)	always divisible by some element of {2,5,7,37,79} divisible by 2 if n is even, divisible by 5 if n == 1 mod 4, divisible by 7 if n == 0 mod 3, divisible by 37 if n == 7 mod 12, divisible by 79 if n == 2 mod 3 (in fact, also always divisible by some element of {3,5,7,37,79}) divisible by 3 if n is even, divisible by 5 if n == 1 mod 4, divisible by 7 if n == 0 mod 3, divisible by 37 if n == 7 mod 12, divisible by 79 if n == 2 mod 3	http://factordb.com/index.php?query=%2813*23%5E%28n%2B2%29%2B1439%29%2F22&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
23	L{5}L	(467×23ⁿ⁺¹+347)/22 (n ≥ 0)	always divisible by some element of {2,5,7,13,37} divisible by 2 if n is even, divisible by 5 if n == 1 mod 4, divisible by 7 if n == 0 mod 3, divisible by 13 if n == 1 mod 6, divisible by 37 if n == 11 mod 12 (in fact, also always divisible by some element of {3,5,7,13,37}) divisible by 3 if n is even, divisible by 5 if n == 1 mod 4, divisible by 7 if n == 0 mod 3, divisible by 13 if n == 1 mod 6, divisible by 37 if n == 11 mod 12	http://factordb.com/index.php?query=%28467*23%5E%28n%2B1%29%2B347%29%2F22&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	9{N}	(239×25ⁿ−23)/24 (n ≥ 1)	always divisible by some element of {3,7,31} divisible by 3 if n == 0 mod 3, divisible by 7 if n == 2 mod 3, divisible by 31 if n == 1 mod 3	http://factordb.com/index.php?query=%28239*25%5En-23%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{N}E	(23×25ⁿ⁺¹−239)/24 (n ≥ 1)	always divisible by some element of {3,7,31} divisible by 3 if n == 2 mod 3, divisible by 7 if n == 0 mod 3, divisible by 31 if n == 1 mod 3	http://factordb.com/index.php?query=%2823*25%5E%28n%2B1%29-239%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	27{1}	(1369×25ⁿ−1)/24 (n ≥ 0)	always divisible by some element of {3,7,31} divisible by 3 if n == 0 mod 3, divisible by 7 if n == 2 mod 3, divisible by 31 if n == 1 mod 3 (in fact, also difference-of-two-squares factorization) (1369×25ⁿ−1)/24 = (37×5ⁿ−1) × (37×5ⁿ+1) / 24	http://factordb.com/index.php?query=%281369*25%5En-1%29%2F24&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	JP{0}1	538×27ⁿ⁺¹+1 (n ≥ 0)	always divisible by some element of {5,7,73} divisible by 7 if n is odd, divisible by 5 if n == 2 mod 4, divisible by 73 if n == 0 mod 4	http://factordb.com/index.php?query=538*27%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	1{0}JP	27ⁿ⁺²+538 (n ≥ 0)	always divisible by some element of {5,7,73} divisible by 7 if n is even, divisible by 5 if n == 3 mod 4, divisible by 73 if n == 1 mod 4	http://factordb.com/index.php?query=27%5E%28n%2B2%29%2B538&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	J{0}2	19×27ⁿ⁺¹+2 (n ≥ 0)	always divisible by some element of {5,7,73} divisible by 7 if n is odd, divisible by 5 if n == 0 mod 4, divisible by 73 if n == 2 mod 4	http://factordb.com/index.php?query=19*27%5E%28n%2B1%29%2B2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
29	{2}{5}	(2×29^m+n+3×29ⁿ−5)/28	always divisible by some element of {2,3,5} (nonlinear family) divisible by 2 if n is even, divisible by 3 if m and n are both even or both odd, divisible by 5 if m is even	–
29	{5}{2}	(5×29^m+n−3×29ⁿ−2)/28	always divisible by some element of {2,3,5} (nonlinear family) divisible by 2 if m is even, divisible by 3 if m and n are both even or both odd, divisible by 5 if n is even	–
29	{M}{P}	(22×29^m+n+3×29ⁿ−25)/28	always divisible by some element of {2,3,5} (nonlinear family) divisible by 2 if n is even, divisible by 3 if m and n are both even or both odd, divisible by 5 if m is even	–
29	{P}{M}	(25×29^m+n−3×29ⁿ−22)/28	always divisible by some element of {2,3,5} (nonlinear family) divisible by 2 if m is even, divisible by 3 if m and n are both even or both odd, divisible by 5 if n is even	–
30	A{0}9J	10×30ⁿ⁺²+289 (n ≥ 0)	always divisible by some element of {7,13,19,31} divisible by 7 if n == 0 mod 3, divisible by 13 if n == 4 mod 6, divisible by 19 if n == 2 mod 3, divisible by 31 if n is odd	http://factordb.com/index.php?query=10*30%5E%28n%2B2%29%2B289&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
31	A{N}	(323×31ⁿ−23)/30 (n ≥ 1)	always divisible by some element of {2,13,37} divisible by 2 if n is even, divisible by 13 if n == 3 mod 4, divisible by 37 if n == 1 mod 4	http://factordb.com/index.php?query=%28323*31%5En-23%29%2F30&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
31	{N}D	(23×31ⁿ⁺¹−323)/30 (n ≥ 1)	always divisible by some element of {2,13,37} divisible by 2 if n is odd, divisible by 13 if n == 0 mod 4, divisible by 37 if n == 2 mod 4	http://factordb.com/index.php?query=%2823*31%5E%28n%2B1%29-323%29%2F30&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
31	D{R}	(139×31ⁿ−9)/10 (n ≥ 1)	always divisible by some element of {2,13,37} divisible by 2 if n is odd, divisible by 13 if n == 0 mod 4, divisible by 37 if n == 2 mod 4	http://factordb.com/index.php?query=%28139*31%5En-9%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
31	{R}E	(9×31ⁿ⁺¹−139)/10 (n ≥ 1)	always divisible by some element of {2,13,37} divisible by 2 if n is even, divisible by 13 if n == 3 mod 4, divisible by 37 if n == 1 mod 4	http://factordb.com/index.php?query=%289*31%5E%28n%2B1%29-139%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
31	O{5}	(145×31ⁿ−1)/6 (n ≥ 1)	always divisible by some element of {2,3,7,19} divisible by 2 if n is even, divisible by 3 if n == 0 mod 3, divisible by 7 if n == 1 mod 6, divisible by 19 if n == 5 mod 6	http://factordb.com/index.php?query=%28145*31%5En-1%29%2F6&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
31	J{T}	(599×31ⁿ−29)/30 (n ≥ 1)	always divisible by some element of {2,3,7,19} divisible by 2 if n is odd, divisible by 3 if n == 1 mod 3, divisible by 7 if n == 2 mod 6, divisible by 19 if n == 0 mod 6	http://factordb.com/index.php?query=%28599*31%5En-29%29%2F30&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
31	{T}A	(29×31ⁿ⁺¹−599)/30 (n ≥ 1)	always divisible by some element of {2,3,7,19} divisible by 2 if n is even, divisible by 3 if n == 1 mod 3, divisible by 7 if n == 3 mod 6, divisible by 19 if n == 5 mod 6	http://factordb.com/index.php?query=%2829*31%5E%28n%2B1%29-599%29%2F30&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	8{0}V	8×32ⁿ⁺¹+31 (n ≥ 0)	always divisible by some element of {3,5,41} divisible by 3 if n is odd, divisible by 5 if n == 2 mod 4, divisible by 41 if n == 0 mod 4	http://factordb.com/index.php?query=8*32%5E%28n%2B1%29%2B31&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	{G}L	(16×32ⁿ⁺¹+139)/31 (n ≥ 1)	always divisible by some element of {3,5,41} divisible by 3 if n is even, divisible by 5 if n == 3 mod 4, divisible by 41 if n == 1 mod 4	http://factordb.com/index.php?query=%2816*32%5E%28n%2B1%29%2B139%29%2F31&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{1}	(9ⁿ−1)/8 (n ≥ 2)	difference-of-two-squares factorization (9ⁿ−1)/8 = (3ⁿ−1) × (3ⁿ+1) / 8	http://factordb.com/index.php?query=%289%5En-1%29%2F8&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
8	1{0}1	8ⁿ⁺¹+1 (n ≥ 0)	sum-of-two-cubes factorization 8ⁿ⁺¹+1 = (2ⁿ⁺¹+1) × (4ⁿ⁺¹−2ⁿ⁺¹+1)	http://factordb.com/index.php?query=8%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	3{1}	(25×9ⁿ−1)/8 (n ≥ 1)	difference-of-two-squares factorization (25×9ⁿ−1)/8 = (5×3ⁿ−1) × (5×3ⁿ+1) / 8	http://factordb.com/index.php?query=%2825*9%5En-1%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	3{8}	4×9ⁿ−1 (n ≥ 1)	difference-of-two-squares factorization 4×9ⁿ−1 = (2×3ⁿ−1) × (2×3ⁿ+1)	http://factordb.com/index.php?query=4*9%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	{8}5	9ⁿ⁺¹−4 (n ≥ 1)	difference-of-two-squares factorization 9ⁿ⁺¹−4 = (3ⁿ⁺¹−2) × (3ⁿ⁺¹+2)	http://factordb.com/index.php?query=9%5E%28n%2B1%29-4&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	3{8}35	4×9ⁿ⁺²−49 (n ≥ 0)	difference-of-two-squares factorization 4×9ⁿ⁺²−49 = (2×3ⁿ⁺²−7) × (2×3ⁿ⁺²+7)	http://factordb.com/index.php?query=4*9%5E%28n%2B2%29-49&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	8{F}	9×16ⁿ−1 (n ≥ 1)	difference-of-two-squares factorization 9×16ⁿ−1 = (3×4ⁿ−1) × (3×4ⁿ+1)	http://factordb.com/index.php?query=9*16%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{F}7	16ⁿ⁺¹−9 (n ≥ 1)	difference-of-two-squares factorization 16ⁿ⁺¹−9 = (4ⁿ⁺¹−3) × (4ⁿ⁺¹+3)	http://factordb.com/index.php?query=16%5E%28n%2B1%29-9&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{4}1	(4×16ⁿ⁺¹−49)/15 (n ≥ 1)	difference-of-two-squares factorization (4×16ⁿ⁺¹−49)/15 = (2×4ⁿ⁺¹−7) × (2×4ⁿ⁺¹+7) / 15	http://factordb.com/index.php?query=%284*16%5E%28n%2B1%29-49%29%2F15&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	B{4}1	(169×16ⁿ⁺¹−49)/15 (n ≥ 0)	difference-of-two-squares factorization (169×16ⁿ⁺¹−49)/15 = (13×4ⁿ⁺¹−7) × (13×4ⁿ⁺¹+7) / 15	http://factordb.com/index.php?query=%28169*16%5E%28n%2B1%29-49%29%2F15&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	1{5}	(4×16ⁿ−1)/3 (n ≥ 1)	difference-of-two-squares factorization (4×16ⁿ−1)/3 = (2×4ⁿ−1) × (2×4ⁿ+1) / 3	http://factordb.com/index.php?query=%284*16%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	8{5}	(25×16ⁿ−1)/3 (n ≥ 1)	difference-of-two-squares factorization (25×16ⁿ−1)/3 = (5×4ⁿ−1) × (5×4ⁿ+1) / 3	http://factordb.com/index.php?query=%2825*16%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	10{5}	(49×16ⁿ−1)/3 (n ≥ 1)	difference-of-two-squares factorization (49×16ⁿ−1)/3 = (7×4ⁿ−1) × (7×4ⁿ+1) / 3	http://factordb.com/index.php?query=%2849*16%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	A1{5}	(484×16ⁿ−1)/3 (n ≥ 0)	difference-of-two-squares factorization (484×16ⁿ−1)/3 = (22×4ⁿ−1) × (22×4ⁿ+1) / 3	http://factordb.com/index.php?query=%28484*16%5En-1%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	7{3}	(36×16ⁿ−1)/5 (n ≥ 1)	difference-of-two-squares factorization (36×16ⁿ−1)/5 = (6×4ⁿ−1) × (6×4ⁿ+1) / 5	http://factordb.com/index.php?query=%2836*16%5En-1%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	3{F}AF	4×16ⁿ⁺²−81 (n ≥ 0)	difference-of-two-squares factorization 4×16ⁿ⁺²−81 = (2×4ⁿ⁺²−9) × (2×4ⁿ⁺²+9)	http://factordb.com/index.php?query=4*16%5E%28n%2B2%29-81&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	30{F}AF	49×16ⁿ⁺²−81 (n ≥ 0)	difference-of-two-squares factorization 49×16ⁿ⁺²−81 = (7×4ⁿ⁺²−9) × (7×4ⁿ⁺²+9)	http://factordb.com/index.php?query=49*16%5E%28n%2B2%29-81&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	3{F}A0F	4×16ⁿ⁺³−1521 (n ≥ 0)	difference-of-two-squares factorization 4×16ⁿ⁺³−1521 = (2×4ⁿ⁺³−39) × (2×4ⁿ⁺³+39)	http://factordb.com/index.php?query=4*16%5E%28n%2B3%29-1521&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	30{F}A0F	49×16ⁿ⁺³−1521 (n ≥ 0)	difference-of-two-squares factorization 49×16ⁿ⁺³−1521 = (7×4ⁿ⁺³−39) × (7×4ⁿ⁺³+39)	http://factordb.com/index.php?query=49*16%5E%28n%2B3%29-1521&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{3}23	(16ⁿ⁺²−81)/5 (n ≥ 0)	difference-of-two-squares factorization (16ⁿ⁺²−81)/5 = (4ⁿ⁺²−9) × (4ⁿ⁺²+9) / 5 (in fact, difference-of-two-4th-powers factorization) (16ⁿ⁺²−81)/5 = (2ⁿ⁺²−3) × (2ⁿ⁺²+3) × (4ⁿ⁺²+9) / 5	http://factordb.com/index.php?query=%2816%5E%28n%2B2%29-81%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{5}45	(16ⁿ⁺²−49)/3 (n ≥ 0)	difference-of-two-squares factorization (16ⁿ⁺²−49)/3 = (4ⁿ⁺²−7) × (4ⁿ⁺²+7) / 3	http://factordb.com/index.php?query=%2816%5E%28n%2B2%29-49%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{C}B	(4×16ⁿ⁺¹−9)/5 (n ≥ 1)	difference-of-two-squares factorization (4×16ⁿ⁺¹−9)/5 = (2×4ⁿ⁺¹−3) × (2×4ⁿ⁺¹+3) / 5	http://factordb.com/index.php?query=%284*16%5E%28n%2B1%29-9%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{C}D	(4×16ⁿ⁺¹+1)/5 (n ≥ 1)	Aurifeuillean factorization of x⁴+4×y⁴ (4×16ⁿ⁺¹+1)/5 = (2×4ⁿ⁺¹−2×2ⁿ⁺¹+1) × (2×4ⁿ⁺¹+2×2ⁿ⁺¹+1) / 5	http://factordb.com/index.php?query=%284*16%5E%28n%2B1%29%2B1%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{C}DD	(4×16ⁿ⁺²+81)/5 (n ≥ 0)	Aurifeuillean factorization of x⁴+4×y⁴ (4×16ⁿ⁺²+81)/5 = (2×4ⁿ⁺²−6×2ⁿ⁺²+9) × (2×4ⁿ⁺²+6×2ⁿ⁺²+9) / 5	http://factordb.com/index.php?query=%284*16%5E%28n%2B2%29%2B81%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{1}	(25ⁿ−1)/24 (n ≥ 2)	difference-of-two-squares factorization (25ⁿ−1)/24 = (5ⁿ−1) × (5ⁿ+1) / 24	http://factordb.com/index.php?query=%2825%5En-1%29%2F24&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	2{1}	(49×25ⁿ−1)/24 (n ≥ 1)	difference-of-two-squares factorization (49×25ⁿ−1)/24 = (7×5ⁿ−1) × (7×5ⁿ+1) / 24	http://factordb.com/index.php?query=%2849*25%5En-1%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	5{1}	(121×25ⁿ−1)/24 (n ≥ 1)	difference-of-two-squares factorization (121×25ⁿ−1)/24 = (11×5ⁿ−1) × (11×5ⁿ+1) / 24	http://factordb.com/index.php?query=%28121*25%5En-1%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	7{1}	(169×25ⁿ−1)/24 (n ≥ 1)	difference-of-two-squares factorization (169×25ⁿ−1)/24 = (13×5ⁿ−1) × (13×5ⁿ+1) / 24	http://factordb.com/index.php?query=%28169*25%5En-1%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	C{1}	(289×25ⁿ−1)/24 (n ≥ 1)	difference-of-two-squares factorization (289×25ⁿ−1)/24 = (17×5ⁿ−1) × (17×5ⁿ+1) / 24	http://factordb.com/index.php?query=%28289*25%5En-1%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	F{1}	(361×25ⁿ−1)/24 (n ≥ 1)	difference-of-two-squares factorization (361×25ⁿ−1)/24 = (19×5ⁿ−1) × (19×5ⁿ+1) / 24	http://factordb.com/index.php?query=%28361*25%5En-1%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	M{1}	(529×25ⁿ−1)/24 (n ≥ 1)	difference-of-two-squares factorization (529×25ⁿ−1)/24 = (23×5ⁿ−1) × (23×5ⁿ+1) / 24	http://factordb.com/index.php?query=%28529*25%5En-1%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	7C{1}	(4489×25ⁿ−1)/24 (n ≥ 0)	difference-of-two-squares factorization (4489×25ⁿ−1)/24 = (67×5ⁿ−1) × (67×5ⁿ+1) / 24	http://factordb.com/index.php?query=%284489*25%5En-1%29%2F24&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	D5{1}	(7921×25ⁿ−1)/24 (n ≥ 0)	difference-of-two-squares factorization (7921×25ⁿ−1)/24 = (89×5ⁿ−1) × (89×5ⁿ+1) / 24	http://factordb.com/index.php?query=%287921*25%5En-1%29%2F24&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	1{3}	(9×25ⁿ−1)/8 (n ≥ 1)	difference-of-two-squares factorization (9×25ⁿ−1)/8 = (3×5ⁿ−1) × (3×5ⁿ+1) / 8	http://factordb.com/index.php?query=%289*25%5En-1%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	1{8}	(4×25ⁿ−1)/3 (n ≥ 1)	difference-of-two-squares factorization (4×25ⁿ−1)/3 = (2×5ⁿ−1) × (2×5ⁿ+1) / 3	http://factordb.com/index.php?query=%284*25%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	5{8}	(16×25ⁿ−1)/3 (n ≥ 1)	difference-of-two-squares factorization (16×25ⁿ−1)/3 = (4×5ⁿ−1) × (4×5ⁿ+1) / 3	http://factordb.com/index.php?query=%2816*25%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	A{3}	(81×25ⁿ−1)/8 (n ≥ 1)	difference-of-two-squares factorization (81×25ⁿ−1)/8 = (9×5ⁿ−1) × (9×5ⁿ+1) / 8	http://factordb.com/index.php?query=%2881*25%5En-1%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	L{8}	(64×25ⁿ−1)/3 (n ≥ 1)	difference-of-two-squares factorization (64×25ⁿ−1)/3 = (8×5ⁿ−1) × (8×5ⁿ+1) / 3	http://factordb.com/index.php?query=%2864*25%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{3}2	(25ⁿ⁺¹−9)/8 (n ≥ 1)	difference-of-two-squares factorization (25ⁿ⁺¹−9)/8 = (5ⁿ⁺¹−3) × (5ⁿ⁺¹+3) / 8	http://factordb.com/index.php?query=%2825%5E%28n%2B1%29-9%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{8}3	(25ⁿ⁺¹−16)/3 (n ≥ 1)	difference-of-two-squares factorization (25ⁿ⁺¹−16)/3 = (5ⁿ⁺¹−4) × (5ⁿ⁺¹+4) / 3	http://factordb.com/index.php?query=%2825%5E%28n%2B1%29-16%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{8}7	(25ⁿ⁺¹−4)/3 (n ≥ 1)	difference-of-two-squares factorization (25ⁿ⁺¹−4)/3 = (5ⁿ⁺¹−2) × (5ⁿ⁺¹+2) / 3	http://factordb.com/index.php?query=%2825%5E%28n%2B1%29-4%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{1}0E	(25ⁿ⁺²−289)/24 (n ≥ 1)	difference-of-two-squares factorization (25ⁿ⁺²−289)/24 = (5ⁿ⁺²−17) × (5ⁿ⁺²+17) / 24	http://factordb.com/index.php?query=%2825%5E%28n%2B2%29-289%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{1}0J	(25ⁿ⁺²−169)/24 (n ≥ 1)	difference-of-two-squares factorization (25ⁿ⁺²−169)/24 = (5ⁿ⁺²−13) × (5ⁿ⁺²+13) / 24 (special example, as the numbers with length ≥ 8690 in this family contain "prime > b" subsequence, this prime is 1₈₆₈₈J)	http://factordb.com/index.php?query=%2825%5E%28n%2B2%29-169%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{1}0L	(25ⁿ⁺²−121)/24 (n ≥ 1)	difference-of-two-squares factorization (25ⁿ⁺²−121)/24 = (5ⁿ⁺²−11) × (5ⁿ⁺²+11) / 24 (special example, as the numbers with length ≥ 88 in this family contain "prime > b" subsequence, this prime is 1₈₆L)	http://factordb.com/index.php?query=%2825%5E%28n%2B2%29-121%29%2F24&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{3}2I	(25ⁿ⁺²−81)/8 (n ≥ 0)	difference-of-two-squares factorization (25ⁿ⁺²−81)/8 = (5ⁿ⁺²−9) × (5ⁿ⁺²+9) / 8	http://factordb.com/index.php?query=%2825%5E%28n%2B2%29-81%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{8}5I	(25ⁿ⁺²−196)/3 (n ≥ 0)	difference-of-two-squares factorization (25ⁿ⁺²−196)/3 = (5ⁿ⁺²−14) × (5ⁿ⁺²+14) / 3	http://factordb.com/index.php?query=%2825%5E%28n%2B2%29-196%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{8}7C	(25ⁿ⁺²−64)/3 (n ≥ 0)	difference-of-two-squares factorization (25ⁿ⁺²−64)/3 = (5ⁿ⁺²−8) × (5ⁿ⁺²+8) / 3	http://factordb.com/index.php?query=%2825%5E%28n%2B2%29-64%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	3{O}G	4×25ⁿ⁺¹−9 (n ≥ 0)	difference-of-two-squares factorization 4×25ⁿ⁺¹−9 = (2×5ⁿ⁺¹−3) × (2×5ⁿ⁺¹+3)	http://factordb.com/index.php?query=4*25%5E%28n%2B1%29-9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	8{O}L	9×25ⁿ⁺¹−4 (n ≥ 0)	difference-of-two-squares factorization 9×25ⁿ⁺¹−4 = (3×5ⁿ⁺¹−2) × (3×5ⁿ⁺¹+2)	http://factordb.com/index.php?query=9*25%5E%28n%2B1%29-4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	F{O}G	16×25ⁿ⁺¹−9 (n ≥ 0)	difference-of-two-squares factorization 16×25ⁿ⁺¹−9 = (4×5ⁿ⁺¹−3) × (4×5ⁿ⁺¹+3)	http://factordb.com/index.php?query=16*25%5E%28n%2B1%29-9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	8{O}9	9×25ⁿ⁺¹−16 (n ≥ 0)	difference-of-two-squares factorization 9×25ⁿ⁺¹−16 = (3×5ⁿ⁺¹−4) × (3×5ⁿ⁺¹+4)	http://factordb.com/index.php?query=9*25%5E%28n%2B1%29-16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	G{8}7	(49×25ⁿ⁺¹−4)/3 (n ≥ 0)	difference-of-two-squares factorization (49×25ⁿ⁺¹−4)/3 = (7×5ⁿ⁺¹−2) × (7×5ⁿ⁺¹+2) / 3	http://factordb.com/index.php?query=%2849*25%5E%28n%2B1%29-4%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	6{3}2	(49×25ⁿ⁺¹−9)/8 (n ≥ 0)	difference-of-two-squares factorization (49×25ⁿ⁺¹−9)/8 = (7×5ⁿ⁺¹−3) × (7×5ⁿ⁺¹+3) / 8	http://factordb.com/index.php?query=%2849*25%5E%28n%2B1%29-9%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	G{8}3	(49×25ⁿ⁺¹−16)/3 (n ≥ 0)	difference-of-two-squares factorization (49×25ⁿ⁺¹−16)/3 = (7×5ⁿ⁺¹−4) × (7×5ⁿ⁺¹+4) / 3	http://factordb.com/index.php?query=%2849*25%5E%28n%2B1%29-16%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	1{8}7H	(4×25ⁿ⁺²−49)/3 (n ≥ 0)	difference-of-two-squares factorization (4×25ⁿ⁺²−49)/3 = (2×5ⁿ⁺²−7) × (2×5ⁿ⁺²+7) / 3 (special example, as the numbers with length ≥ 78 in this family contain "prime > b" subsequence, this prime is 8₇₅H)	http://factordb.com/index.php?query=%284*25%5E%28n%2B2%29-49%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	5{8}7H	(16×25ⁿ⁺²−49)/3 (n ≥ 0)	difference-of-two-squares factorization (16×25ⁿ⁺²−49)/3 = (4×5ⁿ⁺²−7) × (4×5ⁿ⁺²+7) / 3 (special example, as the numbers with length ≥ 78 in this family contain "prime > b" subsequence, this prime is 8₇₅H)	http://factordb.com/index.php?query=%2816*25%5E%28n%2B2%29-49%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	8{0}1	8×27ⁿ⁺¹+1 (n ≥ 0)	sum-of-two-cubes factorization 8×27ⁿ⁺¹+1 = (2×3ⁿ⁺¹+1) × (4×9ⁿ⁺¹−2×3ⁿ⁺¹+1)	http://factordb.com/index.php?query=8*27%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	1{0}8	27ⁿ⁺¹+8 (n ≥ 0)	sum-of-two-cubes factorization 27ⁿ⁺¹+8 = (3ⁿ⁺¹+2) × (9ⁿ⁺¹−2×3ⁿ⁺¹+4)	http://factordb.com/index.php?query=27%5E%28n%2B1%29%2B8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	{D}E	(27ⁿ⁺¹+1)/2 (n ≥ 1)	sum-of-two-cubes factorization (27ⁿ⁺¹+1)/2 = (3ⁿ⁺¹+1) × (9ⁿ⁺¹−3ⁿ⁺¹+1) / 2	http://factordb.com/index.php?query=%2827%5E%28n%2B1%29%2B1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	7{Q}	8×27ⁿ−1 (n ≥ 1)	difference-of-two-cubes factorization 8×27ⁿ−1 = (2×3ⁿ−1) × (4×9ⁿ+2×3ⁿ+1)	http://factordb.com/index.php?query=8*27%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	{Q}J	27ⁿ⁺¹−8 (n ≥ 1)	difference-of-two-cubes factorization 27ⁿ⁺¹−8 = (3ⁿ⁺¹−2) × (9ⁿ⁺¹+2×3ⁿ⁺¹+4)	http://factordb.com/index.php?query=27%5E%28n%2B1%29-8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	9{G}	(125×27ⁿ−8)/13 (n ≥ 1)	difference-of-two-cubes factorization (125×27ⁿ−8)/13 = (5×3ⁿ−2) × (25×9ⁿ+10×3ⁿ+4) / 13	http://factordb.com/index.php?query=%28125*27%5En-8%29%2F13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	1{0}1	32ⁿ⁺¹+1 (n ≥ 0)	sum-of-two-5th-powers factorization 32ⁿ⁺¹+1 = (2ⁿ⁺¹+1) × (16ⁿ⁺¹−8ⁿ⁺¹+4ⁿ⁺¹−2ⁿ⁺¹+1)	http://factordb.com/index.php?query=32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	{1}	(32ⁿ−1)/31 (n ≥ 2)	difference-of-two-5th-powers factorization (32ⁿ−1)/31 = (2ⁿ−1) × (16ⁿ+8ⁿ+4ⁿ+2ⁿ+1) / 31	http://factordb.com/index.php?query=%2832%5En-1%29%2F31&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	3{7}	(16×36ⁿ−1)/5 (n ≥ 1)	difference-of-two-squares factorization (16×36ⁿ−1)/5 = (4×6ⁿ−1) × (4×6ⁿ+1) / 5	http://factordb.com/index.php?query=%2816*36%5En-1%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	3{Z}	4×36ⁿ−1 (n ≥ 1)	difference-of-two-squares factorization 4×36ⁿ−1 = (2×6ⁿ−1) × (2×6ⁿ+1)	http://factordb.com/index.php?query=4*36%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	8{Z}	9×36ⁿ−1 (n ≥ 1)	difference-of-two-squares factorization 9×36ⁿ−1 = (3×6ⁿ−1) × (3×6ⁿ+1)	http://factordb.com/index.php?query=9*36%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	O{Z}	25×36ⁿ−1 (n ≥ 1)	difference-of-two-squares factorization 25×36ⁿ−1 = (5×6ⁿ−1) × (5×6ⁿ+1)	http://factordb.com/index.php?query=25*36%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{Z}B	36ⁿ⁺¹−25 (n ≥ 1)	difference-of-two-squares factorization 36ⁿ⁺¹−25 = (6ⁿ⁺¹−5) × (6ⁿ⁺¹+5)	http://factordb.com/index.php?query=36%5E%28n%2B1%29-25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	8{Z}B	9×36ⁿ⁺¹−25 (n ≥ 0)	difference-of-two-squares factorization 9×36ⁿ⁺¹−25 = (3×6ⁿ⁺¹−5) × (3×6ⁿ⁺¹+5)	http://factordb.com/index.php?query=9*36%5E%28n%2B1%29-25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	F{Z}B	16×36ⁿ⁺¹−25 (n ≥ 0)	difference-of-two-squares factorization 16×36ⁿ⁺¹−25 = (4×6ⁿ⁺¹−5) × (4×6ⁿ⁺¹+5)	http://factordb.com/index.php?query=16*36%5E%28n%2B1%29-25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{Z}RZ	36ⁿ⁺²−289 (n ≥ 0)	difference-of-two-squares factorization 36ⁿ⁺²−289 = (6ⁿ⁺²−17) × (6ⁿ⁺²+17)	http://factordb.com/index.php?query=36%5E%28n%2B2%29-289&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	O{Z}RZ	25×36ⁿ⁺²−289 (n ≥ 0)	difference-of-two-squares factorization 25×36ⁿ⁺²−289 = (5×6ⁿ⁺²−17) × (5×6ⁿ⁺²+17)	http://factordb.com/index.php?query=25*36%5E%28n%2B2%29-289&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	O{5}	(169×36ⁿ−1)/7 (n ≥ 1)	difference-of-two-squares factorization (169×36ⁿ−1)/7 = (13×6ⁿ−1) × (13×6ⁿ+1) / 7	http://factordb.com/index.php?query=%28169*36%5En-1%29%2F7&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	O{7}	(121×36ⁿ−1)/5 (n ≥ 1)	difference-of-two-squares factorization (121×36ⁿ−1)/5 = (11×6ⁿ−1) × (11×6ⁿ+1) / 5	http://factordb.com/index.php?query=%28121*36%5En-1%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{9}1	(9×36ⁿ⁺¹−289)/35 (n ≥ 1)	difference-of-two-squares factorization (9×36ⁿ⁺¹−289)/35 = (3×6ⁿ⁺¹−17) × (3×6ⁿ⁺¹+17) / 35	http://factordb.com/index.php?query=%289*36%5E%28n%2B1%29-289%29%2F35&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	T{9}1	(1024×36ⁿ⁺¹−289)/35 (n ≥ 0)	difference-of-two-squares factorization (1024×36ⁿ⁺¹−289)/35 = (32×6ⁿ⁺¹−17) × (32×6ⁿ⁺¹+17) / 35	http://factordb.com/index.php?query=%281024*36%5E%28n%2B1%29-289%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{G}D	(16×36ⁿ⁺¹−121)/35 (n ≥ 1)	difference-of-two-squares factorization (16×36ⁿ⁺¹−121)/35 = (4×6ⁿ⁺¹−11) × (4×6ⁿ⁺¹+11) / 35	http://factordb.com/index.php?query=%2816*36%5E%28n%2B1%29-121%29%2F35&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{G}8D	(16×36ⁿ⁺²−10201)/35 (n ≥ 0)	difference-of-two-squares factorization (16×36ⁿ⁺²−10201)/35 = (4×6ⁿ⁺²−101) × (4×6ⁿ⁺²+101) / 35	http://factordb.com/index.php?query=%2816*36%5E%28n%2B2%29-10201%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	R{G}D	(961×36ⁿ⁺¹−121)/35 (n ≥ 0)	difference-of-two-squares factorization (961×36ⁿ⁺¹−121)/35 = (31×6ⁿ⁺¹−11) × (31×6ⁿ⁺¹+11) / 35	http://factordb.com/index.php?query=%28961*36%5E%28n%2B2%29-121%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	3{G}8D	(121×36ⁿ⁺²−10201)/35 (n ≥ 0)	difference-of-two-squares factorization (121×36ⁿ⁺²−10201)/35 = (11×6ⁿ⁺²−101) × (11×6ⁿ⁺²+101) / 35	http://factordb.com/index.php?query=%28121*36%5E%28n%2B2%29-10201%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	R{G}8D	(961×36ⁿ⁺²−10201)/35 (n ≥ 0)	difference-of-two-squares factorization (961×36ⁿ⁺²−10201)/35 = (31×6ⁿ⁺²−101) × (31×6ⁿ⁺²+101) / 35	http://factordb.com/index.php?query=%28961*36%5E%28n%2B2%29-10201%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{K}H	(4×36ⁿ⁺¹−25)/7 (n ≥ 1)	difference-of-two-squares factorization (4×36ⁿ⁺¹−25)/7 = (2×6ⁿ⁺¹−5) × (2×6ⁿ⁺¹+5) / 7	http://factordb.com/index.php?query=%284*36%5E%28n%2B1%29-25%29%2F7&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	B{K}H	(81×36ⁿ⁺¹−25)/7 (n ≥ 0)	difference-of-two-squares factorization (81×36ⁿ⁺¹−25)/7 = (9×6ⁿ⁺¹−5) × (9×6ⁿ⁺¹+5) / 7	http://factordb.com/index.php?query=%2881*36%5E%28n%2B1%29-25%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	3{K}IH	(25×36ⁿ⁺²−529)/7 (n ≥ 0)	difference-of-two-squares factorization (25×36ⁿ⁺²−529)/7 = (5×6ⁿ⁺²−23) × (5×6ⁿ⁺²+23) / 7	http://factordb.com/index.php?query=%2825*36%5E%28n%2B2%29-529%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	B{K}IH	(81×36ⁿ⁺²−529)/7 (n ≥ 0)	difference-of-two-squares factorization (81×36ⁿ⁺²−529)/7 = (9×6ⁿ⁺²−23) × (9×6ⁿ⁺²+23) / 7	http://factordb.com/index.php?query=%2881*36%5E%28n%2B2%29-529%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{S}J	(4×36ⁿ⁺¹−49)/5 (n ≥ 1)	difference-of-two-squares factorization (4×36ⁿ⁺¹−49)/5 = (2×6ⁿ⁺¹−7) × (2×6ⁿ⁺¹+7) / 5	http://factordb.com/index.php?query=%284*36%5E%28n%2B1%29-49%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{S}IJ	(4×36ⁿ⁺²−1849)/5 (n ≥ 0)	difference-of-two-squares factorization (4×36ⁿ⁺²−1849)/5 = (2×6ⁿ⁺²−43) × (2×6ⁿ⁺²+43) / 5	http://factordb.com/index.php?query=%284*36%5E%28n%2B2%29-1849%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	1{S}J	(9×36ⁿ⁺¹−49)/5 (n ≥ 0)	difference-of-two-squares factorization (9×36ⁿ⁺¹−49)/5 = (3×6ⁿ⁺¹−7) × (3×6ⁿ⁺¹+7) / 5	http://factordb.com/index.php?query=%289*36%5E%28n%2B1%29-49%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	C{S}J	(64×36ⁿ⁺¹−49)/5 (n ≥ 0)	difference-of-two-squares factorization (64×36ⁿ⁺¹−49)/5 = (8×6ⁿ⁺¹−7) × (8×6ⁿ⁺¹+7) / 5	http://factordb.com/index.php?query=%2864*36%5E%28n%2B1%29-49%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	X{S}J	(169×36ⁿ⁺¹−49)/5 (n ≥ 0)	difference-of-two-squares factorization (169×36ⁿ⁺¹−49)/5 = (13×6ⁿ⁺¹−7) × (13×6ⁿ⁺¹+7) / 5	http://factordb.com/index.php?query=%28169*36%5E%28n%2B1%29-49%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	1{S}GJ	(9×36ⁿ⁺²−2209)/5 (n ≥ 0)	difference-of-two-squares factorization (9×36ⁿ⁺²−2209)/5 = (3×6ⁿ⁺²−47) × (3×6ⁿ⁺²+47) / 5	http://factordb.com/index.php?query=%289*36%5E%28n%2B2%29-2209%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	9{S}GJ	(49×36ⁿ⁺²−2209)/5 (n ≥ 0)	difference-of-two-squares factorization (49×36ⁿ⁺²−2209)/5 = (7×6ⁿ⁺²−47) × (7×6ⁿ⁺²+47) / 5	http://factordb.com/index.php?query=%2849*36%5E%28n%2B2%29-2209%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	C{S}GJ	(64×36ⁿ⁺²−2209)/5 (n ≥ 0)	difference-of-two-squares factorization (64×36ⁿ⁺²−2209)/5 = (8×6ⁿ⁺²−47) × (8×6ⁿ⁺²+47) / 5	http://factordb.com/index.php?query=%2864*36%5E%28n%2B2%29-2209%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	X{S}GJ	(169×36ⁿ⁺²−2209)/5 (n ≥ 0)	difference-of-two-squares factorization (169×36ⁿ⁺²−2209)/5 = (13×6ⁿ⁺²−47) × (13×6ⁿ⁺²+47) / 5	http://factordb.com/index.php?query=%28169*36%5E%28n%2B2%29-2209%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	1{S}IJ	(9×36ⁿ⁺²−1849)/5 (n ≥ 0)	difference-of-two-squares factorization (9×36ⁿ⁺²−1849)/5 = (3×6ⁿ⁺²−43) × (3×6ⁿ⁺²+43) / 5	http://factordb.com/index.php?query=%289*36%5E%28n%2B2%29-1849%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	9{S}IJ	(49×36ⁿ⁺²−1849)/5 (n ≥ 0)	difference-of-two-squares factorization (49×36ⁿ⁺²−1849)/5 = (7×6ⁿ⁺²−43) × (7×6ⁿ⁺²+43) / 5	http://factordb.com/index.php?query=%2849*36%5E%28n%2B2%29-1849%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	8{D}	9×14ⁿ−1 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, 9×14ⁿ−1 = (3×14^n/2−1) × (3×14^n/2+1) if n is even	http://factordb.com/index.php?query=9*14%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
12	{B}9B	12ⁿ⁺²−25 (n ≥ 0)	combine of factor 13 and difference-of-two-squares factorization divisible by 13 if n is odd, 12ⁿ⁺²−25 = (12^(n+2)/2−5) × (12^(n+2)/2+5) if n is even	http://factordb.com/index.php?query=12%5E%28n%2B2%29-25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	{D}5	14ⁿ⁺¹−9 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is even, 14ⁿ⁺¹−9 = (14^(n+1)/2−3) × (14^(n+1)/2+3) if n is odd	http://factordb.com/index.php?query=14%5E%28n%2B1%29-9&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	1{9}	(25×17ⁿ−9)/16 (n ≥ 1)	combine of factor 2 and difference-of-two-squares factorization divisible by 2 if n is odd, (25×17ⁿ−9)/16 = (5×17^n/2−3) × (5×17^n/2+3) / 16 if n is even	http://factordb.com/index.php?query=%2825*17%5En-9%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	7{9}	(121×17ⁿ−9)/16 (n ≥ 1)	combine of factor 2 and difference-of-two-squares factorization divisible by 2 if n is odd, (121×17ⁿ−9)/16 = (11×17^n/2−3) × (11×17^n/2+3) / 16 if n is even	http://factordb.com/index.php?query=%28121*17%5En-9%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	{9}2	(9×17ⁿ⁺¹−121)/16 (n ≥ 1)	combine of factor 2 and difference-of-two-squares factorization divisible by 2 if n is even, (9×17ⁿ⁺¹−121)/16 = (3×17^(n+1)/2−11) × (3×17^(n+1)/2+11) / 16 if n is odd	http://factordb.com/index.php?query=%289*17%5E%28n%2B1%29-121%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	{9}8	(9×17ⁿ⁺¹−25)/16 (n ≥ 1)	combine of factor 2 and difference-of-two-squares factorization divisible by 2 if n is even, (9×17ⁿ⁺¹−25)/16 = (3×17^(n+1)/2−5) × (3×17^(n+1)/2+5) / 16 if n is odd	http://factordb.com/index.php?query=%289*17%5E%28n%2B1%29-25%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
19	1{6}	(4×19ⁿ−1)/3 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, (4×19ⁿ−1)/3 = (2×19^n/2−1) × (2×19^n/2+1) / 3 if n is even	http://factordb.com/index.php?query=%284*19%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
19	{6}5	(19ⁿ⁺¹−4)/3 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is even, (19ⁿ⁺¹−4)/3 = (19^(n+1)/2−2) × (19^(n+1)/2+2) / 3 if n is odd	http://factordb.com/index.php?query=%2819%5E%28n%2B1%29-4%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
19	7{2}	(64×19ⁿ−1)/9 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, (64×19ⁿ−1)/9 = (8×19^n/2−1) × (8×19^n/2+1) / 9 if n is even	http://factordb.com/index.php?query=%2864*19%5En-1%29%2F9&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
19	89{6}	(484×19ⁿ−1)/3 (n ≥ 0)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, (484×19ⁿ−1)/3 = (22×19^n/2−1) × (22×19^n/2+1) / 3 if n is even	http://factordb.com/index.php?query=%28484*19%5En-1%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3{N}	4×24ⁿ−1 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, 4×24ⁿ−1 = (2×24^n/2−1) × (2×24^n/2+1) if n is even	http://factordb.com/index.php?query=4*24%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	5{N}	6×24ⁿ−1 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is even, 6×24ⁿ−1 = (12×24^(n−1)/2−1) × (12×24^(n−1)/2+1) if n is odd	http://factordb.com/index.php?query=6*24%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	8{N}	9×24ⁿ−1 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, 9×24ⁿ−1 = (3×24^n/2−1) × (3×24^n/2+1) if n is even	http://factordb.com/index.php?query=9*24%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	{6}1	(6×24ⁿ⁺¹−121)/23 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, (6×24ⁿ⁺¹−121)/23 = (12×24^n/2−11) × (12×24^n/2+11) / 23 if n is even	http://factordb.com/index.php?query=%286*24%5E%28n%2B1%29-121%29%2F23&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	{N}LN	24ⁿ⁺²−49 (n ≥ 0)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, 24ⁿ⁺²−49 = (24^(n+2)/2−7) × (24^(n+2)/2+7) if n is even	http://factordb.com/index.php?query=24%5E%28n%2B2%29-49&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
33	F{W}	16×33ⁿ−1 (n ≥ 1)	combine of factor 17 and difference-of-two-squares factorization divisible by 17 if n is odd, 16×33ⁿ−1 = (4×33^n/2−1) × (4×33^n/2+1) if n is even	http://factordb.com/index.php?query=16*33%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
33	{W}H	33ⁿ⁺¹−16 (n ≥ 1)	combine of factor 17 and difference-of-two-squares factorization divisible by 17 if n is even, 33ⁿ⁺¹−16 = (33^(n+1)/2−4) × (33^(n+1)/2+4) if n is odd	http://factordb.com/index.php?query=33%5E%28n%2B1%29-16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
33	L{4}	(169×33ⁿ−1)/8 (n ≥ 1)	combine of factor 17 and difference-of-two-squares factorization divisible by 17 if n is odd, (169×33ⁿ−1)/8 = (13×33^n/2−1) × (13×33^n/2+1) / 8 if n is even	http://factordb.com/index.php?query=%28169*33%5En-1%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
33	3{P}	(121×33ⁿ−25)/32 (n ≥ 1)	combine of factor 2 and difference-of-two-squares factorization divisible by 2 if n is odd, (121×33ⁿ−25)/32 = (11×33^n/2−5) × (11×33^n/2+5) / 32 if n is even	http://factordb.com/index.php?query=%28121*33%5En-25%29%2F32&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
33	D{P}	(441×33ⁿ−25)/32 (n ≥ 1)	combine of factor 2 and difference-of-two-squares factorization divisible by 2 if n is odd, (441×33ⁿ−25)/32 = (21×33^n/2−5) × (21×33^n/2+5) / 32 if n is even	http://factordb.com/index.php?query=%28441*33%5En-25%29%2F32&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
33	{9}4	(9×33ⁿ⁺¹−169)/32 (n ≥ 1)	combine of factor 2 and difference-of-two-squares factorization divisible by 2 if n is even, (9×33ⁿ⁺¹−169)/32 = (3×33^(n+1)/2−13) × (3×33^(n+1)/2+13) / 32 if n is odd	http://factordb.com/index.php?query=%289*33%5E%28n%2B1%29-169%29%2F32&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
33	{I}H	(9×33ⁿ⁺¹−25)/16 (n ≥ 1)	combine of factor 17 and difference-of-two-squares factorization divisible by 17 if n is even, (9×33ⁿ⁺¹−25)/16 = (3×33^(n+1)/2−5) × (3×33^(n+1)/2+5) / 16 if n is odd	http://factordb.com/index.php?query=%289*33%5E%28n%2B1%29-25%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	1{B}	(4×34ⁿ−1)/3 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, (4×34ⁿ−1)/3 = (2×34^n/2−1) × (2×34^n/2+1) / 3 if n is even	http://factordb.com/index.php?query=%284*34%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	G{B}	(49×34ⁿ−1)/3 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, (49×34ⁿ−1)/3 = (7×34^n/2−1) × (7×34^n/2+1) / 3 if n is even	http://factordb.com/index.php?query=%2849*34%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	G{1}	(529×34ⁿ−1)/33 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, (529×34ⁿ−1)/33 = (23×34^n/2−1) × (23×34^n/2+1) / 33 if n is even (special example, as the numbers with length ≥ 14 in this family contain "prime > b" subsequence, this prime is 1₁₃)	http://factordb.com/index.php?query=%28529*34%5En-1%29%2F33&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	V{1}	(1024×34ⁿ−1)/33 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, (1024×34ⁿ−1)/33 = (32×34^n/2−1) × (32×34^n/2+1) / 33 if n is even (special example, as the numbers with length ≥ 14 in this family contain "prime > b" subsequence, this prime is 1₁₃)	http://factordb.com/index.php?query=%281024*34%5En-1%29%2F33&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	D{3}	(144×34ⁿ−1)/11 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, (144×34ⁿ−1)/11 = (12×34^n/2−1) × (12×34^n/2+1) / 11 if n is even	http://factordb.com/index.php?query=%28144*34%5En-1%29%2F11&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	8{X}	9×34ⁿ−1 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, 9×34ⁿ−1 = (3×34^n/2−1) × (3×34^n/2+1) if n is even	http://factordb.com/index.php?query=9*34%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
34	{X}P	34ⁿ⁺¹−9 (n ≥ 1)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is even, 34ⁿ⁺¹−9 = (34^(n+1)/2−3) × (34^(n+1)/2+3) if n is odd	http://factordb.com/index.php?query=34%5E%28n%2B1%29-9&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show

Also families which contain only one very small prime > b: (this is because: for the case of covering congruence, an element in S is indeed in the family and > b, to make the factorizations be trivial; for the case of algebraic factorization (if the numbers are factored as F × G / d), F (or G) is equal to d and G (or F) is a prime > b, to make the factorizations be trivial; for the case of combine of covering congruence and algebraic factorization (if the numbers are factored as F × G / d), an element in S is indeed in the family and > b or/and F (or G) is equal to d and G (or F) is prime > b, to make the factorizations be trivial)

b (2 ≤ b ≤ 36)	family	algebraic ((a×bⁿ+c)/d) form of this family (n is the number of digits in the "{}", also the lower bound of n to make the numbers > b) (note: d divides gcd(a+c,b−1), but d need not be gcd(a+c,b−1), d = gcd(a+c,b−1) if and only if the numbers in the family are not divisible by some prime factor of b−1, i.e. the numbers in the family are coprime to b−1, in fact, d = gcd(a+c,b−1)/gcd(a+c,b−1,(largest trivial factor of the family)))	the only prime > b in this family	this prime > b written in decimal	why this family contains only this prime > b	factorization of the first 200 numbers in this family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0))
9	2{7}5	(23×9ⁿ⁺¹−23)/8 (n ≥ 0)	25	23	always divisible by 23 (in fact, also difference-of-two-squares factorization) (23×9ⁿ⁺¹−23)/8 = 23 × (3ⁿ⁺¹−1) × (3ⁿ⁺¹+1) / 8	http://factordb.com/index.php?query=%2823*9%5E%28n%2B1%29-23%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	5{7}2	(47×9ⁿ⁺¹−47)/8 (n ≥ 0)	52	47	always divisible by 47 (in fact, also difference-of-two-squares factorization) (47×9ⁿ⁺¹−47)/8 = 47 × (3ⁿ⁺¹−1) × (3ⁿ⁺¹+1) / 8	http://factordb.com/index.php?query=%2847*9%5E%28n%2B1%29-47%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	3{7}4	(37×11ⁿ⁺¹−37)/10 (n ≥ 0)	34	37	always divisible by 37	http://factordb.com/index.php?query=%2837*11%5E%28n%2B1%29-37%29%2F10&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	4{7}3	(47×11ⁿ⁺¹−47)/10 (n ≥ 0)	43	47	always divisible by 47	http://factordb.com/index.php?query=%2847*11%5E%28n%2B1%29-47%29%2F10&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	2{0}J	2×27ⁿ⁺¹+19 (n ≥ 0)	2J	73	always divisible by some element of {5,7,73} divisible by 7 if n is odd, divisible by 5 if n == 2 mod 4, divisible by 73 if n == 0 mod 4	http://factordb.com/index.php?query=2*27%5E%28n%2B1%29%2B19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
4	{1}	(4ⁿ−1)/3 (n ≥ 2)	11	5	difference-of-two-squares factorization but 11 is prime, and 11 is the only prime > b in this family (4ⁿ−1)/3 = (2ⁿ−1) × (2ⁿ+1) / 3	http://factordb.com/index.php?query=%284%5En-1%29%2F3&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
8	{1}	(8ⁿ−1)/7 (n ≥ 2)	111	73	difference-of-two-cubes factorization but 111 is prime, and 111 is the only prime > b in this family (8ⁿ−1)/7 = (2ⁿ−1) × (4ⁿ+2ⁿ+1) / 7	http://factordb.com/index.php?query=%288%5En-1%29%2F7&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{1}	(16ⁿ−1)/15 (n ≥ 2)	11	17	difference-of-two-squares factorization but 11 is prime, and 11 is the only prime > b in this family (16ⁿ−1)/15 = (4ⁿ−1) × (4ⁿ+1) / 15 (in fact, difference-of-4th-powers factorization) (16ⁿ−1)/15 = (2ⁿ−1) × (2ⁿ+1) × (4ⁿ+1) / 15	http://factordb.com/index.php?query=%2816%5En-1%29%2F15&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	{1}	(27ⁿ−1)/26 (n ≥ 2)	111	757	difference-of-two-cubes factorization but 111 is prime, and 111 is the only prime > b in this family (27ⁿ−1)/26 = (3ⁿ−1) × (9ⁿ+3ⁿ+1) / 26	http://factordb.com/index.php?query=%2827%5En-1%29%2F26&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	{2}7	(27ⁿ⁺¹+64)/13 (n ≥ 1)	27	61	sum-of-two-cubes factorization but 27 is prime, and 27 is the only prime > b in this family (27ⁿ⁺¹+64)/13 = (3ⁿ⁺¹+4) × (9ⁿ⁺¹−4×3ⁿ⁺¹+16) / 13 (in fact, also combine of Aurifeuillean factorization of x⁴+4×y⁴ and Aurifeuillean factorization of x⁶+27×y⁶ and Aurifeuillean factorization of x¹²+46656×y¹²) (27ⁿ⁺¹+64)/13 = (3ⁿ⁺¹+4) × (3ⁿ⁺¹−2×3^(n+2)/2+4) × (3ⁿ⁺¹+2×3^(n+2)/2+4) if n is even, (27ⁿ⁺¹+64)/13 = (3^(n+1)/2−2×3^(n+1)/4+2) × (3^(n+1)/2+2×3^(n+1)/4+2) × (3ⁿ⁺¹−2×3^(3×n+3)/4+2×3^(n+1)/2−4×3^(n+1)/4+4) × (3ⁿ⁺¹+2×3^3×(n+1)/4+2×3^(n+1)/2+4×3^(n+1)/4+4) / 13 if n == 3 mod 4, (27ⁿ⁺¹+64)/13 = (3ⁿ⁺¹+4) × (3ⁿ⁺¹−2×3^(3×n+5)/4+2×3^(n+3)/2−4×3^(n+3)/4+4) × (3ⁿ⁺¹+2×3^(3×n+5)/4+2×3^(n+3)/2+4×3^(n+3)/4+4) if n == 1 mod 4	http://factordb.com/index.php?query=%2827%5E%28n%2B1%29%2B64%29%2F13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	{G}7	(8×27ⁿ⁺¹−125)/13 (n ≥ 1)	G7	439	difference-of-two-cubes factorization but G7 is prime, and G7 is the only prime > b in this family (8×27ⁿ⁺¹−125)/13 = (2×3ⁿ⁺¹−5) × (4×9ⁿ⁺¹+10×3ⁿ⁺¹+25) / 13	http://factordb.com/index.php?query=%288*27%5E%28n%2B1%29-125%29%2F13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{1}	(36ⁿ−1)/35 (n ≥ 2)	11	37	difference-of-two-squares factorization but 11 is prime, and 11 is the only prime > b in this family (36ⁿ−1)/35 = (6ⁿ−1) × (6ⁿ+1) / 35	http://factordb.com/index.php?query=%2836%5En-1%29%2F35&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show

It is interesting to note that all numbers in families {1}, 2{1}, 5{1}, 7{1}, C{1}, F{1}, M{1}, 1F{1}, 27{1}, 7C{1}, D5{1} in base b = 25 are generalized pentagonal numbers (https://en.wikipedia.org/wiki/Pentagonal_number, https://mathworld.wolfram.com/PentagonalNumber.html, https://www.numbersaplenty.com/set/pentagonal_number/, https://oeis.org/A001318), and all numbers in families {1}, 3{1}, 6{1}, 16{1} in base b = 9 and families 1{3}, A{3} in base b = 25 are triangular numbers (https://en.wikipedia.org/wiki/Triangular_number, https://mathworld.wolfram.com/TriangularNumber.html, https://www.numbersaplenty.com/set/triangular_number/, https://oeis.org/A000217), and all numbers in family {1} in base b = 4 and families 1{5}, 8{5}, 10{5}, A1{5} in base b = 16 and families 1{8}, 5{8}, L{8} in base b = 25 are generalized octagonal numbers (https://en.wikipedia.org/wiki/Octagonal_number, https://mathworld.wolfram.com/OctagonalNumber.html, https://www.numbersaplenty.com/set/octagonal_number/, https://oeis.org/A001082), since all generalized pentagonal numbers × 25 + 1 are also generalized pentagonal numbers, all triangular numbers × 9 + 1 and all triangular numbers × 25 + 3 are also triangular numbers, all generalized octagonal numbers × 4 + 1 and all generalized octagonal numbers × 16 + 5 and all generalized octagonal numbers × 25 + 8 are also generalized octagonal numbers (thus: In base b = 4, all numbers of the form (generalized octagonal numbers){1} are also generalized octagonal numbers; in base b = 9, all numbers of the form (triangular numbers){1} are also triangular numbers; in base b = 16, all numbers of the form (generalized octagonal numbers){5} are also generalized octagonal numbers; in base b = 25, all numbers of the form (generalized pentagonal numbers){1} are also generalized pentagonal numbers, all numbers of the form (triangular numbers){3} are also triangular numbers, all numbers of the form (generalized octagonal numbers){8} are also generalized octagonal numbers), and all generalized pentagonal numbers (except 0, 1, 2, 5, 7) and all triangular numbers (except 0, 1, 3) and all generalized octagonal numbers (except 0, 1, 5) are composite (since all generalized polygonal numbers (https://en.wikipedia.org/wiki/Polygonal_number, https://mathworld.wolfram.com/PolygonalNumber.html, https://oeis.org/A195152, https://oeis.org/A194801, https://oeis.org/A303301) are composite, with only possible exception of indices 0, 1, −1, 2, −2), thus these families contain no primes > b (except the family {1} in base 4, which contains a prime 11 (5 in decimal) > b).

Generalized pentagonal numbers (https://en.wikipedia.org/wiki/Pentagonal_number, https://mathworld.wolfram.com/PentagonalNumber.html, https://www.numbersaplenty.com/set/pentagonal_number/, https://oeis.org/A001318) are very important in number theory, since they appear in the pentagonal number theorem (https://en.wikipedia.org/wiki/Pentagonal_number_theorem, https://mathworld.wolfram.com/PentagonalNumberTheorem.html, https://oeis.org/A010815, https://oeis.org/A195310, https://oeis.org/A175003, https://oeis.org/A238442, https://arxiv.org/pdf/math/0505373.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_172.pdf), https://arxiv.org/pdf/math/0411587.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_173.pdf), http://eulerarchive.maa.org//docs/originals/E542.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_174.pdf), https://arxiv.org/pdf/math/0510054.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_175.pdf)) for both the partition function (https://en.wikipedia.org/wiki/Partition_function_(number_theory), https://mathworld.wolfram.com/PartitionFunctionP.html, https://t5k.org/top20/page.php?id=54, https://t5k.org/primes/search.php?Comment=Partitions&OnList=all&Number=1000000&Style=HTML, https://www.numbersaplenty.com/set/partition_number/, http://www.numericana.com/answer/numbers.htm#partitions, http://www.numericana.com/data/partition.htm, http://www.numbertheory.org/php/partition.html, https://web.archive.org/web/20120719080234/http://www.btinternet.com/~se16/js/partitions.htm, https://oeis.org/A000041) and the sum-of-divisors function (https://en.wikipedia.org/wiki/Divisor_function, https://t5k.org/glossary/xpage/SigmaFunction.html, https://mathworld.wolfram.com/DivisorFunction.html, http://www.javascripter.net/math/calculators/divisorscalculator.htm, https://oeis.org/A000203).

Also, for bases 2 ≤ b ≤ 18, the reasons for families can be ruled out as only containing composites (only count the numbers > b) which are needed to use to prove the "minimal prime problem" in base b are: (only consider the numbers coprime to b, i.e. only consider the number string with the first digit not 0 and the last digit coprime to b) (only listed the bases 2 ≤ b ≤ 18, since for 19 ≤ b ≤ 36 there may be reasons which are still not found by me, e.g. the family {D}GA in base b = 23 (which has a covering set {2,5,7,37,79}, also a covering set {3,5,7,37,79}) and the family L{5}L in base b = 23 (which has a covering set {2,5,7,13,37}, also a covering set {3,5,7,13,37}) are very hard to found)

b	reasons for families can be ruled out as only containing composites (only count the numbers > b) which are needed to use to prove the "minimal prime problem" in base b
2	–
3	Divisible by 2
4	Divisible by 3
5	Divisible by 2 Divisible by 3
6	Divisible by 5
7	Divisible by 2 Divisible by 3 Divisible by 5
8	Divisible by 3 Divisible by 5 Divisible by 7 Sum-of-two-cubes factorization
9	Divisible by 2 Divisible by 5 Divisible by 7 Covering set {2,5} Difference-of-two-squares factorization
10	Divisible by 3 Divisible by 7
11	Divisible by 2 Divisible by 3 Divisible by 5 Divisible by 7 Covering set {2,3}
12	Divisible by 5 Divisible by 7 Divisible by 11 Combine of divisible by 13 and difference-of-two-squares factorization
13	Divisible by 2 Divisible by 3 Divisible by 5 Divisible by 7 Divisible by 11 Covering set {2,7} Covering set {2,5,17} Covering set {5,7,17}
14	Divisible by 3 Divisible by 5 Divisible by 11 Divisible by 13 Covering set {3,5} Combine of divisible by 5 and difference-of-two-squares factorization
15	Divisible by 2 Divisible by 7 Divisible by 11 Divisible by 13
16	Divisible by 3 Divisible by 5 Divisible by 7 Divisible by 11 Divisible by 13 Covering set {3,7,13} Difference-of-two-squares factorization Aurifeuillean factorization of x⁴+4×y⁴
17	Divisible by 2 Divisible by 3 Divisible by 5 Divisible by 7 Divisible by 11 Divisible by 13 Covering set {2,3} Covering set {2,5,29} Covering set {3,5,29} Combine of divisible by 2 and difference-of-two-squares factorization
18	Divisible by 5 Divisible by 7 Divisible by 11 Divisible by 13 Divisible by 17

Some x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b) families could not be proven to contain no primes > b (by covering congruence, algebraic factorization, or combine of them) but no primes > b could be found in the family, even after searching through numbers with over 100000 digits. In such a case, the only way to proceed is to test the primality of larger and larger numbers of such form and hope a prime is eventually discovered.

Many x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b) families contain no small primes > b even though they do contain very large primes. e.g.

b (2 ≤ b ≤ 36)	family	algebraic form	base-b form of the smallest (probable) prime in this family (write "d_n" if there are 5 or more (n) consecutive same digits d)	length of the smallest (probable) prime in this family	length of the smallest (probable) prime in this family in decimal	algebraic ((a×bⁿ+c)/gcd(a+c,b−1)) form of the smallest (probable) prime in this family	factordb entry of the smallest (probable) prime in this family	the smallest (probable) prime in this family written in base b (use lower case letters instead of upper case letters)	the smallest (probable) prime in this family written in decimal	factorization of the first 200 numbers in corresponding family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0))	definitely prime or probable prime?	the entry of the smallest (probable) prime in this family in the top definitely primes page or the top probable primes page
13	9{5}	(113×13ⁿ−5)/12	95₁₉₇₄₂₀	197421	219916	(113×13¹⁹⁷⁴²¹−5)/12	http://factordb.com/index.php?id=1100000003943359311&open=prime	http://factordb.com/index.php?showid=1100000003943359311&base=13	http://factordb.com/index.php?showid=1100000003943359311	http://factordb.com/index.php?query=%28113*13%5En-5%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	probable prime	http://www.primenumbers.net/prptop/searchform.php?form=%28113*13%5E197420-5%29%2F12&action=Search
16	{3}AF	(16ⁿ⁺²+619)/5	3₁₁₆₁₃₇AF	116139	139845	(16¹¹⁶¹³⁹+619)/5	http://factordb.com/index.php?id=1100000003851731988&open=prime	http://factordb.com/index.php?showid=1100000003851731988&base=16	http://factordb.com/index.php?showid=1100000003851731988	http://factordb.com/index.php?query=%2816%5E%28n%2B2%29%2B619%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	probable prime	http://www.primenumbers.net/prptop/searchform.php?form=%2816%5E116139%2B619%29%2F5&action=Search
23	9{E}	(106×23ⁿ−7)/11	9E₈₀₀₈₇₃	800874	1090573	(106×23⁸⁰⁰⁸⁷³−7)/11	http://factordb.com/index.php?id=1100000000782858648&open=prime	http://factordb.com/index.php?showid=1100000000782858648&base=23	http://factordb.com/index.php?showid=1100000000782858648	http://factordb.com/index.php?query=%28106*23%5En-7%29%2F11&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	probable prime	http://www.primenumbers.net/prptop/searchform.php?form=%28106*23%5E800873-7%29%2F11&action=Search
25	71JD{0}1	110488×25ⁿ⁺¹+1	71JD0₄₅₈₅₄₉1	458554	641031	110488×25⁴⁵⁸⁵⁵⁰+1	http://factordb.com/index.php?id=1100000002341496334&open=prime	http://factordb.com/index.php?showid=1100000002341496334&base=25	http://factordb.com/index.php?showid=1100000002341496334	http://factordb.com/index.php?query=110488*25%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	definitely prime, this number can be proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is trivially fully factored	https://t5k.org/primes/page.php?id=111834
32	NU{0}1	766×32ⁿ⁺¹+1	NU0₆₆₁₈₆₃1	661866	996208	766×32⁶⁶¹⁸⁶⁴+1	http://factordb.com/index.php?id=1100000003813355148&open=prime	http://factordb.com/index.php?showid=1100000003813355148&base=32	http://factordb.com/index.php?showid=1100000003813355148	http://factordb.com/index.php?query=766*32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	definitely prime, this number can be proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is trivially fully factored	https://t5k.org/primes/page.php?id=134216
36	{P}SZ	(5×36ⁿ⁺²+821)/7	P₈₁₉₉₃SZ	81995	127609	(5×36⁸¹⁹⁹⁵+821)/7	http://factordb.com/index.php?id=1100000002394962083&open=prime	http://factordb.com/index.php?showid=1100000002394962083&base=36	http://factordb.com/index.php?showid=1100000002394962083	http://factordb.com/index.php?query=%285*36%5E%28n%2B2%29%2B821%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	probable prime	http://www.primenumbers.net/prptop/searchform.php?form=%285*36%5E81995%2B821%29%2F7&action=Search

(Technically, probable (https://en.wikipedia.org/wiki/Probabilistic_algorithm) primality tests (https://t5k.org/prove/prove2.html) were used to show these for the numbers which cannot be proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1) or N+1 test (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2), i.e. for the ordinary primes (https://t5k.org/glossary/xpage/OrdinaryPrime.html) (which have a very small chance of making an error (https://t5k.org/notes/prp_prob.html, https://www.ams.org/journals/mcom/1989-53-188/S0025-5718-1989-0982368-4/S0025-5718-1989-0982368-4.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_22.pdf))) because all known primality tests (https://en.wikipedia.org/wiki/Primality_test, https://www.rieselprime.de/ziki/Primality_test, https://mathworld.wolfram.com/PrimalityTest.html, https://t5k.org/prove/prove3.html, https://t5k.org/prove/prove4.html) run far too slowly (the CPU time (https://en.wikipedia.org/wiki/CPU_time) is longer than the life expectancy of human (https://en.wikipedia.org/wiki/Life_expectancy) for numbers > 10¹⁰⁰⁰⁰⁰, and longer than the age of the universe (https://en.wikipedia.org/wiki/Age_of_the_universe) for numbers > 10⁵⁰⁰⁰⁰⁰, and longer than one quettasecond (https://en.wikipedia.org/wiki/Quetta-) for numbers > 10^3000000, even if we can do 10⁹ bitwise operations (https://en.wikipedia.org/wiki/Bitwise_operation) per second (https://en.wikipedia.org/wiki/Second) to run on these numbers, see https://www.mersenneforum.org/showpost.php?p=627117&postcount=1) to run on numbers of these sizes unless either N−1 (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1) or N+1 (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2) (or both) (unfortunately, none of Wikipedia, Prime Wiki, Mathworld has article for N−1 primality test or N+1 primality test, but a similar article for Pocklington primality test: https://en.wikipedia.org/wiki/Pocklington_primality_test, https://www.rieselprime.de/ziki/Pocklington%27s_theorem, https://mathworld.wolfram.com/PocklingtonsTheorem.html, also see the article for the cyclotomy primality test: https://t5k.org/glossary/xpage/Cyclotomy.html) can be ≥ 1/3 factored (https://en.wikipedia.org/wiki/Integer_factorization, https://www.rieselprime.de/ziki/Factorization, https://mathworld.wolfram.com/PrimeFactorization.html, https://mathworld.wolfram.com/PrimeFactorizationAlgorithms.html, http://www.numericana.com/answer/factoring.htm) or can be ≥ 1/4 factored and the number is not very large (say not > 10¹⁰⁰⁰⁰⁰), or Nⁿ−1 can be ≥ 1/3 factored for a small n. If either N−1 or N+1 (or both) can be ≥ 1/2 factored, then we can use the Pocklington N−1 primality test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, https://en.wikipedia.org/wiki/Pocklington_primality_test, https://www.rieselprime.de/ziki/Pocklington%27s_theorem, https://mathworld.wolfram.com/PocklingtonsTheorem.html, https://stdkmd.net/nrr/pock/, http://factordb.com/nmoverview.php?method=1) (the N−1 case) or the Morrison N+1 primality test (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2) (the N+1 case); if either N−1 or N+1 (or both) can be ≥ 1/3 factored, then we can use the Brillhart-Lehmer-Selfridge primality test (https://www.ams.org/journals/mcom/1975-29-130/S0025-5718-1975-0384673-1/S0025-5718-1975-0384673-1.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_23.pdf), https://en.wikipedia.org/wiki/Pocklington_primality_test#Extensions_and_variants); if either N−1 or N+1 (or both) can be ≥ 1/4 factored but neither can be ≥ 1/3 factored, then we need to use CHG (https://www.mersenneforum.org/attachment.php?attachmentid=21133&d=1571237465, https://t5k.org/bios/page.php?id=797, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/CHG) to prove its primality (see https://www.mersenneforum.org/showpost.php?p=528149&postcount=3 and https://www.mersenneforum.org/showpost.php?p=603181&postcount=438 and https://www.mersenneforum.org/showpost.php?p=277617&postcount=7), however, unlike Brillhart-Lehmer-Selfridge primality test for the numbers N such that N−1 or N+1 (or both) can be ≥ 1/3 factored can run for arbitrarily large numbers N (thus, there are no unproven probable primes N such that N−1 or N+1 (or both) can be ≥ 1/3 factored), CHG for the numbers N such that either N−1 or N+1 (or both) can be ≥ 1/4 factored but neither can be ≥ 1/3 factored cannot run for very large N (say > 10¹⁰⁰⁰⁰⁰), for the examples of the numbers which are proven prime by CHG, see https://t5k.org/primes/page.php?id=126454, https://t5k.org/primes/page.php?id=131964, https://t5k.org/primes/page.php?id=123456, https://t5k.org/primes/page.php?id=130933, https://stdkmd.net/nrr/cert/1/ (search for "CHG"), https://stdkmd.net/nrr/cert/2/ (search for "CHG"), https://stdkmd.net/nrr/cert/3/ (search for "CHG"), https://stdkmd.net/nrr/cert/4/ (search for "CHG"), https://stdkmd.net/nrr/cert/5/ (search for "CHG"), https://stdkmd.net/nrr/cert/6/ (search for "CHG"), https://stdkmd.net/nrr/cert/7/ (search for "CHG"), https://stdkmd.net/nrr/cert/8/ (search for "CHG"), https://stdkmd.net/nrr/cert/9/ (search for "CHG"), http://xenon.stanford.edu/~tjw/pp/index.html (search for "CHG"), however, factordb (http://factordb.com/, https://www.rieselprime.de/ziki/Factoring_Database) lacks the ability to verify CHG proofs, see https://www.mersenneforum.org/showpost.php?p=608362&postcount=165; if neither N−1 nor N+1 can be ≥ 1/4 factored but Nⁿ−1 can be ≥ 1/3 factored for a small n, then we can use the cyclotomy primality test (https://t5k.org/glossary/xpage/Cyclotomy.html, https://t5k.org/prove/prove3_3.html, https://t5k.org/primes/search.php?Comment=Cyclotomy&OnList=all&Number=1000000&Style=HTML, http://factordb.com/nmoverview.php?method=3)), i.e. it is too hard to prove primes for general numbers (https://t5k.org/glossary/xpage/OrdinaryPrime.html) of this size, but they are expected to be primes, since they are > 10²⁵⁰⁰⁰ and the probability that they are in fact composite is < 10⁻²⁰⁰⁰, see https://t5k.org/notes/prp_prob.html and https://www.ams.org/journals/mcom/1989-53-188/S0025-5718-1989-0982368-4/S0025-5718-1989-0982368-4.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_22.pdf).

(Edit: Now the SRSIEVE in MTSIEVE (https://sourceforge.net/projects/mtsieve/, https://www.mersenneforum.org/rogue/mtsieve.html, https://download.mersenne.ca/mtsieve, https://t5k.org/bios/page.php?id=449, https://www.rieselprime.de/ziki/Mtsieve, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/mtsieve_2.4.8) can handle the general case (a×bⁿ+c)/gcd(a+c,b−1) when gcd(a+c,b−1) > 1, see https://github.com/xayahrainie4793/prime-programs-cached-copy/blob/main/mtsieve_2.4.8/CHANGES.txt, thus now we can sieve the sequence (a×bⁿ+c)/gcd(a+c,b−1) directly)

When sieving the sequence (a×bⁿ+c)/gcd(a+c,b−1) (a ≥ 1, b ≥ 2, c ≠ 0, gcd(a,c) = 1, gcd(b,c) = 1), the sieve program should: (below, r is a linear function of n, m is a constant like a, b, c (m ≥ 2))

General:

1.1. If (a×bⁿ+c)/gcd(a+c,b−1) can be written as (m^r−1)/(m−1); display a warning message on the screen that this form is a generalized repunit number and could better be factored algebraically or sieved with another program (remove all composite r, and only sieve with the primes p == 1 mod r).
1.2. If (a×bⁿ+c)/gcd(a+c,b−1) can be written as (m^r+1)/(m+1); display a warning message on the screen that this form is a generalized Wagstaff number and could better be factored algebraically or sieved with another program (remove all composite r, and only sieve with the primes p == 1 mod 2×r).
1.3. If (a×bⁿ+c)/gcd(a+c,b−1) can be written as m^r+1 with even m; display a warning message on the screen that this form is a generalized Fermat number and could better be factored algebraically or sieved with another program (remove all non-power-of-2 r, and no need to sieve, just look for r = 2^s (see https://www.mersenneforum.org/showpost.php?p=95547&postcount=63), and instead use trial division (https://en.wikipedia.org/wiki/Trial_division, https://t5k.org/glossary/xpage/TrialDivision.html, https://www.rieselprime.de/ziki/Trial_factoring, https://mathworld.wolfram.com/TrialDivision.html, http://www.numericana.com/answer/factoring.htm#trial, https://www.mersenne.ca/tf1G/, https://www.mersenne.ca/tfmissed.php, https://oeis.org/A189172) with the primes p == 1 mod 2×r).
1.4. If (a×bⁿ+c)/gcd(a+c,b−1) can be written as (m^r+1)/2 with odd m; display a warning message on the screen that this form is a generalized half Fermat number and could better be factored algebraically or sieved with another program (remove all non-power-of-2 r, and no need to sieve, just look for r = 2^s (see https://www.mersenneforum.org/showpost.php?p=95547&postcount=63), and instead use trial division (https://en.wikipedia.org/wiki/Trial_division, https://t5k.org/glossary/xpage/TrialDivision.html, https://www.rieselprime.de/ziki/Trial_factoring, https://mathworld.wolfram.com/TrialDivision.html, http://www.numericana.com/answer/factoring.htm#trial, https://www.mersenne.ca/tf1G/, https://www.mersenne.ca/tfmissed.php, https://oeis.org/A189172) with the primes p == 1 mod 2×r).

Remove all n cases:

2.1. If a, b, −c are all squares; remove all n.
2.2. If a, b, c are all r-th powers for an odd r > 1; remove all n.
2.3. If one of a and c is also a 4th power, and the other is of the form 4×m⁴, and b is also a 4th power; remove all n. These are Aurifeuillean factors.

Remove partial n cases:

3.1. If a and −c are both squares; remove all n == 0 mod 2.
3.2. If a and c are both r-th powers for an odd r > 1; for each such r, remove all n == 0 mod r.
3.3. If one of a and c is also a 4th power, and the other is of the form 4×m⁴; remove all n == 0 mod 4.
3.4. If one of a and c is also a 4th power, and the other is of the form 4×m⁴, and b is a square; remove all n == 0 mod 2.
3.5. If a, c, 4×b are all 4th powers; remove all n == 1 mod 2.
3.6. If a and c are both 4th powers, and 2×b is a square; remove all n == 2 mod 4.

#1 and #2 should all be checked first before preceding, #3.3 and #3.4 and #3.5 are more Aurifeuillean factors.

The sequences (m^r−1)/(m−1), (m^r+1)/(m+1), m^r+1 (with even m), (m^r+1)/2 (with odd m) are special examples, since they are Lucas sequences (https://en.wikipedia.org/wiki/Lucas_sequence, https://mathworld.wolfram.com/LucasSequence.html, https://t5k.org/top20/page.php?id=23, https://t5k.org/primes/search.php?Comment=Generalized%20Lucas%20number&OnList=all&Number=1000000&Style=HTML) like the Fibonacci numbers (https://en.wikipedia.org/wiki/Fibonacci_number, https://t5k.org/glossary/xpage/FibonacciNumber.html, https://mathworld.wolfram.com/FibonacciNumber.html, https://www.numbersaplenty.com/set/Fibonacci_number/, https://t5k.org/top20/page.php?id=39, https://t5k.org/primes/search.php?Comment=^Fibonacci%20number&OnList=all&Number=1000000&Style=HTML, https://pzktupel.de/Primetables/TableFibonacci.php, https://oeis.org/A000045, https://oeis.org/A005478, https://oeis.org/A001605) and the Lucas numbers (https://en.wikipedia.org/wiki/Lucas_number, https://t5k.org/glossary/xpage/LucasNumber.html, https://mathworld.wolfram.com/LucasNumber.html, https://www.numbersaplenty.com/set/Lucas_number/, https://t5k.org/top20/page.php?id=48, https://t5k.org/primes/search.php?Comment=^Lucas%20number&OnList=all&Number=1000000&Style=HTML, https://pzktupel.de/Primetables/TableLucas.php, https://oeis.org/A000032, https://oeis.org/A000204, https://oeis.org/A005479, https://oeis.org/A001606), (m^r−1)/(m−1) is the Lucas sequence U_r(m+1,m), (m^r+1)/(m+1) is the Lucas sequence U_r(m−1,−m), m^r+1 (with even m) is the Lucas sequence V_r(m+1,m), (m^r+1)/2 (with odd m) is half of the Lucas sequence V_r(m+1,m) (this Lucas sequence V only contains even numbers), thus they have the divisibility properties of the Lucas sequences like the Fibonacci numbers and the Lucas numbers (which are the Lucas sequences U_n(1,−1) and V_n(1,−1), respectively) (another example of "half of the Lucas sequence V" is the sequence https://oeis.org/A001333, which is half of the Lucas sequence V_r(2,−1) (this Lucas sequence V also only contains even numbers), it has the divisibility property as the Lucas sequences V), i.e. they are strong divisibility sequences (https://en.wikipedia.org/wiki/Divisibility_sequence), (m^r−1)/(m−1) and (m^r+1)/(m+1) can be prime if r is a prime, m^r+1 (with even m) and (m^r+1)/2 (with odd m) can be prime if r is a power of 2, since otherwise m^r±1 is a binomial number (https://en.wikipedia.org/wiki/Binomial_number, https://mathworld.wolfram.com/BinomialNumber.html) which can be factored algebraically (and this algebraic factorization is nontrivial), thus they cannot be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them) unless there are other algebraic factorization of them, like the case of (9ⁿ−1)/8 with n ≥ 2 (the family {1} in base b = 9, which has difference-of-two-squares factorization) and 8ⁿ⁺¹+1 with n ≥ 1 (the family 1{0}1 in base b = 8, which has sum-of-two-cubes factorization).

(these are exactly the n such that (a×bⁿ+c)/gcd(a+c,b−1) has algebraic factorization, and (a×bⁿ+c)/gcd(a+c,b−1) can be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them) if and only if there is a prime p such that there is no n satisfies these two conditions simultaneously: "(a×bⁿ+c)/gcd(a+c,b−1) does not have algebraic factorization" and "(a×bⁿ+c)/gcd(a+c,b−1) is a p-rough number" (if and only if (a×bⁿ+c)/gcd(a+c,b−1) can be proven to only contain composites or only contain finitely many primes by covering congruence, then there is a prime p such that there is no n such that (a×bⁿ+c)/gcd(a+c,b−1) is a p-rough number, if and only if (a×bⁿ+c)/gcd(a+c,b−1) can be proven to only contain composites or only contain finitely many primes by algebraic factorization, then (a×bⁿ+c)/gcd(a+c,b−1) has algebraic factorization for all n, and if and only if (a×bⁿ+c)/gcd(a+c,b−1) can be proven to only contain composites or only contain finitely many primes by combine of covering congruence and algebraic factorization, then there is a prime p such that there is no n satisfies these two conditions simultaneously: "(a×bⁿ+c)/gcd(a+c,b−1) does not have algebraic factorization" and "(a×bⁿ+c)/gcd(a+c,b−1) is a p-rough number"), thus, if and only if (a×bⁿ+c)/gcd(a+c,b−1) can be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then the sieve file of (a×bⁿ+c)/gcd(a+c,b−1) can be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them) will be empty)

For examples:

b (2 ≤ b ≤ 36)	family	algebraic ((a×bⁿ+c)/gcd(a+c,b−1)) form of the family	the sieve program should	reason	this family corresponding to	factorization of the first 200 numbers in this family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0))
35	{1}	(35ⁿ−1)/34	display a warning message on the screen that this form is a generalized repunit number and could better be factored algebraically or sieved with another program (remove all n such that n is composite, and only sieve with the primes p == 1 mod n)	this form can be written as (35ⁿ−1)/34	1₃₁₃ (the ?th minimal prime in base 35)	http://factordb.com/index.php?query=%2835%5En-1%29%2F34&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	4{D}	(9×27ⁿ−1)/2	display a warning message on the screen that this form is a generalized repunit number and could better be factored algebraically or sieved with another program (remove all n such that 3×n+2 is composite, and only sieve with the primes p == 1 mod 3×n+2)	this form can be written as (3^3×n+2−1)/2	4D₂₃ (the 99696th minimal prime in base 27)	http://factordb.com/index.php?query=%289*27%5En-1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	1{V}	2×32ⁿ−1	display a warning message on the screen that this form is a generalized repunit number and could better be factored algebraically or sieved with another program (remove all n such that 5×n+1 is composite, and only sieve with the primes p == 1 mod 5×n+1)	this form can be written as 2^5×n+1−1	1V₆ (the 72855th minimal prime in base 32)	http://factordb.com/index.php?query=2*32%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{U}V	(6×36ⁿ⁺¹)/7	display a warning message on the screen that this form is a generalized Wagstaff number and could better be factored algebraically or sieved with another program (remove all n such that 2×n+3 is composite, and only sieve with the primes p == 1 mod 2×n+3)	this form can be written as (6^2×n+3+1)/7	U₄V (the 12765th minimal prime in base 36)	http://factordb.com/index.php?query=%286*36%5E%28n%2B1%29%2B1%29%2F7&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	4{0}1	4×32ⁿ⁺¹+1	display a warning message on the screen that this form is a generalized Fermat number and could better be factored algebraically or sieved with another program (remove all n such that 5×n+7 is not power of 2, and no need to sieve, just look for n = (2^4×s+1−7)/5 (2^r == 7 mod 5 if and only if r == 1 mod 4), and instead use trial division with the primes p == 1 mod 10×n+14)	this form can be written as 2^5×n+7+1	unsolved family	http://factordb.com/index.php?query=4*32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	G{0}1	16×32ⁿ⁺¹+1	display a warning message on the screen that this form is a generalized Fermat number and could better be factored algebraically or sieved with another program (remove all n such that 5×n+9 is not power of 2, and no need to sieve, just look for n = (2^4×s+2−9)/5 (2^r == 9 mod 5 if and only if r == 2 mod 4), and instead use trial division with the primes p == 1 mod 10×n+18)	this form can be written as 2^5×n+9+1	unsolved family	http://factordb.com/index.php?query=16*32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
31	{F}G	(31ⁿ⁺¹+1)/2	display a warning message on the screen that this form is a generalized half Fermat number and could better be factored algebraically or sieved with another program (remove all n such that n+1 is not power of 2, and no need to sieve, just look for n = 2^s−1, and instead use trial division with the primes p == 1 mod 2×n+2)	this form can be written as (31ⁿ⁺¹+1)/2	unsolved family	http://factordb.com/index.php?query=%2831%5E%28n%2B1%29%2B1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	4{D}E	(9×27ⁿ⁺¹+1)/2	display a warning message on the screen that this form is a generalized half Fermat number and could better be factored algebraically or sieved with another program (remove all n such that 3×n+5 is not power of 2, and no need to sieve, just look for n = (2^2×s+1−5)/3 (2^r == 5 mod 3 if and only if r == 1 mod 2), and instead use trial division with the primes p == 1 mod 6×n+10)	this form can be written as (3^3×n+5+1)/2	4D₁₀E (the 88466th minimal prime in base 27)	http://factordb.com/index.php?query=%289*27%5E%28n%2B1%29%2B1%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	3{8}	4×9ⁿ−1	remove all n	4, 9, 1 are all squares	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=4*9%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	3{1}	(25×9ⁿ−1)/8	remove all n	25, 9, 1 are all squares	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=%2825*9%5En-1%29%2F8&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	8{F}	9×16ⁿ−1	remove all n	9, 16, 1 are all squares	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=9*16%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	8{0}1	8×27ⁿ⁺¹+1	remove all n	8, 27, 1 are all cubes	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=8*27%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	9{G}	(125×27ⁿ−8)/13	remove all n	125, 27, −8 are all cubes	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=%28125*27%5En-8%29%2F13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{C}DD	(4×16ⁿ⁺²+81)/5	remove all n	16 and 4×4×81 are both 4th powers	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=%284*16%5E%28n%2B2%29%2B81%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
8	{4}1	(4×8ⁿ⁺¹−25)/7	remove all n such that n+1 == 0 mod 2 (i.e. remove all n == 1 mod 2)	4 and 25 are both squares	4₈1 (the 70th minimal prime in base 8)	http://factordb.com/index.php?query=%284*8%5E%28n%2B1%29-25%29%2F7&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	{G}99	(16×20ⁿ⁺²−2809)/19	remove all n such that n+2 == 0 mod 2 (i.e. remove all n == 0 mod 2)	16 and 2809 are both squares	G₄₄₇99 (the 3307th minimal prime in base 20)	http://factordb.com/index.php?query=%2816*20%5E%28n%2B2%29-2809%29%2F19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	{7}2L	(22ⁿ⁺²−289)/3	remove all n such that n+2 == 0 mod 2 (i.e. remove all n == 0 mod 2)	1 and 289 are both squares	7₃₈₁₅2L (the 8002nd minimal prime in base 22)	http://factordb.com/index.php?query=%2822%5E%28n%2B2%29-289%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
23	2E{B}	(121×23ⁿ−1)/2	remove all n == 0 mod 2	121 and 1 are both squares	2EB₂₉₅₈₃ (the 65156th minimal prime in base 23)	http://factordb.com/index.php?query=%28121*23%5En-1%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	O{5}	(121×26ⁿ−1)/5	remove all n == 0 mod 2	121 and 1 are both squares	O5₁₅₀₉ (the 25235th minimal prime in base 26)	http://factordb.com/index.php?query=%28121*26%5En-1%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
35	{Y}V	35ⁿ⁺¹−4	remove all n such that n+1 == 0 mod 2 (i.e. remove all n == 1 mod 2)	1 and 4 are both squares	Y₁₂V (the ?th minimal prime in base 35)	http://factordb.com/index.php?query=35%5E%28n%2B1%29-4&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
5	1{0}13	5ⁿ⁺²+8	remove all n such that n+2 == 0 mod 3 (i.e. remove all n == 1 mod 3)	1 and 8 are both cubes	10₉₃13 (the 22nd minimal prime in base 5)	http://factordb.com/index.php?query=5%5E%28n%2B2%29%2B8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
23	8{0}1	8×23ⁿ⁺¹+1	remove all n such that n+1 == 0 mod 3 (i.e. remove all n == 2 mod 3)	8 and 1 are both cubes	unsolved family	http://factordb.com/index.php?query=8*23%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	1{0}1F	17ⁿ⁺²+32	remove all n such that n+2 == 0 mod 5 (i.e. remove all n == 3 mod 5)	1 and 32 are both 5th powers	10₉₀₁₉1F (the 10400th minimal prime in base 17)	http://factordb.com/index.php?query=17%5E%28n%2B2%29%2B32&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	79{0}1	128×17ⁿ⁺¹+1	remove all n such that n+1 == 0 mod 7 (i.e. remove all n == 6 mod 7)	128 and 1 are both 7th powers	790₂₂₄1 (the 10307th minimal prime in base 17)	http://factordb.com/index.php?query=128*17%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
23	4{0}1	4×23ⁿ⁺¹+1	remove all n such that n+1 == 0 mod 4 (i.e. remove all n == 3 mod 4)	4×4×1 is a 4th power	40₃₄₁1 (the 64770th minimal prime in base 23)	http://factordb.com/index.php?query=4*23%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	{S}T	(4×36ⁿ⁺¹+1)/5	remove all n such that n+1 == 0 mod 2 (i.e. remove all n == 1 mod 2)	4×4×1 is a 4th power and 36 is a square	S₄₄T (the 35018th minimal prime in base 36)	http://factordb.com/index.php?query=%284*36%5E%28n%2B1%29%2B1%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show

Also the forms satisfying both "General" and "Remove all n cases", in this case the program should not display a warning message on the screen and instead stop immediately (just like the forms only satisfying "Remove all n cases"):

b (2 ≤ b ≤ 36)	family	algebraic ((a×bⁿ+c)/gcd(a+c,b−1)) form of the family	the sieve program should	reason	this family corresponding to	factorization of the first 200 numbers in this family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0))
9	{1}	(9ⁿ−1)/8	remove all n	1, 9, 1 are all squares	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=%289%5En-1%29%2F8&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	1{5}	(4×16ⁿ−1)/3	remove all n	4, 16, 1 are all squares	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=%284*16%5En-1%29%2F3&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
25	{1}	(25ⁿ−1)/24	remove all n	1, 25, 1 are all squares	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=%2825%5En-1%29%2F24&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	{1}	(32ⁿ−1)/31	remove all n	1, 32, 1 are all 5th powers	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=%2832%5En-1%29%2F31&use=n&n=2&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	{C}D	(4×16ⁿ+1)/5	remove all n	16 and 4×4×1 are both 4th powers	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=%284*16%5E%28n%2B1%29%2B1%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
8	1{0}1	8ⁿ⁺¹+1	remove all n	1, 8, 1 are all cubes	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=8%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
27	{D}E	(27ⁿ⁺¹+1)/2	remove all n	1, 27, 1 are all cubes	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=%2827%5E%28n%2B1%29%2B1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
32	1{0}1	32ⁿ⁺¹+1	remove all n	1, 32, 1 are all 5th powers	ruled out as only contain composites (only count the numbers > b)	http://factordb.com/index.php?query=32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show

Coordination with existing code:

If all n are removed by algebraic factors for sequence (a×bⁿ+c)/gcd(a+c,b−1), program should stop immediately. This means that this family can be proven to only contain composites.
If some n are removed by algebraic factors for sequence (a×bⁿ+c)/gcd(a+c,b−1), program continues sieving for removing the numbers with small prime factors.
Program should be able to handle input of one or multiple sequences (a×bⁿ+c)/gcd(a+c,b−1) at the screen or in a file. Some sequences (a×bⁿ+c)/gcd(a+c,b−1) could have algebraic factors while others do not.
Program should be able to handle an already sieved file as input, check the file for algebraic factors, remove them, and then continue sieving more deeply. Once again some sequences (a×bⁿ+c)/gcd(a+c,b−1) could have algebraic factors while others do not.

Once the numbers with small divisors had been removed, it remained to test the remaining numbers using a probable primality test. For this we used the software LLR by Jean Penné (http://jpenne.free.fr/index2.html, https://t5k.org/bios/page.php?id=431, https://www.rieselprime.de/ziki/LLR, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/llr403win64, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/llr403linux64) or PFGW (https://sourceforge.net/projects/openpfgw/, https://t5k.org/bios/page.php?id=175, https://www.rieselprime.de/ziki/PFGW, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/pfgw_win_4.0.3). Although undocumented, it is possible to run these two programs on numbers of the form (a×bⁿ+c)/d when d > 1 (however, of course, the numbers (a×bⁿ+c)/d with |c| ≠ 1 or/and d ≠ 1 or/and a > bⁿ can only be probable primes (https://en.wikipedia.org/wiki/Probable_prime, https://t5k.org/glossary/xpage/PRP.html, https://www.rieselprime.de/ziki/Probable_prime, https://mathworld.wolfram.com/ProbablePrime.html, http://www.primenumbers.net/prptop/prptop.php, https://web.archive.org/web/20240202224722/https://stdkmd.net/nrr/records.htm#probableprimenumbers, https://stdkmd.net/nrr/repunit/prpfactors.htm, https://www.mersenne.ca/prp.php?show=1, https://www.alfredreichlg.de/10w7/prp.html, http://factordb.com/listtype.php?t=1) tested; the numbers a×2ⁿ±1 (with a < 2ⁿ) are the fastest to test, a×2ⁿ+1 numbers are tested using the Proth algorithm (https://en.wikipedia.org/wiki/Proth%27s_theorem, https://www.rieselprime.de/ziki/Proth%27s_theorem, https://mathworld.wolfram.com/ProthsTheorem.html, http://www.numericana.com/answer/primes.htm#proth), a×2ⁿ−1 numbers are tested using the Lucas-Lehmer-Riesel algorithm (https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer%E2%80%93Riesel_test); the numbers a×bⁿ±1 (with b > 2, a < bⁿ) can also be definitely prime (https://en.wikipedia.org/wiki/Provable_prime, https://web.archive.org/web/20240202224722/https://stdkmd.net/nrr/records.htm#primenumbers, http://factordb.com/listtype.php?t=4) tested, a×bⁿ+1 numbers are tested using the N−1 Pocklington algorithm (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, https://en.wikipedia.org/wiki/Pocklington_primality_test, https://www.rieselprime.de/ziki/Pocklington%27s_theorem, https://mathworld.wolfram.com/PocklingtonsTheorem.html, https://stdkmd.net/nrr/pock/, http://factordb.com/nmoverview.php?method=1), a×bⁿ−1 numbers are tested using the N+1 Morrison algorithm (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2)), so this program required no modifications. A script was also written which allowed one to run srsieve while LLR or PFGW was testing the remaining candidates, so that when a divisor was found by srsieve on a number which had not yet been tested by LLR or PFGW it would be removed from the list of candidates.

For the primes < 10²⁵⁰⁰⁰ for the "easy" bases (bases b with ≤ 150 minimal primes > 10²⁹⁹ (base b = 26 has 82 known minimal (probable) primes > 10²⁹⁹ and 4 unsolved families, base b = 36 has 75 known minimal (probable) primes > 10²⁹⁹ and 4 unsolved families, base b = 17 has 99 known minimal (probable) primes > 10²⁹⁹ and 18 unsolved families, base b = 21 has 80 known minimal (probable) primes > 10²⁹⁹ and 12 unsolved families, base b = 19 has 201 known minimal (probable) primes > 10²⁹⁹ and 23 unsolved families), i.e. bases b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36), we employed PRIMO by Marcel Martin (http://www.ellipsa.eu/public/primo/primo.html, http://www.rieselprime.de/dl/Primo309.zip, https://t5k.org/bios/page.php?id=46, https://www.rieselprime.de/ziki/Primo, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/primo-433-lx64, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/Primo309) or CM by Andreas Enge (https://www.multiprecision.org/cm/index.html, https://t5k.org/bios/page.php?id=5485, https://github.com/xayahrainie4793/prime-programs-cached-copy/tree/main/cm), two different elliptic curve primality proving (https://t5k.org/prove/prove4_2.html, https://en.wikipedia.org/wiki/Elliptic_curve_primality, https://t5k.org/glossary/xpage/ECPP.html, https://mathworld.wolfram.com/EllipticCurvePrimalityProving.html, http://irvinemclean.com/maths/pfaq7.htm, https://t5k.org/top20/page.php?id=27, https://t5k.org/primes/search.php?Comment=ECPP&OnList=all&Number=1000000&Style=HTML, http://www.ellipsa.eu/public/primo/records.html, http://www.lix.polytechnique.fr/~morain/Prgms/ecpp.english.html, https://www.multiprecision.org/cm/ecpp.html, https://www.ams.org/journals/mcom/1993-61-203/S0025-5718-1993-1199989-X/S0025-5718-1993-1199989-X.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_256.pdf), https://arxiv.org/pdf/2404.05506.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_428.pdf)) implementations, to compute primality certificates (https://en.wikipedia.org/wiki/Primality_certificate, https://t5k.org/glossary/xpage/Certificate.html, https://mathworld.wolfram.com/PrimalityCertificate.html, http://www.ellipsa.eu/public/primo/records.html, http://www.lix.polytechnique.fr/Labo/Francois.Morain/Primes/myprimes.html, https://stdkmd.net/nrr/cert/, https://alfredreichlg.de/cert/certificates.tpm.html, https://alfredreichlg.de/10w7/certifiedprimes.html, http://xenon.stanford.edu/~tjw/pp/index.html, http://factordb.com/certoverview.php, http://5.199.134.130/certificates.tar.xz, http://5.199.134.130/certificates.tar.xz.SHA256SUM, http://5.199.134.130/certificates.tar.xz.par2, http://5.199.134.130/certificates.tar.xz.vol00+10.par2, http://5.199.134.130/certificates/) for the candidates for minimal prime base b which are > 10²⁹⁹ and neither N−1 nor N+1 can be ≥ 1/3 factored (need CHG proof if either N−1 or N+1 (or both) can be ≥ 1/4 factored but neither can be ≥ 1/3 factored, but factordb (http://factordb.com/, https://www.rieselprime.de/ziki/Factoring_Database) lacks the ability to verify CHG proofs, see https://www.mersenneforum.org/showpost.php?p=608362&postcount=165).

We have completely solved this problem for bases b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24 (i.e. we have found all minimal primes in these bases and proved that they are all such primes and proved that they are definitely primes (https://en.wikipedia.org/wiki/Provable_prime, http://factordb.com/listtype.php?t=4) (i.e. not merely probable primes)) (thus, currently we can complete the classification of the minimal primes in these bases, and the "minimal prime problem" for these bases are theorems (https://en.wikipedia.org/wiki/Theorem, https://mathworld.wolfram.com/Theorem.html, https://t5k.org/notes/proofs/), they can be called "minimal prime theorems", only bases b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24 currently have "minimal prime theorems", and like the four color theorem (https://en.wikipedia.org/wiki/Four_color_theorem, https://mathworld.wolfram.com/Four-ColorTheorem.html) and the theorem that the Ramsey number (https://en.wikipedia.org/wiki/Ramsey%27s_theorem, https://mathworld.wolfram.com/RamseyNumber.html, https://oeis.org/A212954) R(4,5) = 25, the harder parts of the proof (https://en.wikipedia.org/wiki/Mathematical_proof, https://mathworld.wolfram.com/Proof.html, https://t5k.org/notes/proofs/) are completed by computers instead of humans, such as the proof for base b = 24 (the largest base b which is currently completely solved, including the primality proving (https://en.wikipedia.org/wiki/Primality_test, https://www.rieselprime.de/ziki/Primality_test, https://mathworld.wolfram.com/PrimalityTest.html, https://t5k.org/prove/prove3.html, https://t5k.org/prove/prove4.html) for all primes in the set), computing data up to linear families (i.e. only linear families left) (see https://github.com/curtisbright/mepn-data/commit/7acfa0656d3c6b759f95a031f475a30f7664a122 for the original minimal prime problem in bases 2 ≤ b ≤ 26) and computing the primality certificate (https://en.wikipedia.org/wiki/Primality_certificate, https://t5k.org/glossary/xpage/Certificate.html, https://mathworld.wolfram.com/PrimalityCertificate.html, http://www.ellipsa.eu/public/primo/records.html, http://www.lix.polytechnique.fr/Labo/Francois.Morain/Primes/myprimes.html, https://stdkmd.net/nrr/cert/, https://alfredreichlg.de/cert/certificates.tpm.html, https://alfredreichlg.de/10w7/certifiedprimes.html, http://xenon.stanford.edu/~tjw/pp/index.html, http://factordb.com/certoverview.php, http://5.199.134.130/certificates.tar.xz, http://5.199.134.130/certificates.tar.xz.SHA256SUM, http://5.199.134.130/certificates.tar.xz.par2, http://5.199.134.130/certificates.tar.xz.vol00+10.par2, http://5.199.134.130/certificates/) for the largest minimal prime in base b = 24 (i.e. N00N₈₁₂₉LN, its algebraic form is 13249×24⁸¹³¹−49) (see http://factordb.com/cert.php?id=1100000003593391606 and https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/primality-certificates/certificate24_3409 for its primality certificate) are completed by computers instead of humans (I am very glad that the problem in base b = 24 can be completely solved, since the number 24 is an important number in number theory, see https://sites.google.com/view/24-important-number-theory and https://oeis.org/A018253 and https://math.ucr.edu/home/baez/numbers/24.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_176.pdf) and https://arxiv.org/pdf/1104.5052.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_177.pdf)), the fully proof for base b = 24 is almost impossible to be written by hand (only bases b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12 is possible to write the fully proof by hand), also we have completely solved this problem for bases b = 11, 13, 16, 22, 30 if we allow probable primes (https://en.wikipedia.org/wiki/Probable_prime, https://t5k.org/glossary/xpage/PRP.html, https://www.rieselprime.de/ziki/Probable_prime, https://mathworld.wolfram.com/ProbablePrime.html, http://www.primenumbers.net/prptop/prptop.php, https://web.archive.org/web/20240202224722/https://stdkmd.net/nrr/records.htm#probableprimenumbers, https://stdkmd.net/nrr/repunit/prpfactors.htm, https://www.mersenne.ca/prp.php?show=1, https://www.alfredreichlg.de/10w7/prp.html, http://factordb.com/listtype.php?t=1) > 10²⁵⁰⁰⁰ in place of proven primes (thus, we have completely solved this problem for bases b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 30 if we allow probable primes > 10²⁵⁰⁰⁰ in place of proven primes), besides, we have completely solved this problem for bases b = 17, 19, 21, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36 (if we allow strong probable primes in place of proven primes) except the 793+? families x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b) listed in the "left b" files (see the condensed table below for the searching limit of these families) (thus, currently the "minimal prime problem" for these bases are still unsolved problems (https://en.wikipedia.org/wiki/Open_problem, https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics, https://t5k.org/glossary/xpage/OpenQuestion.html, https://mathworld.wolfram.com/UnsolvedProblems.html, https://t5k.org/notes/conjectures/)).

There are totally 2028110+? ~ 2028875+? minimal primes in bases 2 ≤ b ≤ 36 (counted with multiplicity, e.g. the prime p = 41 is 221 in base b = 4, 131 in base b = 5, 56 in base b = 7, 51 in base b = 8, 45 in base b = 9, 41 in base b = 10, 38 in base b = 11, 35 in base b = 12, 32 in base b = 13, 2D in base b = 14, 2B in base b = 15, 29 in base b = 16, 27 in base b = 17, 25 in base b = 18, 23 in base b = 19, 21 in base b = 20, 1K in base b = 21, 1J in base b = 22, 1I in base b = 23, 1H in base b = 24, 1G in base b = 25, 1F in base b = 26, 1E in base b = 27, 1D in base b = 28, 1C in base b = 29, 1B in base b = 30, 1A in base b = 31, 19 in base b = 32, 18 in base b = 33, 17 in base b = 34, 16 in base b = 35, 15 in base b = 36, all are minimal primes and counted with 32 primes; and the prime p = 577 is 711 in base b = 9, 577 in base b = 10, 485 in base b = 11, 401 in base b = 12, 355 in base b = 13, 241 in base b = 16, 1GG in base b = 17, 1B7 in base b = 19, 145 in base b = 22, 122 in base b = 23, 101 in base b = 24, N2 in base b = 25, M5 in base b = 26, LA in base b = 27, KH in base b = 28, JQ in base b = 29, J7 in base b = 30, IJ in base b = 31, I1 in base b = 32, HG in base b = 33, GX in base b = 34, GH in base b = 35, G1 in base b = 36, all are minimal primes and counted with 23 primes; and the prime p = 1063 is 887 in base b = 11, 747 in base b = 12, 63A in base b = 13, 3B9 in base b = 17, 2HI in base b = 19, 247 in base b = 22, 205 in base b = 23, 1HD in base b = 25, 1EN in base b = 26, 17J in base b = 29, 139 in base b = 31, 117 in base b = 32, W7 in base b = 33, V9 in base b = 34, UD in base b = 35, TJ in base b = 36, all are minimal primes and counted with 16 primes, in fact, by definition, every prime p is a minimal prime in every base sqrt(p) < b < p, and I conjectured that all primes p other than 2, 3, 5, 7, 11, 17, 19, 23, 37, 47, 53, 67, 167, 233 are minimal primes in at least one base b < sqrt(p), and all primes p other than 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 79, 83, 89, 101, 103, 107, 137, 139, 163, 167, 191, 199, 233, 239 are minimal primes in at least two bases b < sqrt(p), and all primes p other than 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 191, 199, 211, 223, 229, 233, 239, 263, 317, 353, 461, 479 are minimal primes in at least three bases b < sqrt(p), and all primes p other than 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 229, 233, 239, 251, 263, 269, 283, 293, 317, 331, 347, 349, 353, 359, 367, 373, 383, 389, 461, 479, 503, 509, 523, 563, 593, 1039 are minimal primes in at least four bases b < sqrt(p), etc. also, for every n, all sufficiently large (https://en.wikipedia.org/wiki/Sufficiently_large, https://mathworld.wolfram.com/SufficientlyLarge.html) primes p are minimal primes in at least n bases b < sqrt(p) (of course, there are bases b > 36 (which are not in this project) mentioned)) and totally 765+? families x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b) for which we cannot determine whether they contain a prime (only count the numbers > b) or not (even if we allow strong probable primes).

The largest probable prime we found was the number A3₅₉₂₁₉₇A (expressed as a base b = 13 string) or (41×13⁵⁹²¹⁹⁸+27)/4 in standard notation. It contains 659677 decimal digits and at the time of discovery (Nov. 24, 2023) was the 183rd largest known probable prime according to Henri and Renaud Lifchitz's ranking.

Some of the left families may cover another left family, e.g. the base 19 left family 5{H}5 covers another base 19 left family 5{H}05, and if the smallest prime in family 5{H}5 in base 19 has length n, and the family 5{H}05 in base 19 has no prime with length ≤ n, then family 5{H}05 in base 19 can be removed from the unsolved families for base 19, however, if the smallest prime in family 5{H}5 in base 19 has length n, but the family 5{H}05 in base 19 is not tested to length n or more, then family 5{H}05 in base 19 should not be removed from the unsolved families for base 19, since a number in family 5{H}05 covers the prime in family 5{H}5 with length n if and only if the length of this number is ≥ n+1; besides, the base 19 left family FH0{H} covers another base 19 left family FHHH0{H}, and if the smallest prime in family FH0{H} in base 19 has length n, and the family FHHH0{H} in base 19 has no prime with length ≤ n+1, then family FHHH0{H} in base 19 can be removed from the unsolved families for base 19, however, if the smallest prime in family FH0{H} in base 19 has length n, but the family FHHH0{H} in base 19 is not tested to length n+1 or more, then family FHHH0{H} in base 19 should not be removed from the unsolved families for base 19, since a number in family FHHH0{H} covers the prime in family FH0{H} with length n if and only if the length of this number is ≥ n+2; besides, the base 21 left family {9}D covers another base 21 left family F{9}D, and if the smallest prime in family {9}D in base 21 has length n, and the family F{9}D in base 21 has no prime with length ≤ n, then family F{9}D in base 21 can be removed from the unsolved families for base 21, however, if the smallest prime in family {9}D in base 21 has length n, but the family F{9}D in base 21 is not tested to length n or more, then family F{9}D in base 21 should not be removed from the unsolved families for base 21, since a number in family F{9}D covers the prime in family {9}D with length n if and only if the length of this number is ≥ n+1 (if a family has no primes, then we say "the smallest prime in this family has length ∞ (https://en.wikipedia.org/wiki/Infinity, https://t5k.org/glossary/xpage/Infinite.html, https://mathworld.wolfram.com/Infinity.html) (instead of 0 or −1)", see http://gladhoboexpress.blogspot.com/2019/05/prime-sandwiches-made-with-one-derbread.html and http://chesswanks.com/seq/a306861.txt (for the OEIS sequence https://oeis.org/A306861) and http://chesswanks.com/seq/a269254.txt (for the OEIS sequence https://oeis.org/A269254) (since this is more convenient, e.g. the n of the smallest prime in the base 21 family 9_nD, this family has been searched to n = 100000 with no prime or probable prime found, we can use ">100000" for the n of the smallest prime in the base 21 family 9_nD (while for the n of the smallest prime in the base 13 family A3_nA, it is 592199), ">100000" includes infinity (since infinity is > 100000) but does not includes 0 or −1, it is still possible that there is no prime in the base 21 family 9_nD, although by the heuristic argument (https://en.wikipedia.org/wiki/Heuristic_argument, https://t5k.org/glossary/xpage/Heuristic.html, https://mathworld.wolfram.com/Heuristic.html, https://web.archive.org/web/20230911032453/https://www.utm.edu/staff/caldwell/preprints/Heuristics.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_112.pdf), https://arxiv.org/pdf/2103.04483.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_113.pdf)) above, this is very impossible, also "the smallest n ≥ 1 such that (a×bⁿ+c)/gcd(a+c,b−1) is prime" should be the infimum (https://en.wikipedia.org/wiki/Infimum, https://mathworld.wolfram.com/Infimum.html) of the set S of the numbers n ≥ 1 such that (a×bⁿ+c)/gcd(a+c,b−1) is prime, and if there is no n ≥ 1 such that (a×bⁿ+c)/gcd(a+c,b−1) is prime, then this set S is the empty set (https://en.wikipedia.org/wiki/Empty_set, https://mathworld.wolfram.com/EmptySet.html), and by the definition of "inf", the infimum of the empty set is ∞), ∞ is > any finite number, e.g. "the smallest n ≥ 1 such that k×2ⁿ+1 is prime" is ∞ for k = 78557, 157114, 271129, 271577, 314228, 322523, 327739, 482719, ..., while it is 31172165 for k = 10223 and 13018586 for k = 19249, another example is "the smallest n such that (bⁿ−1)/(b−1) is prime" is ∞ for b = 9, 25, 32, 49, 64, 81, 121, 125, 144, 169, 216, 225, 243, 289, 324, 343, 361, 441, 484, 529, 625, 729, 784, 841, 900, 961, 1000, ..., while it is 62903 for b = 691 and 41189 for b = 693).

The final goal of this project is finding all minimal primes and proving that these are all such primes (including the primality proving for the probable primes) in all bases 2 ≤ b ≤ 36, i.e. solving all families in all bases 2 ≤ b ≤ 36. Solving all (left) families in all bases 2 ≤ b ≤ 36 (and proving the primality of all probable primes in the sets of all bases 2 ≤ b ≤ 36) is not possible but we aim to solve many of them (and proving the primality of many of them), at least find a probable prime for many of them (since the smallest prime in a family may be too large (> 10²⁵⁰⁰⁰) to be proved primality, unless its N−1 or/and N+1 can be ≥ 25% factored).

There are also unproven probable primes (however, in this project our results assume that they are in fact primes, since they are > 10²⁵⁰⁰⁰ and the probability that they are in fact composite is < 10⁻²⁰⁰⁰, see https://t5k.org/notes/prp_prob.html and https://www.ams.org/journals/mcom/1989-53-188/S0025-5718-1989-0982368-4/S0025-5718-1989-0982368-4.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_22.pdf)), the unproven probable primes for bases b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 (the "easy" bases (bases b with ≤ 150 minimal primes > 10²⁹⁹ (base b = 26 has 82 known minimal (probable) primes > 10²⁹⁹ and 4 unsolved families, base b = 36 has 75 known minimal (probable) primes > 10²⁹⁹ and 4 unsolved families, base b = 17 has 99 known minimal (probable) primes > 10²⁹⁹ and 18 unsolved families, base b = 21 has 80 known minimal (probable) primes > 10²⁹⁹ and 12 unsolved families, base b = 19 has 201 known minimal (probable) primes > 10²⁹⁹ and 23 unsolved families))) (all of them are Fermat probable primes (https://t5k.org/prove/prove2_2.html, https://en.wikipedia.org/wiki/Fermat_primality_test, https://en.wikipedia.org/wiki/Fermat_pseudoprime, https://t5k.org/glossary/xpage/PRP.html, https://www.rieselprime.de/ziki/Fermat_pseudoprimality_test, https://mathworld.wolfram.com/FermatPseudoprime.html, https://www.numbersaplenty.com/set/Poulet_number/, http://www.numericana.com/answer/pseudo.htm#pseudoprime, http://ntheory.org/data/psps.txt, https://www.cecm.sfu.ca/Pseudoprimes/psps-below-2-to-64.txt.bz2, https://www.cecm.sfu.ca/Pseudoprimes/factored-psps-below-2-to-64.txt.bz2, https://www.cecm.sfu.ca/Pseudoprimes/annotated-psps-below-2-to-64.txt.bz2, https://sites.google.com/view/fermat-pseudoprime, https://sites.google.com/view/bases-fermat-pseudoprime, https://oeis.org/A001567, https://oeis.org/A005935, https://oeis.org/A005936, https://oeis.org/A005938, https://oeis.org/A052155, https://oeis.org/A083737, https://oeis.org/A083739, https://oeis.org/A083876, https://oeis.org/A271221, https://oeis.org/A348258, https://oeis.org/A181780, https://oeis.org/A063994, https://oeis.org/A194946, https://oeis.org/A195327, https://oeis.org/A002997, https://oeis.org/A191311, https://oeis.org/A090086, https://oeis.org/A007535) to all prime bases ≤ 64 (i.e. bases 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61), also for the unproven probable primes for bases 2 ≤ b ≤ 16 I also ran the bases 6, 10, 12 although they are not prime bases (running perfect power (i.e. of the form m^r with r > 1) (https://oeis.org/A001597, https://en.wikipedia.org/wiki/Perfect_power, https://mathworld.wolfram.com/PerfectPower.html, https://www.numbersaplenty.com/set/perfect_power/) bases is useless since a Fermat probable prime to base m must also be a Fermat probable prime to base m^r for all r, thus do not run these bases, in fact, this is also true for Miller–Rabin primality tests, a strong probable prime to base m must also be a strong probable prime to base m^r for all r, thus running perfect power (i.e. of the form m^r with r > 1) (https://oeis.org/A001597, https://en.wikipedia.org/wiki/Perfect_power, https://mathworld.wolfram.com/PerfectPower.html, https://www.numbersaplenty.com/set/perfect_power/) bases is also useless for the Miller–Rabin primality tests), see the "Bases checked" section of the "Primality proving" box in the factordb entries of these probable primes, the "Bases checked" section of the "Primality proving" box in the factordb entries of these probable primes contain all of the bases 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, also contain the bases 6, 10, 12 for the unproven probable primes for bases 2 ≤ b ≤ 16, unfortunately, the "Primality proving" box in factordb only runs the Fermat primality test instead of the Miller–Rabin primality test) are (together with the factorization of the numbers in their corresponding families):

(In progess to add bases b = 17 and b = 21)

(for the factorization of the numbers in these families and the N−1 (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1) and N+1 (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2) of these probable primes, the special number field sieve (https://en.wikipedia.org/wiki/Special_number_field_sieve, https://www.rieselprime.de/ziki/Special_number_field_sieve, https://mathworld.wolfram.com/NumberFieldSieve.html, https://stdkmd.net/nrr/records.htm#BIGSNFS, http://mklasson.com/factors/viewlog.php?sort=2&order=desc&method=snfs&maxrows=10000, https://stdkmd.net/nrr/wanted.htm#smallpolynomial, https://www.mersenne.ca/userfactors/nfs/1, http://escatter11.fullerton.edu/nfs/) or the general number field sieve (https://en.wikipedia.org/wiki/General_number_field_sieve, https://www.rieselprime.de/ziki/General_number_field_sieve, https://mathworld.wolfram.com/NumberFieldSieve.html, https://stdkmd.net/nrr/records.htm#BIGGNFS, http://mklasson.com/factors/viewlog.php?sort=2&order=desc&method=gnfs&maxrows=10000, https://stdkmd.net/nrr/wanted.htm#suitableforgnfs, https://www.mersenne.ca/userfactors/nfs/1, http://escatter11.fullerton.edu/nfs/) may be used, they have SNFS polynomials (https://www.rieselprime.de/ziki/SNFS_polynomial_selection), just like factorization of the numbers in https://stdkmd.net/nrr/aaaab.htm and https://stdkmd.net/nrr/abbbb.htm and https://stdkmd.net/nrr/aaaba.htm and https://stdkmd.net/nrr/abaaa.htm and https://stdkmd.net/nrr/abbba.htm and https://stdkmd.net/nrr/abbbc.htm and http://mklasson.com/factors/index.php and https://cs.stanford.edu/people/rpropper/math/factors/3n-2.txt and https://alfredreichlg.de/10w7/10w7.txt and https://web.archive.org/web/20020320010222/http://proth.cjb.net/ and http://web.archive.org/web/20111104173105/http://www.immortaltheory.com/NumberTheory/2nm3_db.txt and https://www.asahi-net.or.jp/~KC2H-MSM/mathland/aba/index.htm and https://www.alpertron.com.ar/BRILLIANT.HTM and https://www.alpertron.com.ar/BRILLIANT3.HTM and https://www.alpertron.com.ar/BRILLIANT4.HTM and https://www.alpertron.com.ar/BRILLIANT2.HTM and https://oeis.org/wiki/Factors_of_33*2%5En%2B1 and https://oeis.org/wiki/Factors_of_33*2%5En-1 and https://web.archive.org/web/20111018190410/http://www.sr5.psp-project.de/s5stats.html (section "Top ten factors:") and https://web.archive.org/web/20111018190339/http://www.sr5.psp-project.de/r5stats.html (section "Top ten factors:") and https://brnikat.com/nums/cullen_woodall/cw.html and https://oeis.org/wiki/OEIS_sequences_needing_factors#Near_powers.2C_factorials.2C_and_primorials (sections "near-powers with b = 2" and "near-powers with b = 3" and "near-powers with b = 5" and "near-powers with b = 6" and "near-powers with b = 7" and "near-powers with b = 10" and "near-powers with b > 10") and https://www.mersenneforum.org/showthread.php?t=9554 and https://www.mersenneforum.org/showthread.php?t=9167 and https://www.mersenneforum.org/showpost.php?p=644144&postcount=5, see https://stdkmd.net/nrr/records.htm and https://stdkmd.net/nrr/wanted.htm and https://www.mersenneforum.org/showthread.php?t=12962)

(For the Primo input files of more unproven probable primes, see http://factordb.com/primobatch.php and http://factordb.com/primobatch.php?digits=300&files=10&parts=1&start=Generate+zip and http://factordb.com/primobatch.php?digits=300&files=32000&parts=32&start=Generate+zip)

(if the prime is (a×bⁿ+c)/gcd(a+c,b−1) (with a ≥ 1, b ≥ 2, c ≠ 0, gcd(a,c) = 1, gcd(b,c) = 1), then its N−1 is (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1), and its N+1 is (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1), although (a×bⁿ+c)/gcd(a+c,b−1) (with a ≥ 1, b ≥ 2, c ≠ 0, gcd(a,c) = 1, gcd(b,c) = 1) has algebraic factorization if and only if either "there is an integer r > 1 such that a×bⁿ and −c are both rth powers" (in this case, (a×bⁿ+c)/gcd(a+c,b−1) has sum-of-two-rth-powers factorization if c > 0, or difference-of-two-rth-powers factorization if c < 0, although there is no "sum-of-two-rth-powers factorization" for even r, but no such situation (i.e. c > 0 and r is even) exists, since if c > 0 then −c < 0, but negative numbers cannot be squares, however, if r is even then all rth powers are squares (since if s divides r, then all rth powers are sth powers), thus, −c cannot be an rth power if c > 0 and r is even) or "one of a×bⁿ and c is a 4th power, and the other is of the form 4×m⁴" (in this case, (a×bⁿ+c)/gcd(a+c,b−1) has Aurifeuillean factorization of x⁴+4×y⁴), however, since c−gcd(a+c,b−1) and c+gcd(a+c,b−1) may not coprime to a and b, it is not that simple to known whether (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) and (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) have algebraic factorization, (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) has algebraic factorization if and only if either "c−gcd(a+c,b−1) = 0" (if and only if c−gcd(a+c,b−1) = 0, then (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) is trivially fully factored) or "there is an integer r > 1 such that a×bⁿ/gcd(a×bⁿ,c−gcd(a+c,b−1)) and −(c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) are both rth powers" (in this case, (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) has sum-of-two-rth-powers factorization if (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) > 0, or difference-of-two-rth-powers factorization if (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) < 0, although there is no "sum-of-two-rth-powers factorization" for even r, but no such situation (i.e. (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) > 0 and r is even) exists, since if (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) > 0 then −(c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) < 0, but negative numbers cannot be squares, however, if r is even then all rth powers are squares (since if s divides r, then all rth powers are sth powers), thus, −(c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) cannot be an rth power if (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) > 0 and r is even) or "one of a×bⁿ/gcd(a×bⁿ,c−gcd(a+c,b−1)) and (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) is a 4th power, and the other is of the form 4×m⁴" (in this case, (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) has Aurifeuillean factorization of x⁴+4×y⁴), (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) has algebraic factorization if and only if either "c+gcd(a+c,b−1) = 0" (if and only if c+gcd(a+c,b−1) = 0, then (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) is trivially fully factored) or "there is an integer r > 1 such that a×bⁿ/gcd(a×bⁿ,c+gcd(a+c,b−1)) and −(c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) are both rth powers" (in this case, (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) has sum-of-two-rth-powers factorization if (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) > 0, or difference-of-two-rth-powers factorization if (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) < 0, although there is no "sum-of-two-rth-powers factorization" for even r, but no such situation (i.e. (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) > 0 and r is even) exists, since if (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) > 0 then −(c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) < 0, but negative numbers cannot be squares, however, if r is even then all rth powers are squares (since if s divides r, then all rth powers are sth powers), thus, −(c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) cannot be an rth power if (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) > 0 and r is even) or "one of a×bⁿ/gcd(a×bⁿ,c+gcd(a+c,b−1)) and (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) is a 4th power, and the other is of the form 4×m⁴" (in this case, (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) has Aurifeuillean factorization of x⁴+4×y⁴))

b (2 ≤ b ≤ 36)	index of this minimal prime in base b (assuming the primality of all probable primes in base b)	base-b form of this unproven probable prime (which is a minimal prime assuming its primality)	algebraic ((a×bⁿ+c)/gcd(a+c,b−1)) form of this unproven probable prime (which is a minimal prime assuming its primality)	length of this unproven probable prime (which is a minimal prime assuming its primality) written in base b	length of this unproven probable prime (which is a minimal prime assuming its primality) written in decimal	factordb entry of this unproven probable prime (which is a minimal prime assuming its primality)	this unproven probable prime (which is a minimal prime assuming its primality) written in base b (use lower case letters instead of upper case letters)	this unproven probable prime (which is a minimal prime assuming its primality) written in decimal	helper file of this unproven probable prime (which is a minimal prime assuming its primality)	Primo input file of this unproven probable prime (which is a minimal prime assuming its primality)	factorization of the first 200 numbers in corresponding family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0) of this unproven probable prime (which is a minimal prime assuming its primality))
11	1068	57₆₂₆₆₈	(57×11⁶²⁶⁶⁸−7)/10	62669	65263	http://factordb.com/index.php?id=1100000003573679860&open=prime	http://factordb.com/index.php?showid=1100000003573679860&base=11	http://factordb.com/index.php?showid=1100000003573679860	http://factordb.com/helper.php?id=1100000003573679860	http://factordb.com/cert.php?id=1100000003573679860&inputfile	http://factordb.com/index.php?query=%2857*11%5En-7%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3194	C5₂₃₇₅₅C	(149×13²³⁷⁵⁶+79)/12	23757	26464	http://factordb.com/index.php?id=1100000003590647776&open=prime	http://factordb.com/index.php?showid=1100000003590647776&base=13	http://factordb.com/index.php?showid=1100000003590647776	http://factordb.com/helper.php?id=1100000003590647776	http://factordb.com/cert.php?id=1100000003590647776&inputfile	http://factordb.com/index.php?query=%28149*13%5E%28n%2B1%29%2B79%29%2F12&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3195	80₃₂₀₁₇111	8×13³²⁰²⁰+183	32021	35670	http://factordb.com/index.php?id=1100000000490878060&open=prime	http://factordb.com/index.php?showid=1100000000490878060&base=13	http://factordb.com/index.php?showid=1100000000490878060	http://factordb.com/helper.php?id=1100000000490878060	http://factordb.com/cert.php?id=1100000000490878060&inputfile	http://factordb.com/index.php?query=8*13%5E%28n%2B3%29%2B183&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3196	95₁₉₇₄₂₀	(113×13¹⁹⁷⁴²⁰−5)/12	197421	219916	http://factordb.com/index.php?id=1100000003943359311&open=prime	http://factordb.com/index.php?showid=1100000003943359311&base=13	http://factordb.com/index.php?showid=1100000003943359311	(no helper file, since this unproven probable prime is too large (> 10¹⁹⁹⁹⁹⁹) to be PRP-tested in factordb, and factordb does not have helper file for numbers with status (http://factordb.com/status.html, http://factordb.com/distribution.php) "U" (i.e. in http://factordb.com/listtype.php?t=2), factordb only has helper file for numbers with status "P" (i.e. in http://factordb.com/listtype.php?t=4) or "PRP" (i.e. in http://factordb.com/listtype.php?t=1))	(no Primo input file, since this unproven probable prime is too large (> 10¹⁹⁹⁹⁹⁹) to be PRP-tested in factordb, and factordb does not have Primo input file for numbers with status (http://factordb.com/status.html, http://factordb.com/distribution.php) "U" (i.e. in http://factordb.com/listtype.php?t=2), factordb only has Primo input file for numbers with status "PRP" (i.e. in http://factordb.com/listtype.php?t=1))	http://factordb.com/index.php?query=%28113*13%5En-5%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3197	A3₅₉₂₁₉₇A	(41×13⁵⁹²¹⁹⁸+27)/4	592199	659677	http://factordb.com/index.php?id=1100000005489162806&open=prime	http://factordb.com/index.php?showid=1100000005489162806&base=13	http://factordb.com/index.php?showid=1100000005489162806	(no helper file, since this unproven probable prime is too large (> 10¹⁹⁹⁹⁹⁹) to be PRP-tested in factordb, and factordb does not have helper file for numbers with status (http://factordb.com/status.html, http://factordb.com/distribution.php) "U" (i.e. in http://factordb.com/listtype.php?t=2), factordb only has helper file for numbers with status "P" (i.e. in http://factordb.com/listtype.php?t=4) or "PRP" (i.e. in http://factordb.com/listtype.php?t=1))	(no Primo input file, since this unproven probable prime is too large (> 10¹⁹⁹⁹⁹⁹) to be PRP-tested in factordb, and factordb does not have Primo input file for numbers with status (http://factordb.com/status.html, http://factordb.com/distribution.php) "U" (i.e. in http://factordb.com/listtype.php?t=2), factordb only has Primo input file for numbers with status "PRP" (i.e. in http://factordb.com/listtype.php?t=1))	http://factordb.com/index.php?query=%2841*13%5E%28n%2B1%29%2B27%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2345	DB₃₂₂₃₄	(206×16³²²³⁴−11)/15	32235	38815	http://factordb.com/index.php?id=1100000002383583629&open=prime	http://factordb.com/index.php?showid=1100000002383583629&base=16	http://factordb.com/index.php?showid=1100000002383583629	http://factordb.com/helper.php?id=1100000002383583629	http://factordb.com/cert.php?id=1100000002383583629&inputfile	http://factordb.com/index.php?query=%28206*16%5En-11%29%2F15&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2346	4₇₂₇₈₅DD	(4×16⁷²⁷⁸⁷+2291)/15	72787	87644	http://factordb.com/index.php?id=1100000003615909841&open=prime	http://factordb.com/index.php?showid=1100000003615909841&base=16	http://factordb.com/index.php?showid=1100000003615909841	http://factordb.com/helper.php?id=1100000003615909841	http://factordb.com/cert.php?id=1100000003615909841&inputfile	http://factordb.com/index.php?query=%284*16%5E%28n%2B2%29%2B2291%29%2F15&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2347	3₁₁₆₁₃₇AF	(16¹¹⁶¹³⁹+619)/5	116139	139845	http://factordb.com/index.php?id=1100000003851731988&open=prime	http://factordb.com/index.php?showid=1100000003851731988&base=16	http://factordb.com/index.php?showid=1100000003851731988	http://factordb.com/helper.php?id=1100000003851731988	http://factordb.com/cert.php?id=1100000003851731988&inputfile	http://factordb.com/index.php?query=%2816%5E%28n%2B2%29%2B619%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	8003	BK₂₂₀₀₁5	(251×22²²⁰⁰²−335)/21	22003	29538	http://factordb.com/index.php?id=1100000003594696838&open=prime	http://factordb.com/index.php?showid=1100000003594696838&base=22	http://factordb.com/index.php?showid=1100000003594696838	http://factordb.com/helper.php?id=1100000003594696838	http://factordb.com/cert.php?id=1100000003594696838&inputfile	http://factordb.com/index.php?query=%28251*22%5E%28n%2B1%29-335%29%2F21&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25250	5₁₉₃₉₁6F	(26¹⁹³⁹³+179)/5	19393	27440	http://factordb.com/index.php?id=1100000003850151202&open=prime	http://factordb.com/index.php?showid=1100000003850151202&base=26	http://factordb.com/index.php?showid=1100000003850151202	http://factordb.com/helper.php?id=1100000003850151202	http://factordb.com/cert.php?id=1100000003850151202&inputfile	http://factordb.com/index.php?query=%2826%5E%28n%2B2%29%2B179%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25251	7₂₀₂₇₉OL	(7×26²⁰²⁸¹+11393)/25	20281	28697	http://factordb.com/index.php?id=1100000003892628605&open=prime	http://factordb.com/index.php?showid=1100000003892628605&base=26	http://factordb.com/index.php?showid=1100000003892628605	http://factordb.com/helper.php?id=1100000003892628605	http://factordb.com/cert.php?id=1100000003892628605&inputfile	http://factordb.com/index.php?query=%287*26%5E%28n%2B2%29%2B11393%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25252	LD0₂₀₉₇₅7	559×26²⁰⁹⁷⁶+7	20978	29684	http://factordb.com/index.php?id=1100000003892628658&open=prime	http://factordb.com/index.php?showid=1100000003892628658&base=26	http://factordb.com/index.php?showid=1100000003892628658	http://factordb.com/helper.php?id=1100000003892628658	http://factordb.com/cert.php?id=1100000003892628658&inputfile	http://factordb.com/index.php?query=559*26%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25253	6K₂₃₃₀₀5	(34×26²³³⁰¹−79)/5	23302	32972	http://factordb.com/index.php?id=1100000003892628745&open=prime	http://factordb.com/index.php?showid=1100000003892628745&base=26	http://factordb.com/index.php?showid=1100000003892628745	http://factordb.com/helper.php?id=1100000003892628745	http://factordb.com/cert.php?id=1100000003892628745&inputfile	http://factordb.com/index.php?query=%2834*26%5E%28n%2B1%29-79%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25254	J0₄₄₃₀₃KCB	19×26⁴⁴³⁰⁶+13843	44307	62694	http://factordb.com/index.php?id=1100000003968156595&open=prime	http://factordb.com/index.php?showid=1100000003968156595&base=26	http://factordb.com/index.php?showid=1100000003968156595	http://factordb.com/helper.php?id=1100000003968156595	http://factordb.com/cert.php?id=1100000003968156595&inputfile	http://factordb.com/index.php?query=19*26%5E%28n%2B3%29%2B13843&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25255	M0₆₁₁₈₆2BB	22×26⁶¹¹⁸⁹+1649	61190	86583	http://factordb.com/index.php?id=1100000003968169875&open=prime	http://factordb.com/index.php?showid=1100000003968169875&base=26	http://factordb.com/index.php?showid=1100000003968169875	http://factordb.com/helper.php?id=1100000003968169875	http://factordb.com/cert.php?id=1100000003968169875&inputfile	http://factordb.com/index.php?query=22*26%5E%28n%2B3%29%2B1649&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25526	N6₂₄₀₅₁LR	(209×28²⁴⁰⁵³+3967)/9	24054	34810	http://factordb.com/index.php?id=1100000003879667576&open=prime	http://factordb.com/index.php?showid=1100000003879667576&base=28	http://factordb.com/index.php?showid=1100000003879667576	http://factordb.com/helper.php?id=1100000003879667576	http://factordb.com/cert.php?id=1100000003879667576&inputfile	http://factordb.com/index.php?query=%28209*28%5E%28n%2B2%29%2B3967%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25527	5OA₃₁₂₃₈F	(4438×28³¹²³⁹+125)/27	31241	45210	http://factordb.com/index.php?id=1100000003880455200&open=prime	http://factordb.com/index.php?showid=1100000003880455200&base=28	http://factordb.com/index.php?showid=1100000003880455200	http://factordb.com/helper.php?id=1100000003880455200	http://factordb.com/cert.php?id=1100000003880455200&inputfile	http://factordb.com/index.php?query=%284438*28%5E%28n%2B1%29%2B125%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25528	O4O₉₄₅₃₅9	(6092×28⁹⁴⁵³⁶−143)/9	94538	136812	http://factordb.com/index.php?id=1100000000808118231&open=prime	http://factordb.com/index.php?showid=1100000000808118231&base=28	http://factordb.com/index.php?showid=1100000000808118231	http://factordb.com/helper.php?id=1100000000808118231	http://factordb.com/cert.php?id=1100000000808118231&inputfile	http://factordb.com/index.php?query=%286092*28%5E%28n%2B1%29-143%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
30	2618	I0₂₄₆₀₈D	18×30²⁴⁶⁰⁹+13	24610	36352	http://factordb.com/index.php?id=1100000003593967511&open=prime	http://factordb.com/index.php?showid=1100000003593967511&base=30	http://factordb.com/index.php?showid=1100000003593967511	http://factordb.com/helper.php?id=1100000003593967511	http://factordb.com/cert.php?id=1100000003593967511&inputfile	http://factordb.com/index.php?query=18*30%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35284	7K₂₆₅₆₇Z	(53×36²⁶⁵⁶⁸+101)/7	26569	41349	http://factordb.com/index.php?id=1100000003896952461&open=prime	http://factordb.com/index.php?showid=1100000003896952461&base=36	http://factordb.com/index.php?showid=1100000003896952461	http://factordb.com/helper.php?id=1100000003896952461	http://factordb.com/cert.php?id=1100000003896952461&inputfile	http://factordb.com/index.php?query=%2853*36%5E%28n%2B1%29%2B101%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35285	S0₇₅₀₀₇8H	28×36⁷⁵⁰⁰⁹+305	75010	116739	http://factordb.com/index.php?id=1100000004020085177&open=prime	http://factordb.com/index.php?showid=1100000004020085177&base=36	http://factordb.com/index.php?showid=1100000004020085177	http://factordb.com/helper.php?id=1100000004020085177	http://factordb.com/cert.php?id=1100000004020085177&inputfile	http://factordb.com/index.php?query=28*36%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35286	P₈₁₉₉₃SZ	(5×36⁸¹⁹⁹⁵+821)/7	81995	127609	http://factordb.com/index.php?id=1100000002394962083&open=prime	http://factordb.com/index.php?showid=1100000002394962083&base=36	http://factordb.com/index.php?showid=1100000002394962083	http://factordb.com/helper.php?id=1100000002394962083	http://factordb.com/cert.php?id=1100000002394962083&inputfile	http://factordb.com/index.php?query=%285*36%5E%28n%2B2%29%2B821%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show

The unsolved families for bases b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 (the "easy" bases (bases b with ≤ 150 minimal primes > 10²⁹⁹ (base b = 26 has 82 known minimal (probable) primes > 10²⁹⁹ and 4 unsolved families, base b = 36 has 75 known minimal (probable) primes > 10²⁹⁹ and 4 unsolved families, base b = 17 has 99 known minimal (probable) primes > 10²⁹⁹ and 18 unsolved families, base b = 21 has 80 known minimal (probable) primes > 10²⁹⁹ and 12 unsolved families, base b = 19 has 201 known minimal (probable) primes > 10²⁹⁹ and 23 unsolved families))) and the factorization of the numbers in these families:

(you can calculate "equivalent searching limit of length in decimal" by: "current searching limit of length of this family" × log(b), where log is the common logarithm (https://en.wikipedia.org/wiki/Common_logarithm, https://mathworld.wolfram.com/CommonLogarithm.html), i.e. the logarithm with base 10)

b (2 ≤ b ≤ 36)	base-b form of the unsolved family	algebraic ((a×bⁿ+c)/gcd(a+c,b−1)) form of the unsolved family	current searching limit of length of this family	factorization of the first 200 numbers in this family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0))
17	1{7}	(23×17ⁿ−7)/16	100000	http://factordb.com/index.php?query=%2823*17%5En-7%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	1F{0}7	32×17ⁿ⁺¹+7	100000	http://factordb.com/index.php?query=32*17%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	4{7}A	(71×17ⁿ⁺¹+41)/16	100000	http://factordb.com/index.php?query=%2871*17%5E%28n%2B1%29%2B41%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	4{9}	(73×17ⁿ−9)/16	100000	http://factordb.com/index.php?query=%2873*17%5En-9%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	51{0}D	86×17ⁿ⁺¹+13	100000	http://factordb.com/index.php?query=86*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	70F{0}D	2038×17ⁿ⁺¹+13	100000	http://factordb.com/index.php?query=2038*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	8{B}9	(139×17ⁿ⁺¹−43)/16	100000	http://factordb.com/index.php?query=%28139*17%5E%28n%2B1%29-43%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	9{5}9	(149×17ⁿ⁺¹+59)/16	100000	http://factordb.com/index.php?query=%28149*17%5E%28n%2B1%29%2B59%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	95{F}	(2543×17ⁿ−15)/16	100000	http://factordb.com/index.php?query=%282543*17%5En-15%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	97{0}1	160×17ⁿ⁺¹+1	100000	http://factordb.com/index.php?query=160*17%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	A{D}F	(173×17ⁿ⁺¹+19)/16	100000	http://factordb.com/index.php?query=%28173*17%5E%28n%2B1%29%2B19%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	B{0}B3	11×17ⁿ⁺²+190	100000	http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B190&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	B{0}DB	11×17ⁿ⁺²+232	100000	http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B232&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	{B}E9	(11×17ⁿ⁺²+773)/16	100000	http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29%2B773%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	{B}EE	(11×17ⁿ⁺²+853)/16	100000	http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29%2B853%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	F1{9}	(4105×17ⁿ−9)/16	100000	http://factordb.com/index.php?query=%284105*17%5En-9%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	F7{0}1	262×17ⁿ⁺¹+1	100000	http://factordb.com/index.php?query=262*17%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	FD0{D}	(72909×17ⁿ−13)/16	100000	http://factordb.com/index.php?query=%2872909*17%5En-13%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	2{7}9D	(47×21ⁿ⁺²+953)/20	100000	http://factordb.com/index.php?query=%2847*21%5E%28n%2B2%29%2B953%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	2F{C}A	(288×21ⁿ⁺¹−13)/5	100000	http://factordb.com/index.php?query=%28288*21%5E%28n%2B1%29-13%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	5{0}DJ	5×21ⁿ⁺²+292	100000	http://factordb.com/index.php?query=5*21%5E%28n%2B2%29%2B292&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	{7}ID	(7×21ⁿ⁺²+4733)/20	100000	http://factordb.com/index.php?query=%287*21%5E%28n%2B2%29%2B4733%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	{9}D	(9×21ⁿ⁺¹+71)/20	100000	http://factordb.com/index.php?query=%289*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	B3{0}EB	234×21ⁿ⁺²+305	100000	http://factordb.com/index.php?query=234*21%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	B{H}6H	(237×21ⁿ⁺²−4637)/20	100000	http://factordb.com/index.php?query=%28237*21%5E%28n%2B2%29-4637%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	C{F}0K	(51×21ⁿ⁺²−1243)/4	100000	http://factordb.com/index.php?query=%2851*21%5E%28n%2B2%29-1243%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	F{9}D	(309×21ⁿ⁺¹+71)/20	100000	http://factordb.com/index.php?query=%28309*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	{F}35	(3×21ⁿ⁺²−1051)/4	100000	http://factordb.com/index.php?query=%283*21%5E%28n%2B2%29-1051%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	G{0}FK	16×21ⁿ⁺²+335	100000	http://factordb.com/index.php?query=16*21%5E%28n%2B2%29%2B335&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	H{0}7771	17×21ⁿ⁺⁴+68062	100000	http://factordb.com/index.php?query=17*21%5E%28n%2B4%29%2B68062&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	85{M}B	(5347×26ⁿ⁺¹−297)/25	100000	http://factordb.com/index.php?query=%285347*26%5E%28n%2B1%29-297%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	{A}6F	(2×26ⁿ⁺²−497)/5	486722	http://factordb.com/index.php?query=%282*26%5E%28n%2B2%29-497%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	{H}MH	(17×26ⁿ⁺²+3233)/25	100000	http://factordb.com/index.php?query=%2817*26%5E%28n%2B2%29%2B3233%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	{I}GL	(18×26ⁿ⁺²−1243)/25	497679	http://factordb.com/index.php?query=%2818*26%5E%28n%2B2%29-1243%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	O{A}F	(658×28ⁿ⁺¹+125)/27	543203	http://factordb.com/index.php?query=(658*28^(n%2B1)%2B125)/27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	B{0}EUV	11×36ⁿ⁺³+19255	100000	http://factordb.com/index.php?query=11*36%5E%28n%2B3%29%2B19255&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	HM{0}N	634×36ⁿ⁺¹+23	100000	http://factordb.com/index.php?query=634*36%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	N{0}YYN	23×36ⁿ⁺³+45311	100000	http://factordb.com/index.php?query=23*36%5E%28n%2B3%29%2B45311&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	O{L}Z	(123×36ⁿ⁺¹+67)/5	100000	http://factordb.com/index.php?query=%28123*36%5E%28n%2B1%29%2B67%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show

The large proven primes (> 10²⁹⁹) for bases b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 (the "easy" bases (bases b with ≤ 150 minimal primes > 10²⁹⁹ (base b = 26 has 82 known minimal (probable) primes > 10²⁹⁹ and 4 unsolved families, base b = 36 has 75 known minimal (probable) primes > 10²⁹⁹ and 4 unsolved families, base b = 17 has 99 known minimal (probable) primes > 10²⁹⁹ and 18 unsolved families, base b = 21 has 80 known minimal (probable) primes > 10²⁹⁹ and 12 unsolved families, base b = 19 has 201 known minimal (probable) primes > 10²⁹⁹ and 23 unsolved families))) and their primality certificates (https://en.wikipedia.org/wiki/Primality_certificate, https://t5k.org/glossary/xpage/Certificate.html, https://mathworld.wolfram.com/PrimalityCertificate.html, http://www.ellipsa.eu/public/primo/records.html, http://www.lix.polytechnique.fr/Labo/Francois.Morain/Primes/myprimes.html, https://stdkmd.net/nrr/cert/, https://alfredreichlg.de/cert/certificates.tpm.html, https://alfredreichlg.de/10w7/certifiedprimes.html, http://xenon.stanford.edu/~tjw/pp/index.html, http://factordb.com/certoverview.php, http://5.199.134.130/certificates.tar.xz, http://5.199.134.130/certificates.tar.xz.SHA256SUM, http://5.199.134.130/certificates.tar.xz.par2, http://5.199.134.130/certificates.tar.xz.vol00+10.par2, http://5.199.134.130/certificates/) and the factorization of the numbers in their corresponding families:

(In progess to add bases b = 17 and b = 21)

(link to the factorization of the first 200 numbers in corresponding families of these minimal primes (start with the smallest number in these families which is > b), to show the small prime factors (and their period) (i.e. show whether these numbers are rough numbers) and the algebraic factors (and their period) and let you feel the Nash weight (or difficulty) of these families (high or low), all small prime factors (< 10¹², by trial division (https://en.wikipedia.org/wiki/Trial_division, https://t5k.org/glossary/xpage/TrialDivision.html, https://www.rieselprime.de/ziki/Trial_factoring, https://mathworld.wolfram.com/TrialDivision.html, http://www.numericana.com/answer/factoring.htm#trial, https://www.mersenne.ca/tf1G/, https://www.mersenne.ca/tfmissed.php, https://oeis.org/A189172)) and all algebraic factors (https://en.wikipedia.org/w/index.php?title=Factorization&oldid=1143370673#Factoring_other_polynomials, https://mathworld.wolfram.com/PolynomialFactorization.html, http://www.numericana.com/answer/factoring.htm#special, https://stdkmd.net/nrr/repunit/repunitnote.htm#repunit_factorization, https://stdkmd.net/nrr/1/10004.htm#about_algebraic, https://stdkmd.net/nrr/1/10008.htm#about_algebraic, https://stdkmd.net/nrr/1/13333.htm#about_algebraic, https://stdkmd.net/nrr/3/39991.htm#about_algebraic, https://stdkmd.net/nrr/4/40001.htm#about_algebraic, https://stdkmd.net/nrr/4/49992.htm#about_algebraic, https://stdkmd.net/nrr/5/53333.htm#about_algebraic, https://stdkmd.net/nrr/5/53335.htm#about_algebraic, https://stdkmd.net/nrr/5/54444.htm#about_algebraic, https://stdkmd.net/nrr/5/55552.htm#about_algebraic, https://stdkmd.net/nrr/7/71111.htm#about_algebraic, https://stdkmd.net/nrr/7/79999.htm#about_algebraic, https://stdkmd.net/nrr/8/83333.htm#about_algebraic, https://stdkmd.net/nrr/8/83336.htm#about_algebraic, https://stdkmd.net/nrr/8/88878.htm#about_algebraic, https://stdkmd.net/nrr/8/88889.htm#about_algebraic, https://stdkmd.net/nrr/8/89996.htm#about_algebraic, https://stdkmd.net/nrr/8/89999.htm#about_algebraic, https://stdkmd.net/nrr/9/99919.htm#about_algebraic, https://stdkmd.net/nrr/9/99991.htm#about_algebraic, https://stdkmd.net/nrr/9/99992.htm#about_algebraic, http://mklasson.com/factors/viewlog.php?sort=2&order=desc&method=algebraic&maxrows=10000, https://sites.google.com/view/algebraic-factors-of-xn-kyn, https://sites.google.com/view/factorsofk2n-1foroddk20000, https://brnikat.com/nums/cullen_woodall/algebraic.txt, https://www.mersenneforum.org/showpost.php?p=96560&postcount=99, https://www.mersenneforum.org/showpost.php?p=96651&postcount=101, https://www.mersenneforum.org/showthread.php?t=21916, https://www.mersenneforum.org/showpost.php?p=196598&postcount=492, https://www.mersenneforum.org/showpost.php?p=203083&postcount=149, https://www.mersenneforum.org/showpost.php?p=206065&postcount=192, https://www.mersenneforum.org/showpost.php?p=208044&postcount=260, https://www.mersenneforum.org/showpost.php?p=210533&postcount=336, https://www.mersenneforum.org/showpost.php?p=452132&postcount=66, https://www.mersenneforum.org/showpost.php?p=451337&postcount=32, https://www.mersenneforum.org/showpost.php?p=208852&postcount=227, https://www.mersenneforum.org/showpost.php?p=232904&postcount=604, https://www.mersenneforum.org/showpost.php?p=383690&postcount=1, https://www.mersenneforum.org/showpost.php?p=207886&postcount=253, https://www.mersenneforum.org/showpost.php?p=452819&postcount=1445, https://www.numberempire.com/factoringcalculator.php, https://www.alpertron.com.ar/POLFACT.HTM, https://www.emathhelp.net/calculators/algebra-2/factoring-calculator/) of the N−1 (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1) and N+1 (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2) of these primes and the first 200 numbers (start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0)) in corresponding families of these primes were added to factordb (for the examples of the large primes whose N−1 or/and N+1 has algebraic factors, see https://stdkmd.net/nrr/cert/1/#CERT_11101_4809 and https://stdkmd.net/nrr/cert/1/#CERT_15551_2197 and https://stdkmd.net/nrr/cert/1/#CERT_16667_4296 and https://stdkmd.net/nrr/cert/2/#CERT_20111_2692 and https://stdkmd.net/nrr/cert/2/#CERT_23309_10029 and https://stdkmd.net/nrr/cert/3/#CERT_37773_15768 and https://stdkmd.net/nrr/cert/6/#CERT_6805W7_3739 and https://stdkmd.net/nrr/cert/6/#CERT_68883_5132 and https://stdkmd.net/nrr/cert/7/#CERT_79921_11629 and https://stdkmd.net/nrr/cert/8/#CERT_80081_5736 and https://stdkmd.net/nrr/cert/8/#CERT_83W16W7_543 and https://stdkmd.net/nrr/cert/9/#CERT_93307_2197 for the related numbers (although some of them are related to Cunningham numbers, and some of them has N−1 and N+1 does not have algebraic factors but has a large prime factor), e.g. "11101_4809" (decimal (base b = 10) form: 1₄₈₀₇01, algebraic form: (10⁴⁸⁰⁹−91)/9) is related to "Phi_4807_10" (the number Φ₄₈₀₇(10), where Φ is the cyclotomic polynomial), "15551_2197" (decimal (base b = 10) form: 15₂₁₉₆1, algebraic form: (14×10²¹⁹⁷−41)/9, the prime is a cofactor of it (divided it by 11×23×167)) is related to "93307_2197" (decimal (base b = 10) form: 93₂₁₉₅07, algebraic form: (28×10²¹⁹⁷−79)/3), "16667_4296" (decimal (base b = 10) form: 16₄₂₉₅7, algebraic form: (5×10⁴²⁹⁶+1)/3, the prime is a cofactor of it (divided it by 347×821×140235709×806209146522749)) is related to "33337_12891" (decimal (base b = 10) form: 3₁₂₈₉₀7, algebraic form: (10¹²⁸⁹¹+11)/3), "20111_2692" (decimal (base b = 10) form: 201₂₆₉₂, algebraic form: (181×10²⁶⁹²−1)/9, the prime is a cofactor of it (divided it by 3×43)) is related to "20111_2693" (decimal (base b = 10) form: 201₂₆₉₃, algebraic form: (181×10²⁶⁹³−1)/9), "23309_10029" (decimal (base b = 10) form: 23₁₀₀₂₇09, algebraic form: (7×10¹⁰⁰²⁹−73)/3) is related to "Phi_5014_10" (the number Φ₅₀₁₄(10), where Φ is the cyclotomic polynomial), "37773_15768" (decimal (base b = 10) form: 37₁₅₇₆₇3, algebraic form: (34×10¹⁵⁷⁶⁸−43)/9) is related to "Phi_7884_10" (the number Φ₇₈₈₄(10), where Φ is the cyclotomic polynomial), "6805w7_3739" (decimal (base b = 10) form: 6805₃₇₃₈7, algebraic form: (6125×10³⁷³⁹+13)/9, the prime is a cofactor of it (divided it by 3²)) is related to "27227_3741" (decimal (base b = 10) form: 272₃₇₄₀7, algebraic form: (245×10³⁷⁴¹+43)/9), "68883_5132" (decimal (base b = 10) form: 68₅₁₃₁3, algebraic form: (62×10⁵¹³²−53)/9) is related to "Phi_1283_10" (the number Φ₁₂₈₃(10), where Φ is the cyclotomic polynomial), "79921_11629" (decimal (base b = 10) form: 79₁₁₆₂₇21, algebraic form: 8×10¹¹⁶²⁹−79) is related to "Phi_2907_10" (the number Φ₂₉₀₇(10), where Φ is the cyclotomic polynomial), "80081_5736" (decimal (base b = 10) form: 80₅₇₃₄81, algebraic form: 8×10⁵⁷³⁶+81) is related to "Phi_11470_10" (the number Φ₁₁₄₇₀(10), where Φ is the cyclotomic polynomial), "83w16w7_543" (decimal (base b = 10) form: 83₅₄₂16₅₄₂7, algebraic form: (25×10¹⁰⁸⁶−5×10⁵⁴³+1)/3, the prime is a cofactor of it (divided it by 7×109×563041×869047141×147372142447)) is related to "11103_3258" (decimal (base b = 10) form: 1₃₂₅₆03, algebraic form: (10³²⁵⁸−73)/9), etc. the N−1 of "11101_4809" is 100 × R₄₈₀₇(10) (which is equivalent to the Cunningham number 10⁴⁸⁰⁷−1) and Φ₄₈₀₇(10) is an algebraic factor of the Cunningham number 10⁴⁸⁰⁷−1, the N−1 of "93307_2197" is 6 × "15551_2197", the N−1 of "33337_12891" has sum-of-two-cubes factorization and an algebraic factor is 2 × "16667_4296", the N−1 of "20111_2693" is 10 × "20111_2692", the N+1 of "23309_10029" is 210 × R₁₀₀₂₈(10) (which is equivalent to the Cunningham number 10¹⁰⁰²⁸−1) and Φ₅₀₁₄(10) is an algebraic factor of the Cunningham number 10¹⁰⁰²⁸−1, the N+1 of "37773_15768" is 34 × R₁₅₇₆₈(10) (which is equivalent to the Cunningham number 10¹⁵⁷⁶⁸−1) and Φ₇₈₈₄(10) is an algebraic factor of the Cunningham number 10¹⁵⁷⁶⁸−1, the N+1 of "27227_3741" is 4 × "6805w7_3739", the N−1 of "68883_5132" is 62 × R₅₁₃₂(10) (which is equivalent to the Cunningham number 10⁵¹³²−1) and Φ₁₂₈₃(10) is an algebraic factor of the Cunningham number 10⁵¹³²−1, the N−1 of "79921_11629" is 720 × R₁₁₆₂₈(10) (which is equivalent to the Cunningham number 10¹¹⁶²⁸−1) and Φ₂₉₀₇(10) is an algebraic factor of the Cunningham number 10¹¹⁶²⁸−1, the N−1 of "80081_5736" is 80 × S₅₇₃₅(10) (which is equivalent to the Cunningham number 10⁵⁷³⁵+1) and Φ₁₁₄₇₀(10) is an algebraic factor of the Cunningham number 10⁵⁷³⁵+1, the N+1 of "11103_3258" has difference-of-two-6th-powers factorization and an algebraic factor is 4 × "83w16w7_543", etc.), unfortunately, the only numbers having algebraic factors (other than trivially (https://en.wikipedia.org/wiki/Triviality_(mathematics), https://mathworld.wolfram.com/Trivial.html) fully factored (i.e. primes of the form k×bⁿ±1, with small k) and Cunningham numbers (of the form bⁿ±1, see https://en.wikipedia.org/wiki/Cunningham_number, https://mathworld.wolfram.com/CunninghamNumber.html, https://www.numbersaplenty.com/set/Cunningham_number/, https://en.wikipedia.org/wiki/Cunningham_Project, https://t5k.org/glossary/xpage/CunninghamProject.html, https://www.rieselprime.de/ziki/Cunningham_project, https://oeis.org/wiki/OEIS_sequences_needing_factors#Cunningham_numbers (sections "b = 2" and "b = 3" and "b = 10" and "other integer b"), https://homes.cerias.purdue.edu/~ssw/cun/index.html, https://maths-people.anu.edu.au/~brent/factors.html, https://web.archive.org/web/20190315214330/http://cage.ugent.be/~jdemeyer/cunningham/, http://myfactors.mooo.com/, https://doi.org/10.1090/conm/022, https://www.mersenneforum.org/attachment.php?attachmentid=7727&d=1330555980 (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_7.pdf), https://homes.cerias.purdue.edu/~ssw/cun/mine.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_6.pdf), http://homes.cerias.purdue.edu/~ssw/cun1.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_71.pdf)), which are in the "README" file of the "primality-certificates" folder: https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/primality-certificates/README.md) are 17ⁿ⁺²+32 (the corresponding family of the 10400th minimal prime in base b = 17, 10₉₀₁₉1F = 17⁹⁰²¹+32) with n == 3 mod 5 (which has sum-of-two-5th-powers factorization and can be factored to (17^(n+2)/5+2) × (17^4×(n+2)/5−2×17^3×(n+2)/5+4×17^2×(n+2)/5−8×17^(n+2)/5+16)) and 8×18²⁹⁹+12 (the N+1 of the 547th minimal prime in base b = 18, 80₂₉₈B = 8×18²⁹⁹+11) (which has sum-of-two-cubes factorization and can be factored to 12 × (6×18⁹⁹+1) × (2×18¹⁹⁹−6×18⁹⁹+1)) and 18⁷⁶⁸−36 (the N+1 of the 548th minimal prime in base b = 18, H₇₆₆FH = 18⁷⁶⁸−37) (which has difference-of-two-squares factorization and can be factored to (18³⁸⁴−6) × (18³⁸⁴+6)) and (16×20ⁿ⁺²−2809)/19 (the corresponding family of the 3307th minimal prime in base b = 20, G₄₄₇99 = (16×20⁴⁴⁹−2809)/19) with even n (which has difference-of-two-squares factorization and can be factored to (4×20^(n+2)/2−53) × (4×20^(n+2)/2+53) / 19) and 9×21²⁹⁷+243 (the N−1 of the 13316th minimal prime in base b = 21, 90₂₉₅BD = 9×21²⁹⁷+244) (which has sum-of-two-cubes factorization and can be factored to 9 × (21⁹⁹+3) × (21¹⁹⁸−3×21⁹⁹+9)) and (22ⁿ⁺²−289)/3 (the corresponding family of the 8002nd minimal prime in base b = 22, 7₃₈₁₅2L = (22³⁸¹⁷−289)/3) with even n (which has difference-of-two-squares factorization and can be factored to (22^(n+2)/2−17) × (22^(n+2)/2+17) / 3) and (121×26ⁿ−1)/5 (the corresponding family of the 25235th minimal prime in base b = 26, O5₁₅₀₉ = (121×26¹⁵⁰⁹−1)/5) with even n (which has difference-of-two-squares factorization and can be factored to (11×26^n/2−1) × (11×26^n/2+1) / 5) and 25×30ⁿ−1 (the corresponding family of the 2619th minimal prime in base b = 30, OT₃₄₂₀₅ = 25×30³⁴²⁰⁵−1) with even n (which has difference-of-two-squares factorization and can be factored to (5×30^n/2−1) × (5×30^n/2+1)) and 27×36⁴⁵⁹+8 (the N+1 of the 35244th minimal prime in base b = 36, R0₄₅₈7 = 27×36⁴⁵⁹+7) (which has sum-of-two-cubes factorization and can be factored to (3×36¹⁵³+2) × (9×36³⁰⁶−6×36¹⁵³+4)) (of course, 13ⁿ−49 (the N+1 of the 3193rd minimal prime in base b = 13, C₁₀₆₃₁92 = 13¹⁰⁶³³−50, is 13¹⁰⁶³³−49) has difference-of-two-squares factorization (factored to (13^n/2−7) × (13^n/2+7)) if n is even, but 10633 is odd) (of course, (9×17ⁿ−121)/16 (the N+1 of the 10320th minimal prime in base b = 17, 9₂₉₂1 = (9×17²⁹³−137)/16, is (9×17²⁹³−121)/16) has difference-of-two-squares factorization (factored to (3×17^n/2−11) × (3×17^n/2+11) / 16) if n is even, but 293 is odd) (of course, 22ⁿ−128 (the N+1 of the 7995th minimal prime in base b = 22, L₄₈₃G3 = 22⁴⁸⁵−129, is 22⁴⁸⁵−128) has difference-of-two-7th-powers factorization (factored to (22^n/7−2) × (22^6×n/7+2×22^5×n/7+4×22^4×n/7+8×22^3×n/7+16×22^2×n/7+32×22^n/7+64)) if n is divisible by 7, but 485 is not divisible by 7) (of course, 2×24ⁿ+6 (the N−1 of the 3403rd minimal prime in base b = 24, 20₃₁₃7 = 2×24³¹⁴+7, is 2×24³¹⁴+6) has sum-of-two-cubes factorization (factored to 6 × (2×24^(n−1)/3+1) × (4×24^2×(n−1)/3−2×24^(n−1)/3+1)) if n == 1 mod 3, but 314 is not == 1 mod 3) (of course, 2×24ⁿ+8 (the N+1 of the 3403rd minimal prime in base b = 24, 20₃₁₃7 = 2×24³¹⁴+7, is 2×24³¹⁴+8) has Aurifeuillean factorization of x⁴+4×y⁴ (factored to 2 × (24^n/2−2×24^n/4+2) × (24^n/2+2×24^n/4+2)) if n is divisible by 4, but 314 is not divisible by 4) (of course, 4×13ⁿ+1 has Aurifeuillean factorization of x⁴+4×y⁴ (factored to (2×13^n/2−2×13^n/4+1) × (2×13^n/2+2×13^n/4+1)) if n is divisible by 4, but 16×13ⁿ+1 (which is a factor of 128×13ⁿ+8, the N−1 of the 3173rd minimal prime in base b = 13, 9B0₃₉₁9 = 128×13³⁹²+9, is 128×13³⁹²+8) has no algebraic factors for any n, xⁿ+16×yⁿ has no algebraic factors for any n (while xⁿ+4×yⁿ has algebraic factors for n divisible by 4, xⁿ+8×yⁿ has algebraic factors for n divisible by 3, xⁿ+32×yⁿ has algebraic factors for n divisible by 5, xⁿ+64×yⁿ has algebraic factors for n divisible by 3 or/and 4), for the references see https://stdkmd.net/nrr/5/50008.htm and https://stdkmd.net/nrr/8/80005.htm, neither of them has the "Algebraic factorization" section) (of course, 22ⁿ+4 has Aurifeuillean factorization of x⁴+4×y⁴ (factored to (22^n/2−2×22^n/4+2) × (22^n/2+2×22^n/4+2)) if n is divisible by 4, but 22ⁿ+16 (which is a factor of 20×22ⁿ⁺¹+7040, the N−1 of the 7998th minimal prime in base b = 22, K0₇₆₀EC1 = 20×22⁷⁶³+7041, is 20×22⁷⁶³+7040) has no algebraic factors for any n, xⁿ+16×yⁿ has no algebraic factors for any n (while xⁿ+4×yⁿ has algebraic factors for n divisible by 4, xⁿ+8×yⁿ has algebraic factors for n divisible by 3, xⁿ+32×yⁿ has algebraic factors for n divisible by 5, xⁿ+64×yⁿ has algebraic factors for n divisible by 3 or/and 4), for the references see https://stdkmd.net/nrr/5/50008.htm and https://stdkmd.net/nrr/8/80005.htm, neither of them has the "Algebraic factorization" section))

(if the prime is (a×bⁿ+c)/gcd(a+c,b−1) (with a ≥ 1, b ≥ 2, c ≠ 0, gcd(a,c) = 1, gcd(b,c) = 1), then its N−1 is (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1), and its N+1 is (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1), although (a×bⁿ+c)/gcd(a+c,b−1) (with a ≥ 1, b ≥ 2, c ≠ 0, gcd(a,c) = 1, gcd(b,c) = 1) has algebraic factorization if and only if either "there is an integer r > 1 such that a×bⁿ and −c are both rth powers" (in this case, (a×bⁿ+c)/gcd(a+c,b−1) has sum-of-two-rth-powers factorization if c > 0, or difference-of-two-rth-powers factorization if c < 0, although there is no "sum-of-two-rth-powers factorization" for even r, but no such situation (i.e. c > 0 and r is even) exists, since if c > 0 then −c < 0, but negative numbers cannot be squares, however, if r is even then all rth powers are squares (since if s divides r, then all rth powers are sth powers), thus, −c cannot be an rth power if c > 0 and r is even) or "one of a×bⁿ and c is a 4th power, and the other is of the form 4×m⁴" (in this case, (a×bⁿ+c)/gcd(a+c,b−1) has Aurifeuillean factorization of x⁴+4×y⁴), however, since c−gcd(a+c,b−1) and c+gcd(a+c,b−1) may not coprime to a and b, it is not that simple to known whether (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) and (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) have algebraic factorization (however, if there is a prime p divides a but not divides b or c−gcd(a+c,b−1), and p² does not divide a, then (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) does not have algebraic factorization, also, if there is a prime p divides a but not divides either b or c+gcd(a+c,b−1), and p² does not divide a, then (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) does not have algebraic factorization, also, if there is a prime p divides c−gcd(a+c,b−1) but not divides a or b, and p² does not divide c−gcd(a+c,b−1), then (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) does not have algebraic factorization, also, if there is a prime p divides c+gcd(a+c,b−1) but not divides either a or b, and p² does not divide c+gcd(a+c,b−1), then (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) does not have algebraic factorization), (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) has algebraic factorization if and only if either "c−gcd(a+c,b−1) = 0" (if and only if c−gcd(a+c,b−1) = 0, then (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) is trivially fully factored) or "there is an integer r > 1 such that a×bⁿ/gcd(a×bⁿ,c−gcd(a+c,b−1)) and −(c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) are both rth powers" (in this case, (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) has sum-of-two-rth-powers factorization if (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) > 0, or difference-of-two-rth-powers factorization if (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) < 0, although there is no "sum-of-two-rth-powers factorization" for even r, but no such situation (i.e. (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) > 0 and r is even) exists, since if (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) > 0 then −(c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) < 0, but negative numbers cannot be squares, however, if r is even then all rth powers are squares (since if s divides r, then all rth powers are sth powers), thus, −(c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) cannot be an rth power if (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) > 0 and r is even) or "one of a×bⁿ/gcd(a×bⁿ,c−gcd(a+c,b−1)) and (c−gcd(a+c,b−1))/gcd(a×bⁿ,c−gcd(a+c,b−1)) is a 4th power, and the other is of the form 4×m⁴" (in this case, (a×bⁿ+c−gcd(a+c,b−1))/gcd(a+c,b−1) has Aurifeuillean factorization of x⁴+4×y⁴), (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) has algebraic factorization if and only if either "c+gcd(a+c,b−1) = 0" (if and only if c+gcd(a+c,b−1) = 0, then (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) is trivially fully factored) or "there is an integer r > 1 such that a×bⁿ/gcd(a×bⁿ,c+gcd(a+c,b−1)) and −(c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) are both rth powers" (in this case, (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) has sum-of-two-rth-powers factorization if (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) > 0, or difference-of-two-rth-powers factorization if (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) < 0, although there is no "sum-of-two-rth-powers factorization" for even r, but no such situation (i.e. (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) > 0 and r is even) exists, since if (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) > 0 then −(c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) < 0, but negative numbers cannot be squares, however, if r is even then all rth powers are squares (since if s divides r, then all rth powers are sth powers), thus, −(c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) cannot be an rth power if (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) > 0 and r is even) or "one of a×bⁿ/gcd(a×bⁿ,c+gcd(a+c,b−1)) and (c+gcd(a+c,b−1))/gcd(a×bⁿ,c+gcd(a+c,b−1)) is a 4th power, and the other is of the form 4×m⁴" (in this case, (a×bⁿ+c+gcd(a+c,b−1))/gcd(a+c,b−1) has Aurifeuillean factorization of x⁴+4×y⁴))

b (2 ≤ b ≤ 36)	index of this minimal prime in base b	base-b form of this minimal prime	algebraic ((a×bⁿ+c)/gcd(a+c,b−1)) form of this minimal prime	length of this minimal prime written in base b	length of this minimal prime written in decimal	factordb entry of this minimal prime	this minimal prime written in base b (use lower case letters instead of upper case letters)	this minimal prime written in decimal	helper file of this minimal prime	primality certificate of this minimal prime	certificate chain of this minimal prime (for the minimal primes which are proven prime by primality certificate) or factorization of N−1 or N+1 (for the minimal primes which are proven prime by N−1 test or N+1 test)	factorization of the first 200 numbers in corresponding family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0) of this minimal prime)
9	149	76₃₂₉2	(31×9³³⁰−19)/4	331	316	http://factordb.com/index.php?id=1100000002359003642&open=prime	http://factordb.com/index.php?showid=1100000002359003642&base=9	http://factordb.com/index.php?showid=1100000002359003642	http://factordb.com/helper.php?id=1100000002359003642	http://factordb.com/cert.php?id=1100000002359003642	http://factordb.com/certchain.php?fid=1100000002359003642&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2831*9%5E%28n%2B1%29-19%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	150	27₆₈₆07	(23×9⁶⁸⁸−511)/8	689	657	http://factordb.com/index.php?id=1100000002495467486&open=prime	http://factordb.com/index.php?showid=1100000002495467486&base=9	http://factordb.com/index.php?showid=1100000002495467486	http://factordb.com/helper.php?id=1100000002495467486	http://factordb.com/cert.php?id=1100000002495467486	http://factordb.com/certchain.php?fid=1100000002495467486&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2823*9%5E%28n%2B2%29-511%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
9	151	30₁₁₅₈11	3×9¹¹⁶⁰+10	1161	1108	http://factordb.com/index.php?id=1100000002376318423&open=prime	http://factordb.com/index.php?showid=1100000002376318423&base=9	http://factordb.com/index.php?showid=1100000002376318423	http://factordb.com/helper.php?id=1100000002376318423	http://factordb.com/cert.php?id=1100000002376318423	http://factordb.com/certchain.php?fid=1100000002376318423&action=all&fr=0&to=100	http://factordb.com/index.php?query=3*9%5E%28n%2B2%29%2B10&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	1065	A₇₁₃58	11⁷¹⁵−58	715	745	http://factordb.com/index.php?id=1100000003576826487&open=prime	http://factordb.com/index.php?showid=1100000003576826487&base=11	http://factordb.com/index.php?showid=1100000003576826487	http://factordb.com/helper.php?id=1100000003576826487	http://factordb.com/cert.php?id=1100000003576826487	http://factordb.com/certchain.php?fid=1100000003576826487&action=all&fr=0&to=100	http://factordb.com/index.php?query=11%5E%28n%2B2%29-58&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	1066	7₇₅₉44	(7×11⁷⁶¹−367)/10	761	793	http://factordb.com/index.php?id=1100000002505568840&open=prime	http://factordb.com/index.php?showid=1100000002505568840&base=11	http://factordb.com/index.php?showid=1100000002505568840	http://factordb.com/helper.php?id=1100000002505568840	http://factordb.com/cert.php?id=1100000002505568840	http://factordb.com/certchain.php?fid=1100000002505568840&action=all&fr=0&to=100	http://factordb.com/index.php?query=%287*11%5E%28n%2B2%29-367%29%2F10&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
11	1067	557₁₀₁₁	(607×11¹⁰¹¹−7)/10	1013	1055	http://factordb.com/index.php?id=1100000002361376522&open=prime	http://factordb.com/index.php?showid=1100000002361376522&base=11	http://factordb.com/index.php?showid=1100000002361376522	http://factordb.com/helper.php?id=1100000002361376522	http://factordb.com/cert.php?id=1100000002361376522	http://factordb.com/certchain.php?fid=1100000002361376522&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28607*11%5En-7%29%2F10&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3165	50₂₇₀44	5×13²⁷²+56	273	304	http://factordb.com/index.php?id=1100000002632397005&open=prime	http://factordb.com/index.php?showid=1100000002632397005&base=13	http://factordb.com/index.php?showid=1100000002632397005	http://factordb.com/helper.php?id=1100000002632397005	http://factordb.com/cert.php?id=1100000002632397005	http://factordb.com/certchain.php?fid=1100000002632397005&action=all&fr=0&to=100	http://factordb.com/index.php?query=5*13%5E%28n%2B2%29%2B56&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3166	9₂₇₁095	(3×13²⁷⁴−6103)/4	274	306	http://factordb.com/index.php?id=1100000003590431654&open=prime	http://factordb.com/index.php?showid=1100000003590431654&base=13	http://factordb.com/index.php?showid=1100000003590431654	http://factordb.com/helper.php?id=1100000003590431654	http://factordb.com/cert.php?id=1100000003590431654	http://factordb.com/certchain.php?fid=1100000003590431654&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283*13%5E%28n%2B3%29-6103%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3167	10₂₈₆7771	13²⁹⁰+16654	291	324	http://factordb.com/index.php?id=1100000003590431633&open=prime	http://factordb.com/index.php?showid=1100000003590431633&base=13	http://factordb.com/index.php?showid=1100000003590431633	http://factordb.com/helper.php?id=1100000003590431633	http://factordb.com/cert.php?id=1100000003590431633	http://factordb.com/certchain.php?fid=1100000003590431633&action=all&fr=0&to=100	http://factordb.com/index.php?query=13%5E%28n%2B4%29%2B16654&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3168	9₃₀₈1	(3×13³⁰⁹−35)/4	309	345	http://factordb.com/index.php?id=1100000000840126705&open=prime	http://factordb.com/index.php?showid=1100000000840126705&base=13	http://factordb.com/index.php?showid=1100000000840126705	http://factordb.com/helper.php?id=1100000000840126705	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is 39/4×(13³⁰⁸−1), thus factor N−1 is equivalent to factor 13³⁰⁸−1, and for the factorization of 13³⁰⁸−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=308&c0=-&EN=	http://factordb.com/index.php?id=1100000000840126706&open=ecm	http://factordb.com/index.php?query=%283*13%5E%28n%2B1%29-35%29%2F4&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3169	B₃₄₁C4	(11×13³⁴³+61)/12	343	383	http://factordb.com/index.php?id=1100000003590431618&open=prime	http://factordb.com/index.php?showid=1100000003590431618&base=13	http://factordb.com/index.php?showid=1100000003590431618	http://factordb.com/helper.php?id=1100000003590431618	http://factordb.com/cert.php?id=1100000003590431618	http://factordb.com/certchain.php?fid=1100000003590431618&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2811*13%5E%28n%2B2%29%2B61%29%2F12&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3170	8B₃₄₃	(107×13³⁴³−11)/12	344	384	http://factordb.com/index.php?id=1100000002321018736&open=prime	http://factordb.com/index.php?showid=1100000002321018736&base=13	http://factordb.com/index.php?showid=1100000002321018736	http://factordb.com/helper.php?id=1100000002321018736	http://factordb.com/cert.php?id=1100000002321018736	http://factordb.com/certchain.php?fid=1100000002321018736&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28107*13%5En-11%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3171	710₃₇₁111	92×13³⁷⁴+183	376	419	http://factordb.com/index.php?id=1100000003590431609&open=prime	http://factordb.com/index.php?showid=1100000003590431609&base=13	http://factordb.com/index.php?showid=1100000003590431609	http://factordb.com/helper.php?id=1100000003590431609	http://factordb.com/cert.php?id=1100000003590431609	http://factordb.com/certchain.php?fid=1100000003590431609&action=all&fr=0&to=100	http://factordb.com/index.php?query=92*13%5E%28n%2B3%29%2B183&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3172	75₃₇₅7	(89×13³⁷⁶+19)/12	377	420	http://factordb.com/index.php?id=1100000003590431596&open=prime	http://factordb.com/index.php?showid=1100000003590431596&base=13	http://factordb.com/index.php?showid=1100000003590431596	http://factordb.com/helper.php?id=1100000003590431596	http://factordb.com/cert.php?id=1100000003590431596	http://factordb.com/certchain.php?fid=1100000003590431596&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2889*13%5E%28n%2B1%29%2B19%29%2F12&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3173	9B0₃₉₁9	128×13³⁹²+9	394	439	http://factordb.com/index.php?id=1100000002632396790&open=prime	http://factordb.com/index.php?showid=1100000002632396790&base=13	http://factordb.com/index.php?showid=1100000002632396790	http://factordb.com/helper.php?id=1100000002632396790	http://factordb.com/cert.php?id=1100000002632396790	http://factordb.com/certchain.php?fid=1100000002632396790&action=all&fr=0&to=100	http://factordb.com/index.php?query=128*13%5E%28n%2B1%29%2B9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3174	7B0B₃₉₇	(15923×13³⁹⁷−11)/12	400	446	http://factordb.com/index.php?id=1100000003590431574&open=prime	http://factordb.com/index.php?showid=1100000003590431574&base=13	http://factordb.com/index.php?showid=1100000003590431574	http://factordb.com/helper.php?id=1100000003590431574	http://factordb.com/cert.php?id=1100000003590431574	http://factordb.com/certchain.php?fid=1100000003590431574&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2815923*13%5En-11%29%2F12&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3175	10₄₁₄93	13⁴¹⁶+120	417	464	http://factordb.com/index.php?id=1100000002523249240&open=prime	http://factordb.com/index.php?showid=1100000002523249240&base=13	http://factordb.com/index.php?showid=1100000002523249240	http://factordb.com/helper.php?id=1100000002523249240	http://factordb.com/cert.php?id=1100000002523249240	http://factordb.com/certchain.php?fid=1100000002523249240&action=all&fr=0&to=100	http://factordb.com/index.php?query=13%5E%28n%2B2%29%2B120&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3176	81010₄₁₅1	17746×13⁴¹⁶+1	420	468	http://factordb.com/index.php?id=1100000003590431555&open=prime	http://factordb.com/index.php?showid=1100000003590431555&base=13	http://factordb.com/index.php?showid=1100000003590431555	http://factordb.com/helper.php?id=1100000003590431555	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is trivially fully factored	http://factordb.com/index.php?id=1100000003590431556&open=ecm	http://factordb.com/index.php?query=17746*13%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3177	8110₄₃₅1	1366×13⁴³⁶+1	439	489	http://factordb.com/index.php?id=1100000002373259109&open=prime	http://factordb.com/index.php?showid=1100000002373259109&base=13	http://factordb.com/index.php?showid=1100000002373259109	http://factordb.com/helper.php?id=1100000002373259109	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is trivially fully factored	http://factordb.com/index.php?id=1100000002373259124&open=ecm	http://factordb.com/index.php?query=1366*13%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3178	B7₄₈₆	(139×13⁴⁸⁶−7)/12	487	543	http://factordb.com/index.php?id=1100000002321015892&open=prime	http://factordb.com/index.php?showid=1100000002321015892&base=13	http://factordb.com/index.php?showid=1100000002321015892	http://factordb.com/helper.php?id=1100000002321015892	http://factordb.com/cert.php?id=1100000002321015892	http://factordb.com/certchain.php?fid=1100000002321015892&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28139*13%5En-7%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3179	B₅₆₃C	(11×13⁵⁶⁴+1)/12	564	629	http://factordb.com/index.php?id=1100000000000217927&open=prime	http://factordb.com/index.php?showid=1100000000000217927&base=13	http://factordb.com/index.php?showid=1100000000000217927	http://factordb.com/helper.php?id=1100000000000217927	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is 11/12×(13⁵⁶⁴−1), thus factor N−1 is equivalent to factor 13⁵⁶⁴−1, and for the factorization of 13⁵⁶⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=564&c0=-&EN=	http://factordb.com/index.php?id=1100000000271764311&open=ecm	http://factordb.com/index.php?query=%2811*13%5E%28n%2B1%29%2B1%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3180	1B₅₇₆	(23×13⁵⁷⁶−11)/12	577	642	http://factordb.com/index.php?id=1100000002321021456&open=prime	http://factordb.com/index.php?showid=1100000002321021456&base=13	http://factordb.com/index.php?showid=1100000002321021456	http://factordb.com/helper.php?id=1100000002321021456	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is 23/12×(13⁵⁷⁶−1), thus factor N−1 is equivalent to factor 13⁵⁷⁶−1, and for the factorization of 13⁵⁷⁶−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=576&c0=-&EN=	http://factordb.com/index.php?id=1100000002321021531&open=ecm	http://factordb.com/index.php?query=%2823*13%5En-11%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3181	80₆₉₃87	8×13⁶⁹⁵+111	696	776	http://factordb.com/index.php?id=1100000002615636527&open=prime	http://factordb.com/index.php?showid=1100000002615636527&base=13	http://factordb.com/index.php?showid=1100000002615636527	http://factordb.com/helper.php?id=1100000002615636527	http://factordb.com/cert.php?id=1100000002615636527	http://factordb.com/certchain.php?fid=1100000002615636527&action=all&fr=0&to=100	http://factordb.com/index.php?query=8*13%5E%28n%2B2%29%2B111&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3182	CC5₇₁₃	(2021×13⁷¹³−5)/12	715	797	http://factordb.com/index.php?id=1100000002615627353&open=prime	http://factordb.com/index.php?showid=1100000002615627353&base=13	http://factordb.com/index.php?showid=1100000002615627353	http://factordb.com/helper.php?id=1100000002615627353	http://factordb.com/cert.php?id=1100000002615627353	http://factordb.com/certchain.php?fid=1100000002615627353&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282021*13%5En-5%29%2F12&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3183	B₈₃₄74	(11×13⁸³⁶−719)/12	836	932	http://factordb.com/index.php?id=1100000003590430871&open=prime	http://factordb.com/index.php?showid=1100000003590430871&base=13	http://factordb.com/index.php?showid=1100000003590430871	http://factordb.com/helper.php?id=1100000003590430871	http://factordb.com/cert.php?id=1100000003590430871	http://factordb.com/certchain.php?fid=1100000003590430871&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2811*13%5E%28n%2B2%29-719%29%2F12&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3184	9₉₆₈B	(3×13⁹⁶⁹+5)/4	969	1080	http://factordb.com/index.php?id=1100000000258566244&open=prime	http://factordb.com/index.php?showid=1100000000258566244&base=13	http://factordb.com/index.php?showid=1100000000258566244	http://factordb.com/helper.php?id=1100000000258566244	http://factordb.com/cert.php?id=1100000000258566244	http://factordb.com/certchain.php?fid=1100000000258566244&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283*13%5E%28n%2B1%29%2B5%29%2F4&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3185	10₁₂₉₅181	13¹²⁹⁸+274	1299	1446	http://factordb.com/index.php?id=1100000002615445013&open=prime	http://factordb.com/index.php?showid=1100000002615445013&base=13	http://factordb.com/index.php?showid=1100000002615445013	http://factordb.com/helper.php?id=1100000002615445013	http://factordb.com/cert.php?id=1100000002615445013	http://factordb.com/certchain.php?fid=1100000002615445013&action=all&fr=0&to=100	http://factordb.com/index.php?query=13%5E%28n%2B3%29%2B274&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3186	9₁₃₆₂5	(3×13¹³⁶³−19)/4	1363	1519	http://factordb.com/index.php?id=1100000002321017776&open=prime	http://factordb.com/index.php?showid=1100000002321017776&base=13	http://factordb.com/index.php?showid=1100000002321017776	http://factordb.com/helper.php?id=1100000002321017776	http://factordb.com/cert.php?id=1100000002321017776	http://factordb.com/certchain.php?fid=1100000002321017776&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283*13%5E%28n%2B1%29-19%29%2F4&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3187	7₁₅₀₄1	(7×13¹⁵⁰⁵−79)/12	1505	1677	http://factordb.com/index.php?id=1100000002320890755&open=prime	http://factordb.com/index.php?showid=1100000002320890755&base=13	http://factordb.com/index.php?showid=1100000002320890755	http://factordb.com/helper.php?id=1100000002320890755	http://factordb.com/cert.php?id=1100000002320890755	http://factordb.com/certchain.php?fid=1100000002320890755&action=all&fr=0&to=100	http://factordb.com/index.php?query=%287*13%5E%28n%2B1%29-79%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3188	930₁₅₅₁1	120×13¹⁵⁵²+1	1554	1731	http://factordb.com/index.php?id=1100000000765961452&open=prime	http://factordb.com/index.php?showid=1100000000765961452&base=13	http://factordb.com/index.php?showid=1100000000765961452	http://factordb.com/helper.php?id=1100000000765961452	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is trivially fully factored	http://factordb.com/index.php?id=1100000000765961453&open=ecm	http://factordb.com/index.php?query=120*13%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3189	720₂₂₉₇2	93×13²²⁹⁸+2	2300	2562	http://factordb.com/index.php?id=1100000002632396910&open=prime	http://factordb.com/index.php?showid=1100000002632396910&base=13	http://factordb.com/index.php?showid=1100000002632396910	http://factordb.com/helper.php?id=1100000002632396910	http://factordb.com/cert.php?id=1100000002632396910	http://factordb.com/certchain.php?fid=1100000002632396910&action=all&fr=0&to=100	http://factordb.com/index.php?query=93*13%5E%28n%2B1%29%2B2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3190	1770₂₇₀₃17	267×13²⁷⁰⁵+20	2708	3016	http://factordb.com/index.php?id=1100000003590430825&open=prime	http://factordb.com/index.php?showid=1100000003590430825&base=13	http://factordb.com/index.php?showid=1100000003590430825	http://factordb.com/helper.php?id=1100000003590430825	http://factordb.com/cert.php?id=1100000003590430825	http://factordb.com/certchain.php?fid=1100000003590430825&action=all&fr=0&to=100	http://factordb.com/index.php?query=267*13%5E%28n%2B2%29%2B20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3191	390₆₂₆₆1	48×13⁶²⁶⁷+1	6269	6983	http://factordb.com/index.php?id=1100000000765961441&open=prime	http://factordb.com/index.php?showid=1100000000765961441&base=13	http://factordb.com/index.php?showid=1100000000765961441	http://factordb.com/helper.php?id=1100000000765961441	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is trivially fully factored	http://factordb.com/index.php?id=1100000000765961451&open=ecm	http://factordb.com/index.php?query=48*13%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3192	B0₆₅₄₀BBA	11×13⁶⁵⁴³+2012	6544	7290	http://factordb.com/index.php?id=1100000002616382906&open=prime	http://factordb.com/index.php?showid=1100000002616382906&base=13	http://factordb.com/index.php?showid=1100000002616382906	http://factordb.com/helper.php?id=1100000002616382906	http://factordb.com/cert.php?id=1100000002616382906	http://factordb.com/certchain.php?fid=1100000002616382906&action=all&fr=0&to=100	http://factordb.com/index.php?query=11*13%5E%28n%2B3%29%2B2012&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
13	3193	C₁₀₆₃₁92	13¹⁰⁶³³−50	10633	11845	http://factordb.com/index.php?id=1100000003590493750&open=prime	http://factordb.com/index.php?showid=1100000003590493750&base=13	http://factordb.com/index.php?showid=1100000003590493750	http://factordb.com/helper.php?id=1100000003590493750	http://factordb.com/cert.php?id=1100000003590493750	http://factordb.com/certchain.php?fid=1100000003590493750&action=all&fr=0&to=100	http://factordb.com/index.php?query=13%5E%28n%2B2%29-50&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	649	34D₇₀₈	47×14⁷⁰⁸−1	710	814	http://factordb.com/index.php?id=1100000001540144903&open=prime	http://factordb.com/index.php?showid=1100000001540144903&base=14	http://factordb.com/index.php?showid=1100000001540144903	http://factordb.com/helper.php?id=1100000001540144903	proven prime by N+1 test (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2), since N+1 is trivially fully factored	http://factordb.com/index.php?id=1100000001540144907&open=ecm	http://factordb.com/index.php?query=47*14%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
14	650	4D₁₉₆₉₈	5×14¹⁹⁶⁹⁸−1	19699	22578	http://factordb.com/index.php?id=1100000000884560233&open=prime	http://factordb.com/index.php?showid=1100000000884560233&base=14	http://factordb.com/index.php?showid=1100000000884560233	http://factordb.com/helper.php?id=1100000000884560233	proven prime by N+1 test (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2), since N+1 is trivially fully factored	http://factordb.com/index.php?id=1100000000884560625&open=ecm	http://factordb.com/index.php?query=5*14%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2328	880₂₄₆7	136×16²⁴⁷+7	249	300	http://factordb.com/index.php?id=1100000002468140199&open=prime	http://factordb.com/index.php?showid=1100000002468140199&base=16	http://factordb.com/index.php?showid=1100000002468140199	http://factordb.com/helper.php?id=1100000002468140199	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), N−1 is 2³×3×7×13×25703261×(289-digit prime)	http://factordb.com/index.php?id=1100000002468140641&open=ecm	http://factordb.com/index.php?query=136*16%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2329	D4₂₆₃D	(199×16²⁶⁴+131)/15	265	320	http://factordb.com/index.php?id=1100000002468170238&open=prime	http://factordb.com/index.php?showid=1100000002468170238&base=16	http://factordb.com/index.php?showid=1100000002468170238	http://factordb.com/helper.php?id=1100000002468170238	http://factordb.com/cert.php?id=1100000002468170238	http://factordb.com/certchain.php?fid=1100000002468170238&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28199*16%5E%28n%2B1%29%2B131%29%2F15&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2330	E0₂₆₁4DD	14×16²⁶⁴+1245	265	320	http://factordb.com/index.php?id=1100000003588388352&open=prime	http://factordb.com/index.php?showid=1100000003588388352&base=16	http://factordb.com/index.php?showid=1100000003588388352	http://factordb.com/helper.php?id=1100000003588388352	http://factordb.com/cert.php?id=1100000003588388352	http://factordb.com/certchain.php?fid=1100000003588388352&action=all&fr=0&to=100	http://factordb.com/index.php?query=14*16%5E%28n%2B3%29%2B1245&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2331	8C0₂₉₀ED	140×16²⁹²+237	294	354	http://factordb.com/index.php?id=1100000003588388307&open=prime	http://factordb.com/index.php?showid=1100000003588388307&base=16	http://factordb.com/index.php?showid=1100000003588388307	http://factordb.com/helper.php?id=1100000003588388307	http://factordb.com/cert.php?id=1100000003588388307	http://factordb.com/certchain.php?fid=1100000003588388307&action=all&fr=0&to=100	http://factordb.com/index.php?query=140*16%5E%28n%2B2%29%2B237&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2332	DA₃₀₅5	(41×16³⁰⁶−17)/3	307	370	http://factordb.com/index.php?id=1100000003588388284&open=prime	http://factordb.com/index.php?showid=1100000003588388284&base=16	http://factordb.com/index.php?showid=1100000003588388284	http://factordb.com/helper.php?id=1100000003588388284	http://factordb.com/cert.php?id=1100000003588388284	http://factordb.com/certchain.php?fid=1100000003588388284&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2841*16%5E%28n%2B1%29-17%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2333	CE80₄₂₂D	3304×16⁴²³+13	426	513	http://factordb.com/index.php?id=1100000003588388257&open=prime	http://factordb.com/index.php?showid=1100000003588388257&base=16	http://factordb.com/index.php?showid=1100000003588388257	http://factordb.com/helper.php?id=1100000003588388257	http://factordb.com/cert.php?id=1100000003588388257	http://factordb.com/certchain.php?fid=1100000003588388257&action=all&fr=0&to=100	http://factordb.com/index.php?query=3304*16%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2334	5F₅₄₄6F	6×16⁵⁴⁶−145	547	659	http://factordb.com/index.php?id=1100000002604723967&open=prime	http://factordb.com/index.php?showid=1100000002604723967&base=16	http://factordb.com/index.php?showid=1100000002604723967	http://factordb.com/helper.php?id=1100000002604723967	http://factordb.com/cert.php?id=1100000002604723967	http://factordb.com/certchain.php?fid=1100000002604723967&action=all&fr=0&to=100	http://factordb.com/index.php?query=6*16%5E%28n%2B2%29-145&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2335	88F₅₄₅	137×16⁵⁴⁵−1	547	659	http://factordb.com/index.php?id=1100000000413679658&open=prime	http://factordb.com/index.php?showid=1100000000413679658&base=16	http://factordb.com/index.php?showid=1100000000413679658	http://factordb.com/helper.php?id=1100000000413679658	proven prime by N+1 test (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2), since N+1 is trivially fully factored	http://factordb.com/index.php?id=1100000000413877337&open=ecm	http://factordb.com/index.php?query=137*16%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2336	BE0₇₉₂BB	190×16⁷⁹⁴+187	796	959	http://factordb.com/index.php?id=1100000003588387938&open=prime	http://factordb.com/index.php?showid=1100000003588387938&base=16	http://factordb.com/index.php?showid=1100000003588387938	http://factordb.com/helper.php?id=1100000003588387938	http://factordb.com/cert.php?id=1100000003588387938	http://factordb.com/certchain.php?fid=1100000003588387938&action=all&fr=0&to=100	http://factordb.com/index.php?query=190*16%5E%28n%2B2%29%2B187&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2337	D9₁₀₅₂	(68×16¹⁰⁵²−3)/5	1053	1268	http://factordb.com/index.php?id=1100000002321036020&open=prime	http://factordb.com/index.php?showid=1100000002321036020&base=16	http://factordb.com/index.php?showid=1100000002321036020	http://factordb.com/helper.php?id=1100000002321036020	http://factordb.com/cert.php?id=1100000002321036020	http://factordb.com/certchain.php?fid=1100000002321036020&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2868*16%5En-3%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2338	FAF₁₀₆₂45	251×16¹⁰⁶⁴−187	1066	1284	http://factordb.com/index.php?id=1100000003588387610&open=prime	http://factordb.com/index.php?showid=1100000003588387610&base=16	http://factordb.com/index.php?showid=1100000003588387610	http://factordb.com/helper.php?id=1100000003588387610	http://factordb.com/cert.php?id=1100000003588387610	http://factordb.com/certchain.php?fid=1100000003588387610&action=all&fr=0&to=100	http://factordb.com/index.php?query=251*16%5E%28n%2B2%29-187&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2339	F8₁₅₁₇F	(233×16¹⁵¹⁸+97)/15	1519	1830	http://factordb.com/index.php?id=1100000000633744824&open=prime	http://factordb.com/index.php?showid=1100000000633744824&base=16	http://factordb.com/index.php?showid=1100000000633744824	http://factordb.com/helper.php?id=1100000000633744824	http://factordb.com/cert.php?id=1100000000633744824	http://factordb.com/certchain.php?fid=1100000000633744824&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28233*16%5E%28n%2B1%29%2B97%29%2F15&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2340	20₁₇₁₃321	2×16¹⁷¹⁶+801	1717	2067	http://factordb.com/index.php?id=1100000003588386735&open=prime	http://factordb.com/index.php?showid=1100000003588386735&base=16	http://factordb.com/index.php?showid=1100000003588386735	http://factordb.com/helper.php?id=1100000003588386735	http://factordb.com/cert.php?id=1100000003588386735	http://factordb.com/certchain.php?fid=1100000003588386735&action=all&fr=0&to=100	http://factordb.com/index.php?query=2*16%5E%28n%2B3%29%2B801&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2341	300F₁₉₆₀AF	769×16¹⁹⁶²−81	1965	2366	http://factordb.com/index.php?id=1100000003588368750&open=prime	http://factordb.com/index.php?showid=1100000003588368750&base=16	http://factordb.com/index.php?showid=1100000003588368750	http://factordb.com/helper.php?id=1100000003588368750	http://factordb.com/cert.php?id=1100000003588368750	http://factordb.com/certchain.php?fid=1100000003588368750&action=all&fr=0&to=100	http://factordb.com/index.php?query=769*16%5E%28n%2B2%29-81&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2342	90₃₅₄₂91	9×16³⁵⁴⁴+145	3545	4269	http://factordb.com/index.php?id=1100000000633424191&open=prime	http://factordb.com/index.php?showid=1100000000633424191&base=16	http://factordb.com/index.php?showid=1100000000633424191	http://factordb.com/helper.php?id=1100000000633424191	http://factordb.com/cert.php?id=1100000000633424191	http://factordb.com/certchain.php?fid=1100000000633424191&action=all&fr=0&to=100	http://factordb.com/index.php?query=9*16%5E%28n%2B2%29%2B145&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2343	5BC₃₇₀₀D	(459×16³⁷⁰¹+1)/5	3703	4459	http://factordb.com/index.php?id=1100000000993764322&open=prime	http://factordb.com/index.php?showid=1100000000993764322&base=16	http://factordb.com/index.php?showid=1100000000993764322	http://factordb.com/helper.php?id=1100000000993764322	http://factordb.com/cert.php?id=1100000000993764322	http://factordb.com/certchain.php?fid=1100000000993764322&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28459*16%5E%28n%2B1%29%2B1%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
16	2344	D0B₁₇₈₀₄	(3131×16¹⁷⁸⁰⁴−11)/15	17806	21441	http://factordb.com/index.php?id=1100000003589278511&open=prime	http://factordb.com/index.php?showid=1100000003589278511&base=16	http://factordb.com/index.php?showid=1100000003589278511	http://factordb.com/helper.php?id=1100000003589278511	http://factordb.com/cert.php?id=1100000003589278511	http://factordb.com/certchain.php?fid=1100000003589278511&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283131*16%5En-11%29%2F15&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10311	85A₂₄₁55	(1133×17²⁴³−725)/8	245	302	http://factordb.com/index.php?id=1100000003782940703&open=prime	http://factordb.com/index.php?showid=1100000003782940703&base=17	http://factordb.com/index.php?showid=1100000003782940703	http://factordb.com/helper.php?id=1100000003782940703	proven prime by N+1 test (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2), N+1 is 2×1291×942385161439×(286-digit prime)	http://factordb.com/index.php?id=1100000003782944423&open=ecm	http://factordb.com/index.php?query=%281133*17%5E%28n%2B2%29-725%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10312	90₂₄₂701	9×17²⁴⁵+2024	246	303	http://factordb.com/index.php?id=1100000003782940704&open=prime	http://factordb.com/index.php?showid=1100000003782940704&base=17	http://factordb.com/index.php?showid=1100000003782940704	http://factordb.com/helper.php?id=1100000003782940704	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), N−1 is 2⁶×17²×1773259×4348181×603217519×(277-digit prime)	http://factordb.com/index.php?id=1100000003782941925&open=ecm	http://factordb.com/index.php?query=9*17%5E%28n%2B3%29%2B2024&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10313	76E₂₄₆	(1007×17²⁴⁶−7)/8	248	305	http://factordb.com/index.php?id=1100000003782940705&open=prime	http://factordb.com/index.php?showid=1100000003782940705&base=17	http://factordb.com/index.php?showid=1100000003782940705	http://factordb.com/helper.php?id=1100000003782940705	http://factordb.com/cert.php?id=1100000003782940705	http://factordb.com/certchain.php?fid=1100000003782940705&action=all&fr=0&to=100	http://factordb.com/index.php?query=%281007*17%5En-7%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10314	AAE5A5₂₄₆	(14215701×17²⁴⁶−5)/16	251	309	http://factordb.com/index.php?id=1100000003782940706&open=prime	http://factordb.com/index.php?showid=1100000003782940706&base=17	http://factordb.com/index.php?showid=1100000003782940706	http://factordb.com/helper.php?id=1100000003782940706	http://factordb.com/cert.php?id=1100000003782940706	http://factordb.com/certchain.php?fid=1100000003782940706&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2814215701*17%5En-5%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10315	E7₂₅₅A	(231×17²⁵⁶+41)/16	257	317	http://factordb.com/index.php?id=1100000003782940707&open=prime	http://factordb.com/index.php?showid=1100000003782940707&base=17	http://factordb.com/index.php?showid=1100000003782940707	http://factordb.com/helper.php?id=1100000003782940707	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), N−1 is 2⁴×283×619471×62754967151×(296-digit prime)	http://factordb.com/index.php?id=1100000003782941928&open=ecm	http://factordb.com/index.php?query=%28231*17%5E%28n%2B1%29%2B41%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10316	85A5₂₇₀	(38517×17²⁷⁰−5)/16	273	336	http://factordb.com/index.php?id=1100000003782940708&open=prime	http://factordb.com/index.php?showid=1100000003782940708&base=17	http://factordb.com/index.php?showid=1100000003782940708	http://factordb.com/helper.php?id=1100000003782940708	http://factordb.com/cert.php?id=1100000003782940708	http://factordb.com/certchain.php?fid=1100000003782940708&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2838517*17%5En-5%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10317	5A70₂₇₄1	1622×17²⁷⁵+1	278	342	http://factordb.com/index.php?id=1100000003782940709&open=prime	http://factordb.com/index.php?showid=1100000003782940709&base=17	http://factordb.com/index.php?showid=1100000003782940709	http://factordb.com/helper.php?id=1100000003782940709	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is trivially fully factored	http://factordb.com/index.php?id=1100000003782941930&open=ecm	http://factordb.com/index.php?query=1622*17%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10318	D0D₂₇₅F	(3549×17²⁷⁶+19)/16	278	342	http://factordb.com/index.php?id=1100000003782940710&open=prime	http://factordb.com/index.php?showid=1100000003782940710&base=17	http://factordb.com/index.php?showid=1100000003782940710	http://factordb.com/helper.php?id=1100000003782940710	http://factordb.com/cert.php?id=1100000003782940710	http://factordb.com/certchain.php?fid=1100000003782940710&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283549*17%5E%28n%2B1%29%2B19%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10319	70D0₂₈₇B	2036×17²⁸⁸+11	291	358	http://factordb.com/index.php?id=1100000003782940711&open=prime	http://factordb.com/index.php?showid=1100000003782940711&base=17	http://factordb.com/index.php?showid=1100000003782940711	http://factordb.com/helper.php?id=1100000003782940711	http://factordb.com/cert.php?id=1100000003782940711	http://factordb.com/certchain.php?fid=1100000003782940711&action=all&fr=0&to=100	http://factordb.com/index.php?query=2036*17%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10320	9₂₉₂1	(9×17²⁹³−137)/16	293	361	http://factordb.com/index.php?id=1100000000840355814&open=prime	http://factordb.com/index.php?showid=1100000000840355814&base=17	http://factordb.com/index.php?showid=1100000000840355814	http://factordb.com/helper.php?id=1100000000840355814	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is 153/16×(17²⁹²−1), thus factor N−1 is equivalent to factor 17²⁹²−1, and for the factorization of 17²⁹²−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=17&Exp=292&c0=-&EN=	http://factordb.com/index.php?id=1100000000840355817&open=ecm	http://factordb.com/index.php?query=%289*17%5E%28n%2B1%29-137%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10321	A7010₂₉₈5	51154×17²⁹⁹+5	303	373	http://factordb.com/index.php?id=1100000003782940712&open=prime	http://factordb.com/index.php?showid=1100000003782940712&base=17	http://factordb.com/index.php?showid=1100000003782940712	http://factordb.com/helper.php?id=1100000003782940712	http://factordb.com/cert.php?id=1100000003782940712	http://factordb.com/certchain.php?fid=1100000003782940712&action=all&fr=0&to=100	http://factordb.com/index.php?query=51154*17%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10322	97₃₀₉3	(151×17³¹⁰−71)/16	311	383	http://factordb.com/index.php?id=1100000002668315056&open=prime	http://factordb.com/index.php?showid=1100000002668315056&base=17	http://factordb.com/index.php?showid=1100000002668315056	http://factordb.com/helper.php?id=1100000002668315056	http://factordb.com/cert.php?id=1100000002668315056	http://factordb.com/certchain.php?fid=1100000002668315056&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28151*17%5E%28n%2B1%29-71%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10323	7F0₃₀₉5	134×17³¹⁰+5	312	384	http://factordb.com/index.php?id=1100000002748150540&open=prime	http://factordb.com/index.php?showid=1100000002748150540&base=17	http://factordb.com/index.php?showid=1100000002748150540	http://factordb.com/helper.php?id=1100000002748150540	http://factordb.com/cert.php?id=1100000002748150540	http://factordb.com/certchain.php?fid=1100000002748150540&action=all&fr=0&to=100	http://factordb.com/index.php?query=134*17%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10324	BFB₃₂₃	(3243×17³²³−11)/16	325	400	http://factordb.com/index.php?id=1100000003782940713&open=prime	http://factordb.com/index.php?showid=1100000003782940713&base=17	http://factordb.com/index.php?showid=1100000003782940713	http://factordb.com/helper.php?id=1100000003782940713	http://factordb.com/cert.php?id=1100000003782940713	http://factordb.com/certchain.php?fid=1100000003782940713&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283243*17%5En-11%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10325	A0₃₂₈52	10×17³³⁰+87	331	408	http://factordb.com/index.php?id=1100000002748151228&open=prime	http://factordb.com/index.php?showid=1100000002748151228&base=17	http://factordb.com/index.php?showid=1100000002748151228	http://factordb.com/helper.php?id=1100000002748151228	http://factordb.com/cert.php?id=1100000002748151228	http://factordb.com/certchain.php?fid=1100000002748151228&action=all&fr=0&to=100	http://factordb.com/index.php?query=10*17%5E%28n%2B2%29%2B87&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10326	GD₃₃₄3	(269×17³³⁵−173)/16	336	414	http://factordb.com/index.php?id=1100000003782940714&open=prime	http://factordb.com/index.php?showid=1100000003782940714&base=17	http://factordb.com/index.php?showid=1100000003782940714	http://factordb.com/helper.php?id=1100000003782940714	http://factordb.com/cert.php?id=1100000003782940714	http://factordb.com/certchain.php?fid=1100000003782940714&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28269*17%5E%28n%2B1%29-173%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10327	5₃₄₇95	(5×17³⁴⁹+1083)/16	349	429	http://factordb.com/index.php?id=1100000003782940715&open=prime	http://factordb.com/index.php?showid=1100000003782940715&base=17	http://factordb.com/index.php?showid=1100000003782940715	http://factordb.com/helper.php?id=1100000003782940715	http://factordb.com/cert.php?id=1100000003782940715	http://factordb.com/certchain.php?fid=1100000003782940715&action=all&fr=0&to=100	http://factordb.com/index.php?query=%285*17%5E%28n%2B2%29%2B1083%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10328	E5A5₃₄₈	(66261×17³⁴⁸−5)/16	351	432	http://factordb.com/index.php?id=1100000003782940716&open=prime	http://factordb.com/index.php?showid=1100000003782940716&base=17	http://factordb.com/index.php?showid=1100000003782940716	http://factordb.com/helper.php?id=1100000003782940716	http://factordb.com/cert.php?id=1100000003782940716	http://factordb.com/certchain.php?fid=1100000003782940716&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2866261*17%5En-5%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10329	FB0₃₅₉5	266×17³⁶⁰+5	362	446	http://factordb.com/index.php?id=1100000002632835926&open=prime	http://factordb.com/index.php?showid=1100000002632835926&base=17	http://factordb.com/index.php?showid=1100000002632835926	http://factordb.com/helper.php?id=1100000002632835926	http://factordb.com/cert.php?id=1100000002632835926	http://factordb.com/certchain.php?fid=1100000002632835926&action=all&fr=0&to=100	http://factordb.com/index.php?query=266*17%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10330	1070₃₆₃3	296×17³⁶⁴+3	367	451	http://factordb.com/index.php?id=1100000003782940717&open=prime	http://factordb.com/index.php?showid=1100000003782940717&base=17	http://factordb.com/index.php?showid=1100000003782940717	http://factordb.com/helper.php?id=1100000003782940717	http://factordb.com/cert.php?id=1100000003782940717	http://factordb.com/certchain.php?fid=1100000003782940717&action=all&fr=0&to=100	http://factordb.com/index.php?query=296*17%5E%28n%2B1%29%2B3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10331	AE5₃₇₁	(2949×17³⁷¹−5)/16	373	459	http://factordb.com/index.php?id=1100000003782940718&open=prime	http://factordb.com/index.php?showid=1100000003782940718&base=17	http://factordb.com/index.php?showid=1100000003782940718	http://factordb.com/helper.php?id=1100000003782940718	http://factordb.com/cert.php?id=1100000003782940718	http://factordb.com/certchain.php?fid=1100000003782940718&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282949*17%5En-5%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10332	F5₃₈₁9	(245×17³⁸²+59)/16	383	472	http://factordb.com/index.php?id=1100000003782940719&open=prime	http://factordb.com/index.php?showid=1100000003782940719&base=17	http://factordb.com/index.php?showid=1100000003782940719	http://factordb.com/helper.php?id=1100000003782940719	http://factordb.com/cert.php?id=1100000003782940719	http://factordb.com/certchain.php?fid=1100000003782940719&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28245*17%5E%28n%2B1%29%2B59%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10333	10₃₈₃F5	17³⁸⁵+260	386	474	http://factordb.com/index.php?id=1100000002632399724&open=prime	http://factordb.com/index.php?showid=1100000002632399724&base=17	http://factordb.com/index.php?showid=1100000002632399724	http://factordb.com/helper.php?id=1100000002632399724	http://factordb.com/cert.php?id=1100000002632399724	http://factordb.com/certchain.php?fid=1100000002632399724&action=all&fr=0&to=100	http://factordb.com/index.php?query=17%5E%28n%2B2%29%2B260&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10334	6₃₈₉GF	(3×17³⁹¹+1429)/8	391	481	http://factordb.com/index.php?id=1100000000840355826&open=prime	http://factordb.com/index.php?showid=1100000000840355826&base=17	http://factordb.com/index.php?showid=1100000000840355826	http://factordb.com/helper.php?id=1100000000840355826	http://factordb.com/cert.php?id=1100000000840355826	http://factordb.com/certchain.php?fid=1100000000840355826&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283*17%5E%28n%2B2%29%2B1429%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10335	B₃₉₈80B	(11×17⁴⁰¹−16875)/16	401	494	http://factordb.com/index.php?id=1100000003782940720&open=prime	http://factordb.com/index.php?showid=1100000003782940720&base=17	http://factordb.com/index.php?showid=1100000003782940720	http://factordb.com/helper.php?id=1100000003782940720	http://factordb.com/cert.php?id=1100000003782940720	http://factordb.com/certchain.php?fid=1100000003782940720&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2811*17%5E%28n%2B3%29-16875%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10336	B70₄₀₆7	194×17⁴⁰⁷+7	409	504	http://factordb.com/index.php?id=1100000002748151387&open=prime	http://factordb.com/index.php?showid=1100000002748151387&base=17	http://factordb.com/index.php?showid=1100000002748151387	http://factordb.com/helper.php?id=1100000002748151387	http://factordb.com/cert.php?id=1100000002748151387	http://factordb.com/certchain.php?fid=1100000002748151387&action=all&fr=0&to=100	http://factordb.com/index.php?query=194*17%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10337	2B₄₁₇2	(43×17⁴¹⁸−155)/16	419	515	http://factordb.com/index.php?id=1100000003782940721&open=prime	http://factordb.com/index.php?showid=1100000003782940721&base=17	http://factordb.com/index.php?showid=1100000003782940721	http://factordb.com/helper.php?id=1100000003782940721	http://factordb.com/cert.php?id=1100000003782940721	http://factordb.com/certchain.php?fid=1100000003782940721&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2843*17%5E%28n%2B1%29-155%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10338	BF0₄₁₆5	202×17⁴¹⁷+5	419	516	http://factordb.com/index.php?id=1100000002632836900&open=prime	http://factordb.com/index.php?showid=1100000002632836900&base=17	http://factordb.com/index.php?showid=1100000002632836900	http://factordb.com/helper.php?id=1100000002632836900	http://factordb.com/cert.php?id=1100000002632836900	http://factordb.com/certchain.php?fid=1100000002632836900&action=all&fr=0&to=100	http://factordb.com/index.php?query=202*17%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10339	5D0₄₁₇5	98×17⁴¹⁸+5	420	517	http://factordb.com/index.php?id=1100000002632463013&open=prime	http://factordb.com/index.php?showid=1100000002632463013&base=17	http://factordb.com/index.php?showid=1100000002632463013	http://factordb.com/helper.php?id=1100000002632463013	http://factordb.com/cert.php?id=1100000002632463013	http://factordb.com/certchain.php?fid=1100000002632463013&action=all&fr=0&to=100	http://factordb.com/index.php?query=98*17%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10340	D0₄₃₉FB	13×17⁴⁴¹+266	442	544	http://factordb.com/index.php?id=1100000002632836180&open=prime	http://factordb.com/index.php?showid=1100000002632836180&base=17	http://factordb.com/index.php?showid=1100000002632836180	http://factordb.com/helper.php?id=1100000002632836180	http://factordb.com/cert.php?id=1100000002632836180	http://factordb.com/certchain.php?fid=1100000002632836180&action=all&fr=0&to=100	http://factordb.com/index.php?query=13*17%5E%28n%2B2%29%2B266&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10341	7A10₄₄₆5	2194×17⁴⁴⁷+5	450	554	http://factordb.com/index.php?id=1100000003782940722&open=prime	http://factordb.com/index.php?showid=1100000003782940722&base=17	http://factordb.com/index.php?showid=1100000003782940722	http://factordb.com/helper.php?id=1100000003782940722	http://factordb.com/cert.php?id=1100000003782940722	http://factordb.com/certchain.php?fid=1100000003782940722&action=all&fr=0&to=100	http://factordb.com/index.php?query=2194*17%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10342	D0D₄₄₉09	(3549×17⁴⁵¹−3613)/16	453	558	http://factordb.com/index.php?id=1100000003782940723&open=prime	http://factordb.com/index.php?showid=1100000003782940723&base=17	http://factordb.com/index.php?showid=1100000003782940723	http://factordb.com/helper.php?id=1100000003782940723	http://factordb.com/cert.php?id=1100000003782940723	http://factordb.com/certchain.php?fid=1100000003782940723&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283549*17%5E%28n%2B2%29-3613%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10343	79₄₅₄6	(121×17⁴⁵⁵−57)/16	456	561	http://factordb.com/index.php?id=1100000003782940724&open=prime	http://factordb.com/index.php?showid=1100000003782940724&base=17	http://factordb.com/index.php?showid=1100000003782940724	http://factordb.com/helper.php?id=1100000003782940724	http://factordb.com/cert.php?id=1100000003782940724	http://factordb.com/certchain.php?fid=1100000003782940724&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28121*17%5E%28n%2B1%29-57%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10344	9760₄₇₃F	2726×17⁴⁷⁴+15	477	587	http://factordb.com/index.php?id=1100000003782940725&open=prime	http://factordb.com/index.php?showid=1100000003782940725&base=17	http://factordb.com/index.php?showid=1100000003782940725	http://factordb.com/helper.php?id=1100000003782940725	http://factordb.com/cert.php?id=1100000003782940725	http://factordb.com/certchain.php?fid=1100000003782940725&action=all&fr=0&to=100	http://factordb.com/index.php?query=2726*17%5E%28n%2B1%29%2B15&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10345	80C₄₉₂9	(547×17⁴⁹³−15)/4	495	609	http://factordb.com/index.php?id=1100000000840355847&open=prime	http://factordb.com/index.php?showid=1100000000840355847&base=17	http://factordb.com/index.php?showid=1100000000840355847	http://factordb.com/helper.php?id=1100000000840355847	http://factordb.com/cert.php?id=1100000000840355847	http://factordb.com/certchain.php?fid=1100000000840355847&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28547*17%5E%28n%2B1%29-15%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10346	D₅₀₀F4	(13×17⁵⁰²+387)/16	502	618	http://factordb.com/index.php?id=1100000003782940726&open=prime	http://factordb.com/index.php?showid=1100000003782940726&base=17	http://factordb.com/index.php?showid=1100000003782940726	http://factordb.com/helper.php?id=1100000003782940726	http://factordb.com/cert.php?id=1100000003782940726	http://factordb.com/certchain.php?fid=1100000003782940726&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2813*17%5E%28n%2B2%29%2B387%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10347	749₅₀₈2	(1977×17⁵⁰⁹−121)/16	511	629	http://factordb.com/index.php?id=1100000003782940727&open=prime	http://factordb.com/index.php?showid=1100000003782940727&base=17	http://factordb.com/index.php?showid=1100000003782940727	http://factordb.com/helper.php?id=1100000003782940727	http://factordb.com/cert.php?id=1100000003782940727	http://factordb.com/certchain.php?fid=1100000003782940727&action=all&fr=0&to=100	http://factordb.com/index.php?query=%281977*17%5E%28n%2B1%29-121%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10348	A5₅₃₇2	(165×17⁵³⁸−53)/16	539	663	http://factordb.com/index.php?id=1100000002999318480&open=prime	http://factordb.com/index.php?showid=1100000002999318480&base=17	http://factordb.com/index.php?showid=1100000002999318480	http://factordb.com/helper.php?id=1100000002999318480	http://factordb.com/cert.php?id=1100000002999318480	http://factordb.com/certchain.php?fid=1100000002999318480&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28165*17%5E%28n%2B1%29-53%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10349	B0₅₄₂FB	11×17⁵⁴⁴+266	545	671	http://factordb.com/index.php?id=1100000002632836856&open=prime	http://factordb.com/index.php?showid=1100000002632836856&base=17	http://factordb.com/index.php?showid=1100000002632836856	http://factordb.com/helper.php?id=1100000002632836856	http://factordb.com/cert.php?id=1100000002632836856	http://factordb.com/certchain.php?fid=1100000002632836856&action=all&fr=0&to=100	http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B266&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
17	10350	9₆₀₄B	(9×17⁶⁰⁵+23)/16	605	745	http://factordb.com/index.php?id=1100000002321188365&open=prime	http://factordb.com/index.php?showid=1100000002321188365&base=17	http://factordb.com/index.php?showid=1100000002321188365	http://factordb.com/helper.php?id=1100000002321188365	http://factordb.com/cert.php?id=1100000002321188365	http://factordb.com/certchain.php?fid=1100000002321188365&action=all&fr=0&to=100	http://factordb.com/index.php?query=%289*17%5E%28n%2B1%29%2B23%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
18	547	80₂₉₈B	8×18²⁹⁹+11	300	377	http://factordb.com/index.php?id=1100000002355574745&open=prime	http://factordb.com/index.php?showid=1100000002355574745&base=18	http://factordb.com/index.php?showid=1100000002355574745	http://factordb.com/helper.php?id=1100000002355574745	http://factordb.com/cert.php?id=1100000002355574745	http://factordb.com/certchain.php?fid=1100000002355574745&action=all&fr=0&to=100	http://factordb.com/index.php?query=8*18%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
18	548	H₇₆₆FH	18⁷⁶⁸−37	768	965	http://factordb.com/index.php?id=1100000003590430490&open=prime	http://factordb.com/index.php?showid=1100000003590430490&base=18	http://factordb.com/index.php?showid=1100000003590430490	http://factordb.com/helper.php?id=1100000003590430490	http://factordb.com/cert.php?id=1100000003590430490	http://factordb.com/certchain.php?fid=1100000003590430490&action=all&fr=0&to=100	http://factordb.com/index.php?query=18%5E%28n%2B2%29-37&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
18	549	C0₆₂₆₈C5	12×18⁶²⁷⁰+221	6271	7872	http://factordb.com/index.php?id=1100000003590442437&open=prime	http://factordb.com/index.php?showid=1100000003590442437&base=18	http://factordb.com/index.php?showid=1100000003590442437	http://factordb.com/helper.php?id=1100000003590442437	http://factordb.com/cert.php?id=1100000003590442437	http://factordb.com/certchain.php?fid=1100000003590442437&action=all&fr=0&to=100	http://factordb.com/index.php?query=12*18%5E%28n%2B2%29%2B221&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3301	H₂₄₇A0H	(17×20²⁵⁰−59677)/19	250	326	http://factordb.com/index.php?id=1100000003590502619&open=prime	http://factordb.com/index.php?showid=1100000003590502619&base=20	http://factordb.com/index.php?showid=1100000003590502619	http://factordb.com/helper.php?id=1100000003590502619	http://factordb.com/cert.php?id=1100000003590502619	http://factordb.com/certchain.php?fid=1100000003590502619&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2817*20%5E%28n%2B3%29-59677%29%2F19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3302	7₂₄₉A7	(7×20²⁵¹+1133)/19	251	327	http://factordb.com/index.php?id=1100000003590502602&open=prime	http://factordb.com/index.php?showid=1100000003590502602&base=20	http://factordb.com/index.php?showid=1100000003590502602	http://factordb.com/helper.php?id=1100000003590502602	http://factordb.com/cert.php?id=1100000003590502602	http://factordb.com/certchain.php?fid=1100000003590502602&action=all&fr=0&to=100	http://factordb.com/index.php?query=%287*20%5E%28n%2B2%29%2B1133%29%2F19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3303	J7₂₇₀	(368×20²⁷⁰−7)/19	271	353	http://factordb.com/index.php?id=1100000002325395462&open=prime	http://factordb.com/index.php?showid=1100000002325395462&base=20	http://factordb.com/index.php?showid=1100000002325395462	http://factordb.com/helper.php?id=1100000002325395462	http://factordb.com/cert.php?id=1100000002325395462	http://factordb.com/certchain.php?fid=1100000002325395462&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28368*20%5En-7%29%2F19&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3304	J₃₃₀CCC7	20³³⁴−58953	334	435	http://factordb.com/index.php?id=1100000003590502572&open=prime	http://factordb.com/index.php?showid=1100000003590502572&base=20	http://factordb.com/index.php?showid=1100000003590502572	http://factordb.com/helper.php?id=1100000003590502572	http://factordb.com/cert.php?id=1100000003590502572	http://factordb.com/certchain.php?fid=1100000003590502572&action=all&fr=0&to=100	http://factordb.com/index.php?query=20%5E%28n%2B4%29-58953&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3305	40₃₈₇404B	4×20³⁹¹+32091	392	510	http://factordb.com/index.php?id=1100000003590502563&open=prime	http://factordb.com/index.php?showid=1100000003590502563&base=20	http://factordb.com/index.php?showid=1100000003590502563	http://factordb.com/helper.php?id=1100000003590502563	http://factordb.com/cert.php?id=1100000003590502563	http://factordb.com/certchain.php?fid=1100000003590502563&action=all&fr=0&to=100	http://factordb.com/index.php?query=4*20%5E%28n%2B4%29%2B32091&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3306	EC0₄₂₉7	292×20⁴³⁰+7	432	562	http://factordb.com/index.php?id=1100000002633348702&open=prime	http://factordb.com/index.php?showid=1100000002633348702&base=20	http://factordb.com/index.php?showid=1100000002633348702	http://factordb.com/helper.php?id=1100000002633348702	http://factordb.com/cert.php?id=1100000002633348702	http://factordb.com/certchain.php?fid=1100000002633348702&action=all&fr=0&to=100	http://factordb.com/index.php?query=292*20%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3307	G₄₄₇99	(16×20⁴⁴⁹−2809)/19	449	585	http://factordb.com/index.php?id=1100000000840126753&open=prime	http://factordb.com/index.php?showid=1100000000840126753&base=20	http://factordb.com/index.php?showid=1100000000840126753	http://factordb.com/helper.php?id=1100000000840126753	http://factordb.com/cert.php?id=1100000000840126753	http://factordb.com/certchain.php?fid=1100000000840126753&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2816*20%5E%28n%2B2%29-2809%29%2F19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3308	3A₅₂₇3	(67×20⁵²⁸−143)/19	529	688	http://factordb.com/index.php?id=1100000003590502531&open=prime	http://factordb.com/index.php?showid=1100000003590502531&base=20	http://factordb.com/index.php?showid=1100000003590502531	http://factordb.com/helper.php?id=1100000003590502531	http://factordb.com/cert.php?id=1100000003590502531	http://factordb.com/certchain.php?fid=1100000003590502531&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2867*20%5E%28n%2B1%29-143%29%2F19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3309	E₅₆₆C7	(14×20⁵⁶⁸−907)/19	568	739	http://factordb.com/index.php?id=1100000003590502516&open=prime	http://factordb.com/index.php?showid=1100000003590502516&base=20	http://factordb.com/index.php?showid=1100000003590502516	http://factordb.com/helper.php?id=1100000003590502516	http://factordb.com/cert.php?id=1100000003590502516	http://factordb.com/certchain.php?fid=1100000003590502516&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2814*20%5E%28n%2B2%29-907%29%2F19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3310	JCJ₆₂₉	393×20⁶²⁹−1	631	821	http://factordb.com/index.php?id=1100000001559454258&open=prime	http://factordb.com/index.php?showid=1100000001559454258&base=20	http://factordb.com/index.php?showid=1100000001559454258	http://factordb.com/helper.php?id=1100000001559454258	proven prime by N+1 test (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2), since N+1 is trivially fully factored	http://factordb.com/index.php?id=1100000001559454271&open=ecm	http://factordb.com/index.php?query=393*20%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3311	J₆₅₅05J	20⁶⁵⁸−7881	658	857	http://factordb.com/index.php?id=1100000003590502490&open=prime	http://factordb.com/index.php?showid=1100000003590502490&base=20	http://factordb.com/index.php?showid=1100000003590502490	http://factordb.com/helper.php?id=1100000003590502490	http://factordb.com/cert.php?id=1100000003590502490	http://factordb.com/certchain.php?fid=1100000003590502490&action=all&fr=0&to=100	http://factordb.com/index.php?query=20%5E%28n%2B3%29-7881&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3312	50₁₁₆₃AJ	5×20¹¹⁶⁵+219	1166	1517	http://factordb.com/index.php?id=1100000003590502412&open=prime	http://factordb.com/index.php?showid=1100000003590502412&base=20	http://factordb.com/index.php?showid=1100000003590502412	http://factordb.com/helper.php?id=1100000003590502412	http://factordb.com/cert.php?id=1100000003590502412	http://factordb.com/certchain.php?fid=1100000003590502412&action=all&fr=0&to=100	http://factordb.com/index.php?query=5*20%5E%28n%2B2%29%2B219&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3313	CD₂₄₄₉	(241×20²⁴⁴⁹−13)/19	2450	3188	http://factordb.com/index.php?id=1100000002325393915&open=prime	http://factordb.com/index.php?showid=1100000002325393915&base=20	http://factordb.com/index.php?showid=1100000002325393915	http://factordb.com/helper.php?id=1100000002325393915	http://factordb.com/cert.php?id=1100000002325393915	http://factordb.com/certchain.php?fid=1100000002325393915&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28241*20%5En-13%29%2F19&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
20	3314	G0₆₂₆₉D	16×20⁶²⁷⁰+13	6271	8159	http://factordb.com/index.php?id=1100000003590539457&open=prime	http://factordb.com/index.php?showid=1100000003590539457&base=20	http://factordb.com/index.php?showid=1100000003590539457	http://factordb.com/helper.php?id=1100000003590539457	http://factordb.com/cert.php?id=1100000003590539457	http://factordb.com/certchain.php?fid=1100000003590539457&action=all&fr=0&to=100	http://factordb.com/index.php?query=16*20%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13303	E9₂₂₇K	(289×21²²⁸+211)/20	229	303	http://factordb.com/index.php?id=1100000000633439877&open=prime	http://factordb.com/index.php?showid=1100000000633439877&base=21	http://factordb.com/index.php?showid=1100000000633439877	http://factordb.com/helper.php?id=1100000000633439877	http://factordb.com/cert.php?id=1100000000633439877	http://factordb.com/certchain.php?fid=1100000000633439877&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28289*21%5E%28n%2B1%29%2B211%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13304	7₂₃₀1	(7×21²³¹−127)/20	231	305	http://factordb.com/index.php?id=1100000002325398836&open=prime	http://factordb.com/index.php?showid=1100000002325398836&base=21	http://factordb.com/index.php?showid=1100000002325398836	http://factordb.com/helper.php?id=1100000002325398836	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is 147/20×(21²³⁰−1), thus factor N−1 is equivalent to factor 21²³⁰−1, and for the factorization of 21²³⁰−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&Exp=230&c0=-&EN=	http://factordb.com/index.php?id=1100000002325398854&open=ecm	http://factordb.com/index.php?query=%287*21%5E%28n%2B1%29-127%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13305	E7₂₃₆B	(287×21²³⁷+73)/20	238	315	http://factordb.com/index.php?id=1100000003815102868&open=prime	http://factordb.com/index.php?showid=1100000003815102868&base=21	http://factordb.com/index.php?showid=1100000003815102868	http://factordb.com/helper.php?id=1100000003815102868	http://factordb.com/cert.php?id=1100000003815102868	http://factordb.com/certchain.php?fid=1100000003815102868&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28287*21%5E%28n%2B1%29%2B73%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13306	A5₂₃₈B	(41×21²³⁹+23)/4	240	318	http://factordb.com/index.php?id=1100000003815102869&open=prime	http://factordb.com/index.php?showid=1100000003815102869&base=21	http://factordb.com/index.php?showid=1100000003815102869	http://factordb.com/helper.php?id=1100000003815102869	http://factordb.com/cert.php?id=1100000003815102869	http://factordb.com/certchain.php?fid=1100000003815102869&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2841*21%5E%28n%2B1%29%2B23%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13307	C₂₄₆32	(3×21²⁴⁸−998)/5	248	328	http://factordb.com/index.php?id=1100000003815102870&open=prime	http://factordb.com/index.php?showid=1100000003815102870&base=21	http://factordb.com/index.php?showid=1100000003815102870	http://factordb.com/helper.php?id=1100000003815102870	http://factordb.com/cert.php?id=1100000003815102870	http://factordb.com/certchain.php?fid=1100000003815102870&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283*21%5E%28n%2B2%29-998%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13308	D0₂₄₈7E5	13×21²⁵¹+3386	252	333	http://factordb.com/index.php?id=1100000003815102871&open=prime	http://factordb.com/index.php?showid=1100000003815102871&base=21	http://factordb.com/index.php?showid=1100000003815102871	http://factordb.com/helper.php?id=1100000003815102871	http://factordb.com/cert.php?id=1100000003815102871	http://factordb.com/certchain.php?fid=1100000003815102871&action=all&fr=0&to=100	http://factordb.com/index.php?query=13*21%5E%28n%2B3%29%2B3386&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13309	E₂₄₉9IK	(7×21²⁵²−21157)/10	252	334	http://factordb.com/index.php?id=1100000000633439878&open=prime	http://factordb.com/index.php?showid=1100000000633439878&base=21	http://factordb.com/index.php?showid=1100000000633439878	http://factordb.com/helper.php?id=1100000000633439878	http://factordb.com/cert.php?id=1100000000633439878	http://factordb.com/certchain.php?fid=1100000000633439878&action=all&fr=0&to=100	http://factordb.com/index.php?query=%287*21%5E%28n%2B3%29-21157%29%2F10&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13310	1HHH0₂₄₈H	17132×21²⁴⁹+17	253	334	http://factordb.com/index.php?id=1100000003815102872&open=prime	http://factordb.com/index.php?showid=1100000003815102872&base=21	http://factordb.com/index.php?showid=1100000003815102872	http://factordb.com/helper.php?id=1100000003815102872	http://factordb.com/cert.php?id=1100000003815102872	http://factordb.com/certchain.php?fid=1100000003815102872&action=all&fr=0&to=100	http://factordb.com/index.php?query=17132*21%5E%28n%2B1%29%2B17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13311	D₂₅₁7B	(13×21²⁵³−2573)/20	253	335	http://factordb.com/index.php?id=1100000003815102873&open=prime	http://factordb.com/index.php?showid=1100000003815102873&base=21	http://factordb.com/index.php?showid=1100000003815102873	http://factordb.com/helper.php?id=1100000003815102873	http://factordb.com/cert.php?id=1100000003815102873	http://factordb.com/certchain.php?fid=1100000003815102873&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2813*21%5E%28n%2B2%29-2573%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13312	3F0₂₇₃IH	78×21²⁷⁵+395	277	366	http://factordb.com/index.php?id=1100000003815102874&open=prime	http://factordb.com/index.php?showid=1100000003815102874&base=21	http://factordb.com/index.php?showid=1100000003815102874	http://factordb.com/helper.php?id=1100000003815102874	http://factordb.com/cert.php?id=1100000003815102874	http://factordb.com/certchain.php?fid=1100000003815102874&action=all&fr=0&to=100	http://factordb.com/index.php?query=78*21%5E%28n%2B2%29%2B395&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13313	B3₂₇₅B	(223×21²⁷⁶+157)/20	277	366	http://factordb.com/index.php?id=1100000003815102875&open=prime	http://factordb.com/index.php?showid=1100000003815102875&base=21	http://factordb.com/index.php?showid=1100000003815102875	http://factordb.com/helper.php?id=1100000003815102875	http://factordb.com/cert.php?id=1100000003815102875	http://factordb.com/certchain.php?fid=1100000003815102875&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28223*21%5E%28n%2B1%29%2B157%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13314	D0₂₈₀D33J	13×21²⁸⁴+121798	285	377	http://factordb.com/index.php?id=1100000003815102876&open=prime	http://factordb.com/index.php?showid=1100000003815102876&base=21	http://factordb.com/index.php?showid=1100000003815102876	http://factordb.com/helper.php?id=1100000003815102876	http://factordb.com/cert.php?id=1100000003815102876	http://factordb.com/certchain.php?fid=1100000003815102876&action=all&fr=0&to=100	http://factordb.com/index.php?query=13*21%5E%28n%2B4%29%2B121798&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13315	H0₂₈₅60JJ	17×21²⁸⁹+55984	290	384	http://factordb.com/index.php?id=1100000003815102877&open=prime	http://factordb.com/index.php?showid=1100000003815102877&base=21	http://factordb.com/index.php?showid=1100000003815102877	http://factordb.com/helper.php?id=1100000003815102877	http://factordb.com/cert.php?id=1100000003815102877	http://factordb.com/certchain.php?fid=1100000003815102877&action=all&fr=0&to=100	http://factordb.com/index.php?query=17*21%5E%28n%2B4%29%2B55984&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13316	90₂₉₅BD	9×21²⁹⁷+244	298	394	http://factordb.com/index.php?id=1100000002633352280&open=prime	http://factordb.com/index.php?showid=1100000002633352280&base=21	http://factordb.com/index.php?showid=1100000002633352280	http://factordb.com/helper.php?id=1100000002633352280	http://factordb.com/cert.php?id=1100000002633352280	http://factordb.com/certchain.php?fid=1100000002633352280&action=all&fr=0&to=100	http://factordb.com/index.php?query=9*21%5E%28n%2B2%29%2B244&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13317	A09₂₉₆5	(4209×21²⁹⁷−89)/20	299	396	http://factordb.com/index.php?id=1100000003815102878&open=prime	http://factordb.com/index.php?showid=1100000003815102878&base=21	http://factordb.com/index.php?showid=1100000003815102878	http://factordb.com/helper.php?id=1100000003815102878	http://factordb.com/cert.php?id=1100000003815102878	http://factordb.com/certchain.php?fid=1100000003815102878&action=all&fr=0&to=100	http://factordb.com/index.php?query=%284209*21%5E%28n%2B1%29-89%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13318	B0₂₉₈56J	11×21³⁰¹+2350	302	400	http://factordb.com/index.php?id=1100000003815102879&open=prime	http://factordb.com/index.php?showid=1100000003815102879&base=21	http://factordb.com/index.php?showid=1100000003815102879	http://factordb.com/helper.php?id=1100000003815102879	http://factordb.com/cert.php?id=1100000003815102879	http://factordb.com/certchain.php?fid=1100000003815102879&action=all&fr=0&to=100	http://factordb.com/index.php?query=11*21%5E%28n%2B3%29%2B2350&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13319	H0₃₀₂7D	17×21³⁰⁴+160	305	404	http://factordb.com/index.php?id=1100000002633352461&open=prime	http://factordb.com/index.php?showid=1100000002633352461&base=21	http://factordb.com/index.php?showid=1100000002633352461	http://factordb.com/helper.php?id=1100000002633352461	http://factordb.com/cert.php?id=1100000002633352461	http://factordb.com/certchain.php?fid=1100000002633352461&action=all&fr=0&to=100	http://factordb.com/index.php?query=17*21%5E%28n%2B2%29%2B160&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13320	2F₃₀₇A	(11×21³⁰⁸−23)/4	309	408	http://factordb.com/index.php?id=1100000003815102880&open=prime	http://factordb.com/index.php?showid=1100000003815102880&base=21	http://factordb.com/index.php?showid=1100000003815102880	http://factordb.com/helper.php?id=1100000003815102880	http://factordb.com/cert.php?id=1100000003815102880	http://factordb.com/certchain.php?fid=1100000003815102880&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2811*21%5E%28n%2B1%29-23%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13321	6J₃₀₇3H	(139×21³⁰⁹−6779)/20	310	410	http://factordb.com/index.php?id=1100000003815102881&open=prime	http://factordb.com/index.php?showid=1100000003815102881&base=21	http://factordb.com/index.php?showid=1100000003815102881	http://factordb.com/helper.php?id=1100000003815102881	http://factordb.com/cert.php?id=1100000003815102881	http://factordb.com/certchain.php?fid=1100000003815102881&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28139*21%5E%28n%2B2%29-6779%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13322	FC₃₁₀8	(78×21³¹¹−23)/5	312	413	http://factordb.com/index.php?id=1100000000633439879&open=prime	http://factordb.com/index.php?showid=1100000000633439879&base=21	http://factordb.com/index.php?showid=1100000000633439879	http://factordb.com/helper.php?id=1100000000633439879	http://factordb.com/cert.php?id=1100000000633439879	http://factordb.com/certchain.php?fid=1100000000633439879&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2878*21%5E%28n%2B1%29-23%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13323	H10₃₀₇HHH	358×21³¹⁰+7871	312	413	http://factordb.com/index.php?id=1100000003815102882&open=prime	http://factordb.com/index.php?showid=1100000003815102882&base=21	http://factordb.com/index.php?showid=1100000003815102882	http://factordb.com/helper.php?id=1100000003815102882	http://factordb.com/cert.php?id=1100000003815102882	http://factordb.com/certchain.php?fid=1100000003815102882&action=all&fr=0&to=100	http://factordb.com/index.php?query=358*21%5E%28n%2B3%29%2B7871&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13324	70₃₁₈7D	7×21³²⁰+160	321	424	http://factordb.com/index.php?id=1100000002633352116&open=prime	http://factordb.com/index.php?showid=1100000002633352116&base=21	http://factordb.com/index.php?showid=1100000002633352116	http://factordb.com/helper.php?id=1100000002633352116	http://factordb.com/cert.php?id=1100000002633352116	http://factordb.com/certchain.php?fid=1100000002633352116&action=all&fr=0&to=100	http://factordb.com/index.php?query=7*21%5E%28n%2B2%29%2B160&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13325	30₃₁₉BE1	3×21³²²+5146	323	427	http://factordb.com/index.php?id=1100000003815102883&open=prime	http://factordb.com/index.php?showid=1100000003815102883&base=21	http://factordb.com/index.php?showid=1100000003815102883	http://factordb.com/helper.php?id=1100000003815102883	http://factordb.com/cert.php?id=1100000003815102883	http://factordb.com/certchain.php?fid=1100000003815102883&action=all&fr=0&to=100	http://factordb.com/index.php?query=3*21%5E%28n%2B3%29%2B5146&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13326	7I9₃₂₁D	(3309×21³²²+71)/20	324	428	http://factordb.com/index.php?id=1100000003815102884&open=prime	http://factordb.com/index.php?showid=1100000003815102884&base=21	http://factordb.com/index.php?showid=1100000003815102884	http://factordb.com/helper.php?id=1100000003815102884	http://factordb.com/cert.php?id=1100000003815102884	http://factordb.com/certchain.php?fid=1100000003815102884&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283309*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13327	7₃₅₆CD	(7×21³⁵⁸+2213)/20	358	473	http://factordb.com/index.php?id=1100000003815102885&open=prime	http://factordb.com/index.php?showid=1100000003815102885&base=21	http://factordb.com/index.php?showid=1100000003815102885	http://factordb.com/helper.php?id=1100000003815102885	http://factordb.com/cert.php?id=1100000003815102885	http://factordb.com/certchain.php?fid=1100000003815102885&action=all&fr=0&to=100	http://factordb.com/index.php?query=%287*21%5E%28n%2B2%29%2B2213%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13328	F0₃₅₇F9K	15×21³⁶⁰+6824	361	478	http://factordb.com/index.php?id=1100000000633439882&open=prime	http://factordb.com/index.php?showid=1100000000633439882&base=21	http://factordb.com/index.php?showid=1100000000633439882	http://factordb.com/helper.php?id=1100000000633439882	http://factordb.com/cert.php?id=1100000000633439882	http://factordb.com/certchain.php?fid=1100000000633439882&action=all&fr=0&to=100	http://factordb.com/index.php?query=15*21%5E%28n%2B3%29%2B6824&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13329	9F₃₆₈09B	(39×21³⁷¹−26983)/4	372	492	http://factordb.com/index.php?id=1100000003815102886&open=prime	http://factordb.com/index.php?showid=1100000003815102886&base=21	http://factordb.com/index.php?showid=1100000003815102886	http://factordb.com/helper.php?id=1100000003815102886	http://factordb.com/cert.php?id=1100000003815102886	http://factordb.com/certchain.php?fid=1100000003815102886&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2839*21%5E%28n%2B3%29-26983%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13330	20₃₇₁99D	2×21³⁷⁴+4171	375	495	http://factordb.com/index.php?id=1100000003815102887&open=prime	http://factordb.com/index.php?showid=1100000003815102887&base=21	http://factordb.com/index.php?showid=1100000003815102887	http://factordb.com/helper.php?id=1100000003815102887	http://factordb.com/cert.php?id=1100000003815102887	http://factordb.com/certchain.php?fid=1100000003815102887&action=all&fr=0&to=100	http://factordb.com/index.php?query=2*21%5E%28n%2B3%29%2B4171&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13331	F₃₇₉7B	(3×21³⁸¹−691)/4	381	504	http://factordb.com/index.php?id=1100000003815102888&open=prime	http://factordb.com/index.php?showid=1100000003815102888&base=21	http://factordb.com/index.php?showid=1100000003815102888	http://factordb.com/helper.php?id=1100000003815102888	http://factordb.com/cert.php?id=1100000003815102888	http://factordb.com/certchain.php?fid=1100000003815102888&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283*21%5E%28n%2B2%29-691%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13332	DB₃₈₆	(271×21³⁸⁶−11)/20	387	512	http://factordb.com/index.php?id=1100000002325402370&open=prime	http://factordb.com/index.php?showid=1100000002325402370&base=21	http://factordb.com/index.php?showid=1100000002325402370	http://factordb.com/helper.php?id=1100000002325402370	http://factordb.com/cert.php?id=1100000002325402370	http://factordb.com/certchain.php?fid=1100000002325402370&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28271*21%5En-11%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13333	6J₃₉₇	(139×21³⁹⁷−19)/20	398	526	http://factordb.com/index.php?id=1100000002325398467&open=prime	http://factordb.com/index.php?showid=1100000002325398467&base=21	http://factordb.com/index.php?showid=1100000002325398467	http://factordb.com/helper.php?id=1100000002325398467	http://factordb.com/cert.php?id=1100000002325398467	http://factordb.com/certchain.php?fid=1100000002325398467&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28139*21%5En-19%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13334	B10₃₉₉B	232×21⁴⁰⁰+11	402	532	http://factordb.com/index.php?id=1100000002633352355&open=prime	http://factordb.com/index.php?showid=1100000002633352355&base=21	http://factordb.com/index.php?showid=1100000002633352355	http://factordb.com/helper.php?id=1100000002633352355	http://factordb.com/cert.php?id=1100000002633352355	http://factordb.com/certchain.php?fid=1100000002633352355&action=all&fr=0&to=100	http://factordb.com/index.php?query=232*21%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13335	BB0₄₄₀EB	242×21⁴⁴²+305	444	587	http://factordb.com/index.php?id=1100000003815102889&open=prime	http://factordb.com/index.php?showid=1100000003815102889&base=21	http://factordb.com/index.php?showid=1100000003815102889	http://factordb.com/helper.php?id=1100000003815102889	http://factordb.com/cert.php?id=1100000003815102889	http://factordb.com/certchain.php?fid=1100000003815102889&action=all&fr=0&to=100	http://factordb.com/index.php?query=242*21%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13336	43₄₅₉2	(83×21⁴⁶⁰−23)/20	461	609	http://factordb.com/index.php?id=1100000003815102890&open=prime	http://factordb.com/index.php?showid=1100000003815102890&base=21	http://factordb.com/index.php?showid=1100000003815102890	http://factordb.com/helper.php?id=1100000003815102890	http://factordb.com/cert.php?id=1100000003815102890	http://factordb.com/certchain.php?fid=1100000003815102890&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2883*21%5E%28n%2B1%29-23%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13337	50₄₆₈C7D	5×21⁴⁷¹+5452	472	624	http://factordb.com/index.php?id=1100000003815102891&open=prime	http://factordb.com/index.php?showid=1100000003815102891&base=21	http://factordb.com/index.php?showid=1100000003815102891	http://factordb.com/helper.php?id=1100000003815102891	http://factordb.com/cert.php?id=1100000003815102891	http://factordb.com/certchain.php?fid=1100000003815102891&action=all&fr=0&to=100	http://factordb.com/index.php?query=5*21%5E%28n%2B3%29%2B5452&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13338	70₄₉₆8F1	7×21⁴⁹⁹+3844	500	661	http://factordb.com/index.php?id=1100000003815102892&open=prime	http://factordb.com/index.php?showid=1100000003815102892&base=21	http://factordb.com/index.php?showid=1100000003815102892	http://factordb.com/helper.php?id=1100000003815102892	http://factordb.com/cert.php?id=1100000003815102892	http://factordb.com/certchain.php?fid=1100000003815102892&action=all&fr=0&to=100	http://factordb.com/index.php?query=7*21%5E%28n%2B3%29%2B3844&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13339	E0₅₀₀B3B	14×21⁵⁰³+4925	504	667	http://factordb.com/index.php?id=1100000003815102893&open=prime	http://factordb.com/index.php?showid=1100000003815102893&base=21	http://factordb.com/index.php?showid=1100000003815102893	http://factordb.com/helper.php?id=1100000003815102893	http://factordb.com/cert.php?id=1100000003815102893	http://factordb.com/certchain.php?fid=1100000003815102893&action=all&fr=0&to=100	http://factordb.com/index.php?query=14*21%5E%28n%2B3%29%2B4925&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
21	13340	J₅₁₉9H	(19×21⁵²¹−4259)/20	521	689	http://factordb.com/index.php?id=1100000003815102894&open=prime	http://factordb.com/index.php?showid=1100000003815102894&base=21	http://factordb.com/index.php?showid=1100000003815102894	http://factordb.com/helper.php?id=1100000003815102894	http://factordb.com/cert.php?id=1100000003815102894	http://factordb.com/certchain.php?fid=1100000003815102894&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*21%5E%28n%2B2%29-4259%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7984	I7G0₂₅₄H	8882×22²⁵⁵+17	258	347	http://factordb.com/index.php?id=1100000003591372788&open=prime	http://factordb.com/index.php?showid=1100000003591372788&base=22	http://factordb.com/index.php?showid=1100000003591372788	http://factordb.com/helper.php?id=1100000003591372788	http://factordb.com/cert.php?id=1100000003591372788	http://factordb.com/certchain.php?fid=1100000003591372788&action=all&fr=0&to=100	http://factordb.com/index.php?query=8882*22%5E%28n%2B1%29%2B17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7985	D0₂₅₅5EEF	13×22²⁵⁹+60339	260	349	http://factordb.com/index.php?id=1100000003591371932&open=prime	http://factordb.com/index.php?showid=1100000003591371932&base=22	http://factordb.com/index.php?showid=1100000003591371932	http://factordb.com/helper.php?id=1100000003591371932	http://factordb.com/cert.php?id=1100000003591371932	http://factordb.com/certchain.php?fid=1100000003591371932&action=all&fr=0&to=100	http://factordb.com/index.php?query=13*22%5E%28n%2B4%29%2B60339&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7986	IK₃₂₂F	(398×22³²³−125)/21	324	435	http://factordb.com/index.php?id=1100000000840384145&open=prime	http://factordb.com/index.php?showid=1100000000840384145&base=22	http://factordb.com/index.php?showid=1100000000840384145	http://factordb.com/helper.php?id=1100000000840384145	http://factordb.com/cert.php?id=1100000000840384145	http://factordb.com/certchain.php?fid=1100000000840384145&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28398*22%5E%28n%2B1%29-125%29%2F21&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7987	C0₃₄₀G9	12×22³⁴²+361	343	461	http://factordb.com/index.php?id=1100000000840384159&open=prime	http://factordb.com/index.php?showid=1100000000840384159&base=22	http://factordb.com/index.php?showid=1100000000840384159	http://factordb.com/helper.php?id=1100000000840384159	http://factordb.com/cert.php?id=1100000000840384159	http://factordb.com/certchain.php?fid=1100000000840384159&action=all&fr=0&to=100	http://factordb.com/index.php?query=12*22%5E%28n%2B2%29%2B361&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7988	77E₃₄₈K7	(485×22³⁵⁰+373)/3	352	473	http://factordb.com/index.php?id=1100000003591369779&open=prime	http://factordb.com/index.php?showid=1100000003591369779&base=22	http://factordb.com/index.php?showid=1100000003591369779	http://factordb.com/helper.php?id=1100000003591369779	http://factordb.com/cert.php?id=1100000003591369779	http://factordb.com/certchain.php?fid=1100000003591369779&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28485*22%5E%28n%2B2%29%2B373%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7989	J₃₇₉KJ	(19×22³⁸¹+443)/21	381	512	http://factordb.com/index.php?id=1100000003591369027&open=prime	http://factordb.com/index.php?showid=1100000003591369027&base=22	http://factordb.com/index.php?showid=1100000003591369027	http://factordb.com/helper.php?id=1100000003591369027	http://factordb.com/cert.php?id=1100000003591369027	http://factordb.com/certchain.php?fid=1100000003591369027&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*22%5E%28n%2B2%29%2B443%29%2F21&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7990	J₃₈₈EJ	(19×22³⁹⁰−2329)/21	390	524	http://factordb.com/index.php?id=1100000003591367729&open=prime	http://factordb.com/index.php?showid=1100000003591367729&base=22	http://factordb.com/index.php?showid=1100000003591367729	http://factordb.com/helper.php?id=1100000003591367729	http://factordb.com/cert.php?id=1100000003591367729	http://factordb.com/certchain.php?fid=1100000003591367729&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*22%5E%28n%2B2%29-2329%29%2F21&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7991	DJ₄₀₀	(292×22⁴⁰⁰−19)/21	401	539	http://factordb.com/index.php?id=1100000002325880110&open=prime	http://factordb.com/index.php?showid=1100000002325880110&base=22	http://factordb.com/index.php?showid=1100000002325880110	http://factordb.com/helper.php?id=1100000002325880110	http://factordb.com/cert.php?id=1100000002325880110	http://factordb.com/certchain.php?fid=1100000002325880110&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28292*22%5En-19%29%2F21&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7992	E₄₀₄K7	(2×22⁴⁰⁶+373)/3	406	545	http://factordb.com/index.php?id=1100000003591366298&open=prime	http://factordb.com/index.php?showid=1100000003591366298&base=22	http://factordb.com/index.php?showid=1100000003591366298	http://factordb.com/helper.php?id=1100000003591366298	http://factordb.com/cert.php?id=1100000003591366298	http://factordb.com/certchain.php?fid=1100000003591366298&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282*22%5E%28n%2B2%29%2B373%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7993	66F₄₅₃B3	(971×22⁴⁵⁵−705)/7	457	613	http://factordb.com/index.php?id=1100000003591365809&open=prime	http://factordb.com/index.php?showid=1100000003591365809&base=22	http://factordb.com/index.php?showid=1100000003591365809	http://factordb.com/helper.php?id=1100000003591365809	http://factordb.com/cert.php?id=1100000003591365809	http://factordb.com/certchain.php?fid=1100000003591365809&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28971*22%5E%28n%2B2%29-705%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7994	L0₄₅₄B63	21×22⁴⁵⁷+5459	458	615	http://factordb.com/index.php?id=1100000003591365331&open=prime	http://factordb.com/index.php?showid=1100000003591365331&base=22	http://factordb.com/index.php?showid=1100000003591365331	http://factordb.com/helper.php?id=1100000003591365331	http://factordb.com/cert.php?id=1100000003591365331	http://factordb.com/certchain.php?fid=1100000003591365331&action=all&fr=0&to=100	http://factordb.com/index.php?query=21*22%5E%28n%2B3%29%2B5459&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7995	L₄₈₃G3	22⁴⁸⁵−129	485	652	http://factordb.com/index.php?id=1100000003591364730&open=prime	http://factordb.com/index.php?showid=1100000003591364730&base=22	http://factordb.com/index.php?showid=1100000003591364730	http://factordb.com/helper.php?id=1100000003591364730	http://factordb.com/cert.php?id=1100000003591364730	http://factordb.com/certchain.php?fid=1100000003591364730&action=all&fr=0&to=100	http://factordb.com/index.php?query=22%5E%28n%2B2%29-129&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7996	E60₄₉₆L	314×22⁴⁹⁷+21	499	670	http://factordb.com/index.php?id=1100000000632703239&open=prime	http://factordb.com/index.php?showid=1100000000632703239&base=22	http://factordb.com/index.php?showid=1100000000632703239	http://factordb.com/helper.php?id=1100000000632703239	http://factordb.com/cert.php?id=1100000000632703239	http://factordb.com/certchain.php?fid=1100000000632703239&action=all&fr=0&to=100	http://factordb.com/index.php?query=314*22%5E%28n%2B1%29%2B21&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7997	I₆₂₆AF	(6×22⁶²⁸−1259)/7	628	843	http://factordb.com/index.php?id=1100000000632724334&open=prime	http://factordb.com/index.php?showid=1100000000632724334&base=22	http://factordb.com/index.php?showid=1100000000632724334	http://factordb.com/helper.php?id=1100000000632724334	http://factordb.com/cert.php?id=1100000000632724334	http://factordb.com/certchain.php?fid=1100000000632724334&action=all&fr=0&to=100	http://factordb.com/index.php?query=%286*22%5E%28n%2B2%29-1259%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7998	K0₇₆₀EC1	20×22⁷⁶³+7041	764	1026	http://factordb.com/index.php?id=1100000000632724415&open=prime	http://factordb.com/index.php?showid=1100000000632724415&base=22	http://factordb.com/index.php?showid=1100000000632724415	http://factordb.com/helper.php?id=1100000000632724415	http://factordb.com/cert.php?id=1100000000632724415	http://factordb.com/certchain.php?fid=1100000000632724415&action=all&fr=0&to=100	http://factordb.com/index.php?query=20*22%5E%28n%2B3%29%2B7041&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	7999	J0₇₆₇IGGJ	19×22⁷⁷¹+199779	772	1037	http://factordb.com/index.php?id=1100000003591362567&open=prime	http://factordb.com/index.php?showid=1100000003591362567&base=22	http://factordb.com/index.php?showid=1100000003591362567	http://factordb.com/helper.php?id=1100000003591362567	http://factordb.com/cert.php?id=1100000003591362567	http://factordb.com/certchain.php?fid=1100000003591362567&action=all&fr=0&to=100	http://factordb.com/index.php?query=19*22%5E%28n%2B4%29%2B199779&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	8000	7₉₅₉K7	(22⁹⁶¹+857)/3	961	1290	http://factordb.com/index.php?id=1100000003591361817&open=prime	http://factordb.com/index.php?showid=1100000003591361817&base=22	http://factordb.com/index.php?showid=1100000003591361817	http://factordb.com/helper.php?id=1100000003591361817	http://factordb.com/cert.php?id=1100000003591361817	http://factordb.com/certchain.php?fid=1100000003591361817&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2822%5E%28n%2B2%29%2B857%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	8001	L₂₃₈₅KE7	22²³⁸⁸−653	2388	3206	http://factordb.com/index.php?id=1100000003591360774&open=prime	http://factordb.com/index.php?showid=1100000003591360774&base=22	http://factordb.com/index.php?showid=1100000003591360774	http://factordb.com/helper.php?id=1100000003591360774	http://factordb.com/cert.php?id=1100000003591360774	http://factordb.com/certchain.php?fid=1100000003591360774&action=all&fr=0&to=100	http://factordb.com/index.php?query=22%5E%28n%2B3%29-653&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
22	8002	7₃₈₁₅2L	(22³⁸¹⁷−289)/3	3817	5124	http://factordb.com/index.php?id=1100000003591359839&open=prime	http://factordb.com/index.php?showid=1100000003591359839&base=22	http://factordb.com/index.php?showid=1100000003591359839	http://factordb.com/helper.php?id=1100000003591359839	http://factordb.com/cert.php?id=1100000003591359839	http://factordb.com/certchain.php?fid=1100000003591359839&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2822%5E%28n%2B2%29-289%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3400	I0₂₄₁I5	18×24²⁴³+437	244	337	http://factordb.com/index.php?id=1100000002633360037&open=prime	http://factordb.com/index.php?showid=1100000002633360037&base=24	http://factordb.com/index.php?showid=1100000002633360037	http://factordb.com/helper.php?id=1100000002633360037	http://factordb.com/cert.php?id=1100000002633360037	http://factordb.com/certchain.php?fid=1100000002633360037&action=all&fr=0&to=100	http://factordb.com/index.php?query=18*24%5E%28n%2B2%29%2B437&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3401	D0₂₅₉KKD	13×24²⁶²+12013	263	363	http://factordb.com/index.php?id=1100000003593270725&open=prime	http://factordb.com/index.php?showid=1100000003593270725&base=24	http://factordb.com/index.php?showid=1100000003593270725	http://factordb.com/helper.php?id=1100000003593270725	http://factordb.com/cert.php?id=1100000003593270725	http://factordb.com/certchain.php?fid=1100000003593270725&action=all&fr=0&to=100	http://factordb.com/index.php?query=13*24%5E%28n%2B3%29%2B12013&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3402	C7₂₉₈	(283×24²⁹⁸−7)/23	299	413	http://factordb.com/index.php?id=1100000002326181235&open=prime	http://factordb.com/index.php?showid=1100000002326181235&base=24	http://factordb.com/index.php?showid=1100000002326181235	http://factordb.com/helper.php?id=1100000002326181235	http://factordb.com/cert.php?id=1100000002326181235	http://factordb.com/certchain.php?fid=1100000002326181235&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28283*24%5En-7%29%2F23&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3403	20₃₁₃7	2×24³¹⁴+7	315	434	http://factordb.com/index.php?id=1100000002355610241&open=prime	http://factordb.com/index.php?showid=1100000002355610241&base=24	http://factordb.com/index.php?showid=1100000002355610241	http://factordb.com/helper.php?id=1100000002355610241	http://factordb.com/cert.php?id=1100000002355610241	http://factordb.com/certchain.php?fid=1100000002355610241&action=all&fr=0&to=100	http://factordb.com/index.php?query=2*24%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3404	BC0₃₃₁B	276×24³³²+11	334	461	http://factordb.com/index.php?id=1100000002633359842&open=prime	http://factordb.com/index.php?showid=1100000002633359842&base=24	http://factordb.com/index.php?showid=1100000002633359842	http://factordb.com/helper.php?id=1100000002633359842	http://factordb.com/cert.php?id=1100000002633359842	http://factordb.com/certchain.php?fid=1100000002633359842&action=all&fr=0&to=100	http://factordb.com/index.php?query=276*24%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3405	N₂₆₄₄LLN	24²⁶⁴⁷−1201	2647	3654	http://factordb.com/index.php?id=1100000003593270089&open=prime	http://factordb.com/index.php?showid=1100000003593270089&base=24	http://factordb.com/index.php?showid=1100000003593270089	http://factordb.com/helper.php?id=1100000003593270089	http://factordb.com/cert.php?id=1100000003593270089	http://factordb.com/certchain.php?fid=1100000003593270089&action=all&fr=0&to=100	http://factordb.com/index.php?query=24%5E%28n%2B3%29-1201&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3406	D₂₆₉₈LD	(13×24²⁷⁰⁰+4403)/23	2700	3727	http://factordb.com/index.php?id=1100000003593269876&open=prime	http://factordb.com/index.php?showid=1100000003593269876&base=24	http://factordb.com/index.php?showid=1100000003593269876	http://factordb.com/helper.php?id=1100000003593269876	http://factordb.com/cert.php?id=1100000003593269876	http://factordb.com/certchain.php?fid=1100000003593269876&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2813*24%5E%28n%2B2%29%2B4403%29%2F23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3407	A0₂₉₅₁8ID	10×24²⁹⁵⁴+5053	2955	4079	http://factordb.com/index.php?id=1100000003593269654&open=prime	http://factordb.com/index.php?showid=1100000003593269654&base=24	http://factordb.com/index.php?showid=1100000003593269654	http://factordb.com/helper.php?id=1100000003593269654	http://factordb.com/cert.php?id=1100000003593269654	http://factordb.com/certchain.php?fid=1100000003593269654&action=all&fr=0&to=100	http://factordb.com/index.php?query=10*24%5E%28n%2B3%29%2B5053&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3408	88N₅₉₅₁	201×24⁵⁹⁵¹−1	5953	8216	http://factordb.com/index.php?id=1100000003593275880&open=prime	http://factordb.com/index.php?showid=1100000003593275880&base=24	http://factordb.com/index.php?showid=1100000003593275880	http://factordb.com/helper.php?id=1100000003593275880	proven prime by N+1 test (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2), since N+1 is trivially fully factored	http://factordb.com/index.php?id=1100000003593373246&open=ecm	http://factordb.com/index.php?query=201*24%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
24	3409	N00N₈₁₂₉LN	13249×24⁸¹³¹−49	8134	11227	http://factordb.com/index.php?id=1100000003593391606&open=prime	http://factordb.com/index.php?showid=1100000003593391606&base=24	http://factordb.com/index.php?showid=1100000003593391606	http://factordb.com/helper.php?id=1100000003593391606	http://factordb.com/cert.php?id=1100000003593391606	http://factordb.com/certchain.php?fid=1100000003593391606&action=all&fr=0&to=100	http://factordb.com/index.php?query=13249*24%5E%28n%2B2%29-49&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25174	OL0₂₁₄M9	645×26²¹⁶+581	218	309	http://factordb.com/index.php?id=1100000000840631576&open=prime	http://factordb.com/index.php?showid=1100000000840631576&base=26	http://factordb.com/index.php?showid=1100000000840631576	http://factordb.com/helper.php?id=1100000000840631576	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), N−1 is 2²×5²×7×223×42849349×(296-digit prime)	http://factordb.com/index.php?id=1100000000840631577&open=ecm	http://factordb.com/index.php?query=645*26%5E%28n%2B2%29%2B581&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25175	1A₂₁₉P	(7×26²²⁰+73)/5	221	312	http://factordb.com/index.php?id=1100000000840631595&open=prime	http://factordb.com/index.php?showid=1100000000840631595&base=26	http://factordb.com/index.php?showid=1100000000840631595	http://factordb.com/helper.php?id=1100000000840631595	http://factordb.com/cert.php?id=1100000000840631595	http://factordb.com/certchain.php?fid=1100000000840631595&action=all&fr=0&to=100	http://factordb.com/index.php?query=%287*26%5E%28n%2B1%29%2B73%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25176	A₂₂₃DP	(2×26²²⁵+463)/5	225	318	http://factordb.com/index.php?id=1100000003850155262&open=prime	http://factordb.com/index.php?showid=1100000003850155262&base=26	http://factordb.com/index.php?showid=1100000003850155262	http://factordb.com/helper.php?id=1100000003850155262	http://factordb.com/cert.php?id=1100000003850155262	http://factordb.com/certchain.php?fid=1100000003850155262&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282*26%5E%28n%2B2%29%2B463%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25177	6J₂₂₅	(169×26²²⁵−19)/25	226	320	http://factordb.com/index.php?id=1100000002328050895&open=prime	http://factordb.com/index.php?showid=1100000002328050895&base=26	http://factordb.com/index.php?showid=1100000002328050895	http://factordb.com/helper.php?id=1100000002328050895	http://factordb.com/cert.php?id=1100000002328050895	http://factordb.com/certchain.php?fid=1100000002328050895&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28169*26%5En-19%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25178	O₂₂₈5	(24×26²²⁹−499)/25	229	325	http://factordb.com/index.php?id=1100000002328059255&open=prime	http://factordb.com/index.php?showid=1100000002328059255&base=26	http://factordb.com/index.php?showid=1100000002328059255	http://factordb.com/helper.php?id=1100000002328059255	http://factordb.com/cert.php?id=1100000002328059255	http://factordb.com/certchain.php?fid=1100000002328059255&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2824*26%5E%28n%2B1%29-499%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25179	K0₂₃₀K0IP	20×26²³⁴+352013	235	333	http://factordb.com/index.php?id=1100000000840631669&open=prime	http://factordb.com/index.php?showid=1100000000840631669&base=26	http://factordb.com/index.php?showid=1100000000840631669	http://factordb.com/helper.php?id=1100000000840631669	http://factordb.com/cert.php?id=1100000000840631669	http://factordb.com/certchain.php?fid=1100000000840631669&action=all&fr=0&to=100	http://factordb.com/index.php?query=20*26%5E%28n%2B4%29%2B352013&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25180	B0₂₃₆OB	11×26²³⁸+635	239	338	http://factordb.com/index.php?id=1100000002634136234&open=prime	http://factordb.com/index.php?showid=1100000002634136234&base=26	http://factordb.com/index.php?showid=1100000002634136234	http://factordb.com/helper.php?id=1100000002634136234	http://factordb.com/cert.php?id=1100000002634136234	http://factordb.com/certchain.php?fid=1100000002634136234&action=all&fr=0&to=100	http://factordb.com/index.php?query=11*26%5E%28n%2B2%29%2B635&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25181	11G0₂₃₉9	718×26²⁴⁰+9	243	343	http://factordb.com/index.php?id=1100000000840631687&open=prime	http://factordb.com/index.php?showid=1100000000840631687&base=26	http://factordb.com/index.php?showid=1100000000840631687	http://factordb.com/helper.php?id=1100000000840631687	http://factordb.com/cert.php?id=1100000000840631687	http://factordb.com/certchain.php?fid=1100000000840631687&action=all&fr=0&to=100	http://factordb.com/index.php?query=718*26%5E%28n%2B1%29%2B9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25182	K0₂₄₁E5	20×26²⁴³+369	244	346	http://factordb.com/index.php?id=1100000002634136479&open=prime	http://factordb.com/index.php?showid=1100000002634136479&base=26	http://factordb.com/index.php?showid=1100000002634136479	http://factordb.com/helper.php?id=1100000002634136479	http://factordb.com/cert.php?id=1100000002634136479	http://factordb.com/certchain.php?fid=1100000002634136479&action=all&fr=0&to=100	http://factordb.com/index.php?query=20*26%5E%28n%2B2%29%2B369&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25183	J₂₄₃0L	(19×26²⁴⁵−12319)/25	245	347	http://factordb.com/index.php?id=1100000003850155263&open=prime	http://factordb.com/index.php?showid=1100000003850155263&base=26	http://factordb.com/index.php?showid=1100000003850155263	http://factordb.com/helper.php?id=1100000003850155263	http://factordb.com/cert.php?id=1100000003850155263	http://factordb.com/certchain.php?fid=1100000003850155263&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*26%5E%28n%2B2%29-12319%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25184	B₂₅₁I9	(11×26²⁵³+4489)/25	253	358	http://factordb.com/index.php?id=1100000003850155264&open=prime	http://factordb.com/index.php?showid=1100000003850155264&base=26	http://factordb.com/index.php?showid=1100000003850155264	http://factordb.com/helper.php?id=1100000003850155264	http://factordb.com/cert.php?id=1100000003850155264	http://factordb.com/certchain.php?fid=1100000003850155264&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2811*26%5E%28n%2B2%29%2B4489%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25185	F₂₅₀0PCF	(3×26²⁵⁴−1284793)/5	254	360	http://factordb.com/index.php?id=1100000000840631708&open=prime	http://factordb.com/index.php?showid=1100000000840631708&base=26	http://factordb.com/index.php?showid=1100000000840631708	http://factordb.com/helper.php?id=1100000000840631708	http://factordb.com/cert.php?id=1100000000840631708	http://factordb.com/certchain.php?fid=1100000000840631708&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283*26%5E%28n%2B4%29-1284793%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25186	4E7₂₆₂	(2957×26²⁶²−7)/25	264	373	http://factordb.com/index.php?id=1100000003850155265&open=prime	http://factordb.com/index.php?showid=1100000003850155265&base=26	http://factordb.com/index.php?showid=1100000003850155265	http://factordb.com/helper.php?id=1100000003850155265	http://factordb.com/cert.php?id=1100000003850155265	http://factordb.com/certchain.php?fid=1100000003850155265&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282957*26%5En-7%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25187	E7₂₆₄OL	(357×26²⁶⁶+11393)/25	267	378	http://factordb.com/index.php?id=1100000003850155266&open=prime	http://factordb.com/index.php?showid=1100000003850155266&base=26	http://factordb.com/index.php?showid=1100000003850155266	http://factordb.com/helper.php?id=1100000003850155266	http://factordb.com/cert.php?id=1100000003850155266	http://factordb.com/certchain.php?fid=1100000003850155266&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28357*26%5E%28n%2B2%29%2B11393%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25188	EIL₂₆₇	(9571×26²⁶⁷−21)/25	269	381	http://factordb.com/index.php?id=1100000000840631801&open=prime	http://factordb.com/index.php?showid=1100000000840631801&base=26	http://factordb.com/index.php?showid=1100000000840631801	http://factordb.com/helper.php?id=1100000000840631801	http://factordb.com/cert.php?id=1100000000840631801	http://factordb.com/certchain.php?fid=1100000000840631801&action=all&fr=0&to=100	http://factordb.com/index.php?query=%289571*26%5En-21%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25189	6₂₆₈4F	(6×26²⁷⁰−1081)/25	270	382	http://factordb.com/index.php?id=1100000000840631976&open=prime	http://factordb.com/index.php?showid=1100000000840631976&base=26	http://factordb.com/index.php?showid=1100000000840631976	http://factordb.com/helper.php?id=1100000000840631976	http://factordb.com/cert.php?id=1100000000840631976	http://factordb.com/certchain.php?fid=1100000000840631976&action=all&fr=0&to=100	http://factordb.com/index.php?query=%286*26%5E%28n%2B2%29-1081%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25190	D020₂₇₃H	8790×26²⁷⁴+17	277	392	http://factordb.com/index.php?id=1100000003850155267&open=prime	http://factordb.com/index.php?showid=1100000003850155267&base=26	http://factordb.com/index.php?showid=1100000003850155267	http://factordb.com/helper.php?id=1100000003850155267	http://factordb.com/cert.php?id=1100000003850155267	http://factordb.com/certchain.php?fid=1100000003850155267&action=all&fr=0&to=100	http://factordb.com/index.php?query=8790*26%5E%28n%2B1%29%2B17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25191	B₂₉₁KB	(11×26²⁹³+5839)/25	293	415	http://factordb.com/index.php?id=1100000003850155268&open=prime	http://factordb.com/index.php?showid=1100000003850155268&base=26	http://factordb.com/index.php?showid=1100000003850155268	http://factordb.com/helper.php?id=1100000003850155268	http://factordb.com/cert.php?id=1100000003850155268	http://factordb.com/certchain.php?fid=1100000003850155268&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2811*26%5E%28n%2B2%29%2B5839%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25192	5₂₉₃O5	(26²⁹⁵+2469)/5	295	417	http://factordb.com/index.php?id=1100000003850155269&open=prime	http://factordb.com/index.php?showid=1100000003850155269&base=26	http://factordb.com/index.php?showid=1100000003850155269	http://factordb.com/helper.php?id=1100000003850155269	http://factordb.com/cert.php?id=1100000003850155269	http://factordb.com/certchain.php?fid=1100000003850155269&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2826%5E%28n%2B2%29%2B2469%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25193	D7₃₀₀	(332×26³⁰⁰−7)/25	301	426	http://factordb.com/index.php?id=1100000002328053362&open=prime	http://factordb.com/index.php?showid=1100000002328053362&base=26	http://factordb.com/index.php?showid=1100000002328053362	http://factordb.com/helper.php?id=1100000002328053362	http://factordb.com/cert.php?id=1100000002328053362	http://factordb.com/certchain.php?fid=1100000002328053362&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28332*26%5En-7%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25194	E₃₀₅IL	(14×26³⁰⁷+2761)/25	307	435	http://factordb.com/index.php?id=1100000000840632032&open=prime	http://factordb.com/index.php?showid=1100000000840632032&base=26	http://factordb.com/index.php?showid=1100000000840632032	http://factordb.com/helper.php?id=1100000000840632032	http://factordb.com/cert.php?id=1100000000840632032	http://factordb.com/certchain.php?fid=1100000000840632032&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2814*26%5E%28n%2B2%29%2B2761%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25195	PO5₃₁₂	(3371×26³¹²−1)/5	314	445	http://factordb.com/index.php?id=1100000003850155270&open=prime	http://factordb.com/index.php?showid=1100000003850155270&base=26	http://factordb.com/index.php?showid=1100000003850155270	http://factordb.com/helper.php?id=1100000003850155270	http://factordb.com/cert.php?id=1100000003850155270	http://factordb.com/certchain.php?fid=1100000003850155270&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283371*26%5En-1%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25196	47₃₁₄	(107×26³¹⁴−7)/25	315	445	http://factordb.com/index.php?id=1100000002328050727&open=prime	http://factordb.com/index.php?showid=1100000002328050727&base=26	http://factordb.com/index.php?showid=1100000002328050727	http://factordb.com/helper.php?id=1100000002328050727	http://factordb.com/cert.php?id=1100000002328050727	http://factordb.com/certchain.php?fid=1100000002328050727&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28107*26%5En-7%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25197	A₃₃₅60F	(2×26³³⁸−14797)/5	338	478	http://factordb.com/index.php?id=1100000000840632163&open=prime	http://factordb.com/index.php?showid=1100000000840632163&base=26	http://factordb.com/index.php?showid=1100000000840632163	http://factordb.com/helper.php?id=1100000000840632163	http://factordb.com/cert.php?id=1100000000840632163	http://factordb.com/certchain.php?fid=1100000000840632163&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282*26%5E%28n%2B3%29-14797%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25198	O5K5₃₄₁	(81871×26³⁴¹−1)/5	344	487	http://factordb.com/index.php?id=1100000003850155271&open=prime	http://factordb.com/index.php?showid=1100000003850155271&base=26	http://factordb.com/index.php?showid=1100000003850155271	http://factordb.com/helper.php?id=1100000003850155271	http://factordb.com/cert.php?id=1100000003850155271	http://factordb.com/certchain.php?fid=1100000003850155271&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2887871*26%5En-1%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25199	9K₃₄₃AP	(49×26³⁴⁵−1279)/5	346	490	http://factordb.com/index.php?id=1100000000840632228&open=prime	http://factordb.com/index.php?showid=1100000000840632228&base=26	http://factordb.com/index.php?showid=1100000000840632228	http://factordb.com/helper.php?id=1100000000840632228	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is 1274/5×(26³⁴⁴−1), thus factor N−1 is equivalent to factor 26³⁴⁴−1, and for the factorization of 26³⁴⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&Exp=344&c0=-&EN=	http://factordb.com/index.php?id=1100000000840632232&open=ecm	http://factordb.com/index.php?query=%2849*26%5E%28n%2B2%29-1279%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25200	8₃₅₄1	(8×26³⁵⁵−183)/25	355	502	http://factordb.com/index.php?id=1100000000840632517&open=prime	http://factordb.com/index.php?showid=1100000000840632517&base=26	http://factordb.com/index.php?showid=1100000000840632517	http://factordb.com/helper.php?id=1100000000840632517	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is 208/25×(26³⁵⁴−1), thus factor N−1 is equivalent to factor 26³⁵⁴−1, and for the factorization of 26³⁵⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&Exp=354&c0=-&EN=	http://factordb.com/index.php?id=1100000000840632623&open=ecm	http://factordb.com/index.php?query=%288*26%5E%28n%2B1%29-183%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25201	L0₃₅₆66K9	21×26³⁶⁰+110041	361	511	http://factordb.com/index.php?id=1100000000840632748&open=prime	http://factordb.com/index.php?showid=1100000000840632748&base=26	http://factordb.com/index.php?showid=1100000000840632748	http://factordb.com/helper.php?id=1100000000840632748	http://factordb.com/cert.php?id=1100000000840632748	http://factordb.com/certchain.php?fid=1100000000840632748&action=all&fr=0&to=100	http://factordb.com/index.php?query=21*26%5E%28n%2B4%29%2B110041&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25202	K0₃₅₈KIP	20×26³⁶¹+14013	362	513	http://factordb.com/index.php?id=1100000000840632880&open=prime	http://factordb.com/index.php?showid=1100000000840632880&base=26	http://factordb.com/index.php?showid=1100000000840632880	http://factordb.com/helper.php?id=1100000000840632880	http://factordb.com/cert.php?id=1100000000840632880	http://factordb.com/certchain.php?fid=1100000000840632880&action=all&fr=0&to=100	http://factordb.com/index.php?query=20*26%5E%28n%2B3%29%2B14013&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25203	J0₃₆₀A0P	19×26³⁶³+6785	364	515	http://factordb.com/index.php?id=1100000003850155272&open=prime	http://factordb.com/index.php?showid=1100000003850155272&base=26	http://factordb.com/index.php?showid=1100000003850155272	http://factordb.com/helper.php?id=1100000003850155272	http://factordb.com/cert.php?id=1100000003850155272	http://factordb.com/certchain.php?fid=1100000003850155272&action=all&fr=0&to=100	http://factordb.com/index.php?query=19*26%5E%28n%2B3%29%2B6785&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25204	OK6₃₇₆9	(16106×26³⁷⁷+69)/25	379	537	http://factordb.com/index.php?id=1100000000840633320&open=prime	http://factordb.com/index.php?showid=1100000000840633320&base=26	http://factordb.com/index.php?showid=1100000000840633320	http://factordb.com/helper.php?id=1100000000840633320	http://factordb.com/cert.php?id=1100000000840633320	http://factordb.com/certchain.php?fid=1100000000840633320&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2816106*26%5E%28n%2B1%29%2B69%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25205	J₄₀₆7	(19×26⁴⁰⁷−319)/25	407	576	http://factordb.com/index.php?id=1100000002328055467&open=prime	http://factordb.com/index.php?showid=1100000002328055467&base=26	http://factordb.com/index.php?showid=1100000002328055467	http://factordb.com/helper.php?id=1100000002328055467	http://factordb.com/cert.php?id=1100000002328055467	http://factordb.com/certchain.php?fid=1100000002328055467&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*26%5E%28n%2B1%29-319%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25206	9B₄₃₇	(236×26⁴³⁷−11)/25	438	620	http://factordb.com/index.php?id=1100000002328051905&open=prime	http://factordb.com/index.php?showid=1100000002328051905&base=26	http://factordb.com/index.php?showid=1100000002328051905	http://factordb.com/helper.php?id=1100000002328051905	http://factordb.com/cert.php?id=1100000002328051905	http://factordb.com/certchain.php?fid=1100000002328051905&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28236*26%5En-11%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25207	3₄₄₂GL	(3×26⁴⁴⁴+8897)/25	444	628	http://factordb.com/index.php?id=1100000003850155273&open=prime	http://factordb.com/index.php?showid=1100000003850155273&base=26	http://factordb.com/index.php?showid=1100000003850155273	http://factordb.com/helper.php?id=1100000003850155273	http://factordb.com/cert.php?id=1100000003850155273	http://factordb.com/certchain.php?fid=1100000003850155273&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283*26%5E%28n%2B2%29%2B8897%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25208	1M₄₉₁P	(47×26⁴⁹²+53)/25	493	697	http://factordb.com/index.php?id=1100000000840633390&open=prime	http://factordb.com/index.php?showid=1100000000840633390&base=26	http://factordb.com/index.php?showid=1100000000840633390	http://factordb.com/helper.php?id=1100000000840633390	http://factordb.com/cert.php?id=1100000000840633390	http://factordb.com/certchain.php?fid=1100000000840633390&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2847*26%5E%28n%2B1%29%2B53%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25209	40₅₀₉GL	4×26⁵¹¹+437	512	724	http://factordb.com/index.php?id=1100000000840633483&open=prime	http://factordb.com/index.php?showid=1100000000840633483&base=26	http://factordb.com/index.php?showid=1100000000840633483	http://factordb.com/helper.php?id=1100000000840633483	http://factordb.com/cert.php?id=1100000000840633483	http://factordb.com/certchain.php?fid=1100000000840633483&action=all&fr=0&to=100	http://factordb.com/index.php?query=4*26%5E%28n%2B2%29%2B437&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25210	BFA₅₁₁5	(1507×26⁵¹²−27)/5	514	727	http://factordb.com/index.php?id=1100000003850155274&open=prime	http://factordb.com/index.php?showid=1100000003850155274&base=26	http://factordb.com/index.php?showid=1100000003850155274	http://factordb.com/helper.php?id=1100000003850155274	http://factordb.com/cert.php?id=1100000003850155274	http://factordb.com/certchain.php?fid=1100000003850155274&action=all&fr=0&to=100	http://factordb.com/index.php?query=%281507*26%5E%28n%2B1%29-27%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25211	LK₅₁₈5	(109×26⁵¹⁹−79)/5	520	736	http://factordb.com/index.php?id=1100000003850155276&open=prime	http://factordb.com/index.php?showid=1100000003850155276&base=26	http://factordb.com/index.php?showid=1100000003850155276	http://factordb.com/helper.php?id=1100000003850155276	http://factordb.com/cert.php?id=1100000003850155276	http://factordb.com/certchain.php?fid=1100000003850155276&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28109*26%5E%28n%2B1%29-79%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25212	MI₅₄₃3	(568×26⁵⁴⁴−393)/25	545	772	http://factordb.com/index.php?id=1100000003850155277&open=prime	http://factordb.com/index.php?showid=1100000003850155277&base=26	http://factordb.com/index.php?showid=1100000003850155277	http://factordb.com/helper.php?id=1100000003850155277	http://factordb.com/cert.php?id=1100000003850155277	http://factordb.com/certchain.php?fid=1100000003850155277&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28568*26%5E%28n%2B1%29-393%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25213	E4E₅₅₉7	(9214×26⁵⁶⁰−189)/25	562	795	http://factordb.com/index.php?id=1100000003850155278&open=prime	http://factordb.com/index.php?showid=1100000003850155278&base=26	http://factordb.com/index.php?showid=1100000003850155278	http://factordb.com/helper.php?id=1100000003850155278	http://factordb.com/cert.php?id=1100000003850155278	http://factordb.com/certchain.php?fid=1100000003850155278&action=all&fr=0&to=100	http://factordb.com/index.php?query=%289214*26%5E%28n%2B1%29-189%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25214	80₅₇₇C7	8×26⁵⁷⁹+319	580	821	http://factordb.com/index.php?id=1100000002634136160&open=prime	http://factordb.com/index.php?showid=1100000002634136160&base=26	http://factordb.com/index.php?showid=1100000002634136160	http://factordb.com/helper.php?id=1100000002634136160	http://factordb.com/cert.php?id=1100000002634136160	http://factordb.com/certchain.php?fid=1100000002634136160&action=all&fr=0&to=100	http://factordb.com/index.php?query=8*26%5E%28n%2B2%29%2B319&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25215	9E0₆₁₉B	248×26⁶²⁰+11	622	880	http://factordb.com/index.php?id=1100000002634136193&open=prime	http://factordb.com/index.php?showid=1100000002634136193&base=26	http://factordb.com/index.php?showid=1100000002634136193	http://factordb.com/helper.php?id=1100000002634136193	http://factordb.com/cert.php?id=1100000002634136193	http://factordb.com/certchain.php?fid=1100000002634136193&action=all&fr=0&to=100	http://factordb.com/index.php?query=248*26%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25216	G60₆₁₈KJ	422×26⁶²⁰+539	622	880	http://factordb.com/index.php?id=1100000003850155283&open=prime	http://factordb.com/index.php?showid=1100000003850155283&base=26	http://factordb.com/index.php?showid=1100000003850155283	http://factordb.com/helper.php?id=1100000003850155283	http://factordb.com/cert.php?id=1100000003850155283	http://factordb.com/certchain.php?fid=1100000003850155283&action=all&fr=0&to=100	http://factordb.com/index.php?query=422*26%5E%28n%2B2%29%2B539&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25217	OO0₆₂₀D3	648×26⁶²²+341	624	883	http://factordb.com/index.php?id=1100000003850155285&open=prime	http://factordb.com/index.php?showid=1100000003850155285&base=26	http://factordb.com/index.php?showid=1100000003850155285	http://factordb.com/helper.php?id=1100000003850155285	http://factordb.com/cert.php?id=1100000003850155285	http://factordb.com/certchain.php?fid=1100000003850155285&action=all&fr=0&to=100	http://factordb.com/index.php?query=648*26%5E%28n%2B2%29%2B341&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25218	K0₆₅₃IP	20×26⁶⁵⁵+493	656	929	http://factordb.com/index.php?id=1100000000840633594&open=prime	http://factordb.com/index.php?showid=1100000000840633594&base=26	http://factordb.com/index.php?showid=1100000000840633594	http://factordb.com/helper.php?id=1100000000840633594	http://factordb.com/cert.php?id=1100000000840633594	http://factordb.com/certchain.php?fid=1100000000840633594&action=all&fr=0&to=100	http://factordb.com/index.php?query=20*26%5E%28n%2B2%29%2B493&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25219	J00J₆₉₈L	(321119×26⁶⁹⁹+31)/25	702	994	http://factordb.com/index.php?id=1100000003850155288&open=prime	http://factordb.com/index.php?showid=1100000003850155288&base=26	http://factordb.com/index.php?showid=1100000003850155288	http://factordb.com/helper.php?id=1100000003850155288	http://factordb.com/cert.php?id=1100000003850155288	http://factordb.com/certchain.php?fid=1100000003850155288&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28321119*26%5E%28n%2B1%29%2B31%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25220	B0₇₇₂90J	11×26⁷⁷⁵+6103	776	1098	http://factordb.com/index.php?id=1100000003850155290&open=prime	http://factordb.com/index.php?showid=1100000003850155290&base=26	http://factordb.com/index.php?showid=1100000003850155290	http://factordb.com/helper.php?id=1100000003850155290	http://factordb.com/cert.php?id=1100000003850155290	http://factordb.com/certchain.php?fid=1100000003850155290&action=all&fr=0&to=100	http://factordb.com/index.php?query=11*26%5E%28n%2B3%29%2B6103&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25221	J₈₄₄B	(19×26⁸⁴⁵−219)/25	845	1196	http://factordb.com/index.php?id=1100000002328055693&open=prime	http://factordb.com/index.php?showid=1100000002328055693&base=26	http://factordb.com/index.php?showid=1100000002328055693	http://factordb.com/helper.php?id=1100000002328055693	http://factordb.com/cert.php?id=1100000002328055693	http://factordb.com/certchain.php?fid=1100000002328055693&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*26%5E%28n%2B1%29-219%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25222	H₈₅₅M0H	(17×26⁸⁵⁸+73433)/25	858	1214	http://factordb.com/index.php?id=1100000003850155291&open=prime	http://factordb.com/index.php?showid=1100000003850155291&base=26	http://factordb.com/index.php?showid=1100000003850155291	http://factordb.com/helper.php?id=1100000003850155291	http://factordb.com/cert.php?id=1100000003850155291	http://factordb.com/certchain.php?fid=1100000003850155291&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2817*26%5E%28n%2B3%29%2B73433%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25223	J₈₆₁OOL	(19×26⁸⁶⁴+87781)/25	864	1223	http://factordb.com/index.php?id=1100000003850155296&open=prime	http://factordb.com/index.php?showid=1100000003850155296&base=26	http://factordb.com/index.php?showid=1100000003850155296	http://factordb.com/helper.php?id=1100000003850155296	http://factordb.com/cert.php?id=1100000003850155296	http://factordb.com/certchain.php?fid=1100000003850155296&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*26%5E%28n%2B3%29%2B87781%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25224	B0₉₇₉H	11×26⁹⁸⁰+17	981	1388	http://factordb.com/index.php?id=1100000002355639467&open=prime	http://factordb.com/index.php?showid=1100000002355639467&base=26	http://factordb.com/index.php?showid=1100000002355639467	http://factordb.com/helper.php?id=1100000002355639467	http://factordb.com/cert.php?id=1100000002355639467	http://factordb.com/certchain.php?fid=1100000002355639467&action=all&fr=0&to=100	http://factordb.com/index.php?query=11*26%5E%28n%2B1%29%2B17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25225	L0₉₉₁4000J	21×26⁹⁹⁶+1827923	997	1411	http://factordb.com/index.php?id=1100000003850155301&open=prime	http://factordb.com/index.php?showid=1100000003850155301&base=26	http://factordb.com/index.php?showid=1100000003850155301	http://factordb.com/helper.php?id=1100000003850155301	http://factordb.com/cert.php?id=1100000003850155301	http://factordb.com/certchain.php?fid=1100000003850155301&action=all&fr=0&to=100	http://factordb.com/index.php?query=21*26%5E%28n%2B5%29%2B1827923&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25226	E0₁₁₀₁K2B	14×26¹¹⁰⁴+13583	1105	1564	http://factordb.com/index.php?id=1100000003850155305&open=prime	http://factordb.com/index.php?showid=1100000003850155305&base=26	http://factordb.com/index.php?showid=1100000003850155305	http://factordb.com/helper.php?id=1100000003850155305	http://factordb.com/cert.php?id=1100000003850155305	http://factordb.com/certchain.php?fid=1100000003850155305&action=all&fr=0&to=100	http://factordb.com/index.php?query=14*26%5E%28n%2B3%29%2B13583&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25227	G₁₁₀₅OO9	(16×26¹¹⁰⁸+140209)/25	1108	1568	http://factordb.com/index.php?id=1100000000840633717&open=prime	http://factordb.com/index.php?showid=1100000000840633717&base=26	http://factordb.com/index.php?showid=1100000000840633717	http://factordb.com/helper.php?id=1100000000840633717	http://factordb.com/cert.php?id=1100000000840633717	http://factordb.com/certchain.php?fid=1100000000840633717&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2816*26%5E%28n%2B3%29%2B140209%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25228	MC0₁₁₀₉N	584×26¹¹¹⁰+23	1112	1574	http://factordb.com/index.php?id=1100000002634136576&open=prime	http://factordb.com/index.php?showid=1100000002634136576&base=26	http://factordb.com/index.php?showid=1100000002634136576	http://factordb.com/helper.php?id=1100000002634136576	http://factordb.com/cert.php?id=1100000002634136576	http://factordb.com/certchain.php?fid=1100000002634136576&action=all&fr=0&to=100	http://factordb.com/index.php?query=584*26%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25229	G₁₁₅₉9	(16×26¹¹⁶⁰−191)/25	1160	1642	http://factordb.com/index.php?id=1100000000840633844&open=prime	http://factordb.com/index.php?showid=1100000000840633844&base=26	http://factordb.com/index.php?showid=1100000000840633844	http://factordb.com/helper.php?id=1100000000840633844	http://factordb.com/cert.php?id=1100000000840633844	http://factordb.com/certchain.php?fid=1100000000840633844&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2816*26%5E%28n%2B1%29-191%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25230	A₁₂₉₅06F	(2×26¹²⁹⁸−34297)/5	1298	1837	http://factordb.com/index.php?id=1100000000840633998&open=prime	http://factordb.com/index.php?showid=1100000000840633998&base=26	http://factordb.com/index.php?showid=1100000000840633998	http://factordb.com/helper.php?id=1100000000840633998	http://factordb.com/cert.php?id=1100000000840633998	http://factordb.com/certchain.php?fid=1100000000840633998&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282*26%5E%28n%2B3%29-34297%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25231	KIA₁₂₉₈F	(2692×26¹²⁹⁹+23)/5	1301	1841	http://factordb.com/index.php?id=1100000000840634108&open=prime	http://factordb.com/index.php?showid=1100000000840634108&base=26	http://factordb.com/index.php?showid=1100000000840634108	http://factordb.com/helper.php?id=1100000000840634108	http://factordb.com/cert.php?id=1100000000840634108	http://factordb.com/certchain.php?fid=1100000000840634108&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282692*26%5E%28n%2B1%29%2B23%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25232	L7₁₃₁₉OL	(532×26¹³²¹+11393)/25	1322	1871	http://factordb.com/index.php?id=1100000003850155311&open=prime	http://factordb.com/index.php?showid=1100000003850155311&base=26	http://factordb.com/index.php?showid=1100000003850155311	http://factordb.com/helper.php?id=1100000003850155311	http://factordb.com/cert.php?id=1100000003850155311	http://factordb.com/certchain.php?fid=1100000003850155311&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28532*26%5E%28n%2B2%29%2B11393%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25233	J₁₃₆₅L	(19×26¹³⁶⁶+31)/25	1366	1933	http://factordb.com/index.php?id=1100000002328055922&open=prime	http://factordb.com/index.php?showid=1100000002328055922&base=26	http://factordb.com/index.php?showid=1100000002328055922	http://factordb.com/helper.php?id=1100000002328055922	http://factordb.com/cert.php?id=1100000002328055922	http://factordb.com/certchain.php?fid=1100000002328055922&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*26%5E%28n%2B1%29%2B31%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25234	2₁₄₉₈H	(2×26¹⁴⁹⁹+373)/25	1499	2120	http://factordb.com/index.php?id=1100000002328050300&open=prime	http://factordb.com/index.php?showid=1100000002328050300&base=26	http://factordb.com/index.php?showid=1100000002328050300	http://factordb.com/helper.php?id=1100000002328050300	http://factordb.com/cert.php?id=1100000002328050300	http://factordb.com/certchain.php?fid=1100000002328050300&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282*26%5E%28n%2B1%29%2B373%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25235	O5₁₅₀₉	(121×26¹⁵⁰⁹−1)/5	1510	2137	http://factordb.com/index.php?id=1100000000894500022&open=prime	http://factordb.com/index.php?showid=1100000000894500022&base=26	http://factordb.com/index.php?showid=1100000000894500022	http://factordb.com/helper.php?id=1100000000894500022	http://factordb.com/cert.php?id=1100000000894500022	http://factordb.com/certchain.php?fid=1100000000894500022&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28121*26%5En-1%29%2F5&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25236	DM₁₅₁₉P	(347×26¹⁵²⁰+53)/25	1521	2152	http://factordb.com/index.php?id=1100000003850155312&open=prime	http://factordb.com/index.php?showid=1100000003850155312&base=26	http://factordb.com/index.php?showid=1100000003850155312	http://factordb.com/helper.php?id=1100000003850155312	http://factordb.com/cert.php?id=1100000003850155312	http://factordb.com/certchain.php?fid=1100000003850155312&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28347*26%5E%28n%2B1%29%2B53%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25237	J0₁₅₂₃P	19×26¹⁵²⁴+25	1525	2158	http://factordb.com/index.php?id=1100000002355640604&open=prime	http://factordb.com/index.php?showid=1100000002355640604&base=26	http://factordb.com/index.php?showid=1100000002355640604	http://factordb.com/helper.php?id=1100000002355640604	http://factordb.com/cert.php?id=1100000002355640604	http://factordb.com/certchain.php?fid=1100000002355640604&action=all&fr=0&to=100	http://factordb.com/index.php?query=19*26%5E%28n%2B1%29%2B25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25238	F₁₅₆₉PCF	(3×26¹⁵⁷²+33407)/5	1572	2225	http://factordb.com/index.php?id=1100000000840634210&open=prime	http://factordb.com/index.php?showid=1100000000840634210&base=26	http://factordb.com/index.php?showid=1100000000840634210	http://factordb.com/helper.php?id=1100000000840634210	http://factordb.com/cert.php?id=1100000000840634210	http://factordb.com/certchain.php?fid=1100000000840634210&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283*26%5E%28n%2B3%29%2B33407%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25239	N0₁₆₄₇NEN	23×26¹⁶⁵⁰+15935	1651	2337	http://factordb.com/index.php?id=1100000003850155313&open=prime	http://factordb.com/index.php?showid=1100000003850155313&base=26	http://factordb.com/index.php?showid=1100000003850155313	http://factordb.com/helper.php?id=1100000003850155313	http://factordb.com/cert.php?id=1100000003850155313	http://factordb.com/certchain.php?fid=1100000003850155313&action=all&fr=0&to=100	http://factordb.com/index.php?query=23*26%5E%28n%2B3%29%2B15935&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25240	5₁₈₈₅4P	(26¹⁸⁸⁷−31)/5	1887	2670	http://factordb.com/index.php?id=1100000003850155314&open=prime	http://factordb.com/index.php?showid=1100000003850155314&base=26	http://factordb.com/index.php?showid=1100000003850155314	http://factordb.com/helper.php?id=1100000003850155314	http://factordb.com/cert.php?id=1100000003850155314	http://factordb.com/certchain.php?fid=1100000003850155314&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2826%5E%28n%2B2%29-31%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25241	6K₂₅₅₆A5	(34×26²⁵⁵⁸−1379)/5	2559	3621	http://factordb.com/index.php?id=1100000003850155315&open=prime	http://factordb.com/index.php?showid=1100000003850155315&base=26	http://factordb.com/index.php?showid=1100000003850155315	http://factordb.com/helper.php?id=1100000003850155315	http://factordb.com/cert.php?id=1100000003850155315	http://factordb.com/certchain.php?fid=1100000003850155315&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2834*26%5E%28n%2B2%29-1379%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25242	70₂₆₁₃CN	7×26²⁶¹⁵+335	2616	3702	http://factordb.com/index.php?id=1100000002634136105&open=prime	http://factordb.com/index.php?showid=1100000002634136105&base=26	http://factordb.com/index.php?showid=1100000002634136105	http://factordb.com/helper.php?id=1100000002634136105	http://factordb.com/cert.php?id=1100000002634136105	http://factordb.com/certchain.php?fid=1100000002634136105&action=all&fr=0&to=100	http://factordb.com/index.php?query=7*26%5E%28n%2B2%29%2B335&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25243	E0₂₆₇₃H	14×26²⁶⁷⁴+17	2675	3785	http://factordb.com/index.php?id=1100000002355640062&open=prime	http://factordb.com/index.php?showid=1100000002355640062&base=26	http://factordb.com/index.php?showid=1100000002355640062	http://factordb.com/helper.php?id=1100000002355640062	http://factordb.com/cert.php?id=1100000002355640062	http://factordb.com/certchain.php?fid=1100000002355640062&action=all&fr=0&to=100	http://factordb.com/index.php?query=14*26%5E%28n%2B1%29%2B17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25244	G60₂₇₄₀J	422×26²⁷⁴¹+19	2743	3882	http://factordb.com/index.php?id=1100000002634136363&open=prime	http://factordb.com/index.php?showid=1100000002634136363&base=26	http://factordb.com/index.php?showid=1100000002634136363	http://factordb.com/helper.php?id=1100000002634136363	http://factordb.com/cert.php?id=1100000002634136363	http://factordb.com/certchain.php?fid=1100000002634136363&action=all&fr=0&to=100	http://factordb.com/index.php?query=422*26%5E%28n%2B1%29%2B19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25245	B₂₉₁₅9	(11×26²⁹¹⁶−61)/25	2916	4126	http://factordb.com/index.php?id=1100000002328052611&open=prime	http://factordb.com/index.php?showid=1100000002328052611&base=26	http://factordb.com/index.php?showid=1100000002328052611	http://factordb.com/helper.php?id=1100000002328052611	http://factordb.com/cert.php?id=1100000002328052611	http://factordb.com/certchain.php?fid=1100000002328052611&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2811*26%5E%28n%2B1%29-61%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25246	J₄₂₂₂P	(19×26⁴²²³+131)/25	4223	5976	http://factordb.com/index.php?id=1100000002328056865&open=prime	http://factordb.com/index.php?showid=1100000002328056865&base=26	http://factordb.com/index.php?showid=1100000002328056865	http://factordb.com/helper.php?id=1100000002328056865	http://factordb.com/cert.php?id=1100000002328056865	http://factordb.com/certchain.php?fid=1100000002328056865&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*26%5E%28n%2B1%29%2B131%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25247	K0₄₃₆₄I5	20×26⁴³⁶⁶+473	4367	6180	http://factordb.com/index.php?id=1100000002634136508&open=prime	http://factordb.com/index.php?showid=1100000002634136508&base=26	http://factordb.com/index.php?showid=1100000002634136508	http://factordb.com/helper.php?id=1100000002634136508	http://factordb.com/cert.php?id=1100000002634136508	http://factordb.com/certchain.php?fid=1100000002634136508&action=all&fr=0&to=100	http://factordb.com/index.php?query=20*26%5E%28n%2B2%29%2B473&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25248	M₈₇₇₂P	(22×26⁸⁷⁷³+53)/25	8773	12414	http://factordb.com/index.php?id=1100000000758011195&open=prime	http://factordb.com/index.php?showid=1100000000758011195&base=26	http://factordb.com/index.php?showid=1100000000758011195	http://factordb.com/helper.php?id=1100000000758011195	http://factordb.com/cert.php?id=1100000000758011195	http://factordb.com/certchain.php?fid=1100000000758011195&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2822*26%5E%28n%2B1%29%2B53%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
26	25249	9GDK₁₅₉₂₀P	(32569×26¹⁵⁹²¹+21)/5	15924	22532	http://factordb.com/index.php?id=1100000003850155316&open=prime	http://factordb.com/index.php?showid=1100000003850155316&base=26	http://factordb.com/index.php?showid=1100000003850155316	http://factordb.com/helper.php?id=1100000003850155316	http://factordb.com/cert.php?id=1100000003850155316	http://factordb.com/certchain.php?fid=1100000003850155316&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2832569*26%5E%28n%2B1%29%2B21%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25485	JN₂₀₆	(536×28²⁰⁶−23)/27	207	300	http://factordb.com/index.php?id=1100000002611724435&open=prime	http://factordb.com/index.php?showid=1100000002611724435&base=28	http://factordb.com/index.php?showid=1100000002611724435	http://factordb.com/helper.php?id=1100000002611724435	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), N−1 is 2×1061×1171×74311×(289-digit prime)	http://factordb.com/index.php?id=1100000002611724440&open=ecm	http://factordb.com/index.php?query=%28536*28%5En-23%29%2F27&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25486	3₂₁₁M9	(28²¹³+4841)/9	213	308	http://factordb.com/index.php?id=1100000003850161936&open=prime	http://factordb.com/index.php?showid=1100000003850161936&base=28	http://factordb.com/index.php?showid=1100000003850161936	http://factordb.com/helper.php?id=1100000003850161936	http://factordb.com/cert.php?id=1100000003850161936	http://factordb.com/certchain.php?fid=1100000003850161936&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2828%5E%28n%2B2%29%2B4841%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25487	HD0₂₁₃D	489×28²¹⁴+13	216	313	http://factordb.com/index.php?id=1100000003850161937&open=prime	http://factordb.com/index.php?showid=1100000003850161937&base=28	http://factordb.com/index.php?showid=1100000003850161937	http://factordb.com/helper.php?id=1100000003850161937	http://factordb.com/cert.php?id=1100000003850161937	http://factordb.com/certchain.php?fid=1100000003850161937&action=all&fr=0&to=100	http://factordb.com/index.php?query=489*28%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25488	64O₂₁₇9	(1556×28²¹⁸−143)/9	220	318	http://factordb.com/index.php?id=1100000000840840215&open=prime	http://factordb.com/index.php?showid=1100000000840840215&base=28	http://factordb.com/index.php?showid=1100000000840840215	http://factordb.com/helper.php?id=1100000000840840215	http://factordb.com/cert.php?id=1100000000840840215	http://factordb.com/certchain.php?fid=1100000000840840215&action=all&fr=0&to=100	http://factordb.com/index.php?query=%281556*28%5E%28n%2B1%29-143%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25489	G0₂₁₇A0N	16×28²²⁰+7863	221	320	http://factordb.com/index.php?id=1100000003850161938&open=prime	http://factordb.com/index.php?showid=1100000003850161938&base=28	http://factordb.com/index.php?showid=1100000003850161938	http://factordb.com/helper.php?id=1100000003850161938	http://factordb.com/cert.php?id=1100000003850161938	http://factordb.com/certchain.php?fid=1100000003850161938&action=all&fr=0&to=100	http://factordb.com/index.php?query=16*28%5E%28n%2B3%29%2B7863&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25490	55OA₂₂₆F	(110278×28²²⁷+125)/27	230	333	http://factordb.com/index.php?id=1100000003850161939&open=prime	http://factordb.com/index.php?showid=1100000003850161939&base=28	http://factordb.com/index.php?showid=1100000003850161939	http://factordb.com/helper.php?id=1100000003850161939	http://factordb.com/cert.php?id=1100000003850161939	http://factordb.com/certchain.php?fid=1100000003850161939&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28110278*28%5E%28n%2B1%29%2B125%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25491	L0₂₂₉Q3	21×28²³¹+731	232	336	http://factordb.com/index.php?id=1100000003850161940&open=prime	http://factordb.com/index.php?showid=1100000003850161940&base=28	http://factordb.com/index.php?showid=1100000003850161940	http://factordb.com/helper.php?id=1100000003850161940	http://factordb.com/cert.php?id=1100000003850161940	http://factordb.com/certchain.php?fid=1100000003850161940&action=all&fr=0&to=100	http://factordb.com/index.php?query=21*28%5E%28n%2B2%29%2B731&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25492	B0₂₃₁7ID	11×28²³⁴+6005	235	340	http://factordb.com/index.php?id=1100000003850161941&open=prime	http://factordb.com/index.php?showid=1100000003850161941&base=28	http://factordb.com/index.php?showid=1100000003850161941	http://factordb.com/helper.php?id=1100000003850161941	http://factordb.com/cert.php?id=1100000003850161941	http://factordb.com/certchain.php?fid=1100000003850161941&action=all&fr=0&to=100	http://factordb.com/index.php?query=11*28%5E%28n%2B3%29%2B6005&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25493	PM₂₃₃B	(697×28²³⁴−319)/27	235	341	http://factordb.com/index.php?id=1100000003850161942&open=prime	http://factordb.com/index.php?showid=1100000003850161942&base=28	http://factordb.com/index.php?showid=1100000003850161942	http://factordb.com/helper.php?id=1100000003850161942	http://factordb.com/cert.php?id=1100000003850161942	http://factordb.com/certchain.php?fid=1100000003850161942&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28697*28%5E%28n%2B1%29-319%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25494	K0₂₃₈OF	20×28²⁴⁰+687	241	349	http://factordb.com/index.php?id=1100000000840840142&open=prime	http://factordb.com/index.php?showid=1100000000840840142&base=28	http://factordb.com/index.php?showid=1100000000840840142	http://factordb.com/helper.php?id=1100000000840840142	http://factordb.com/cert.php?id=1100000000840840142	http://factordb.com/certchain.php?fid=1100000000840840142&action=all&fr=0&to=100	http://factordb.com/index.php?query=20*28%5E%28n%2B2%29%2B687&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25495	I₂₆₂E3	(2×28²⁶⁴−383)/3	264	382	http://factordb.com/index.php?id=1100000003850161943&open=prime	http://factordb.com/index.php?showid=1100000003850161943&base=28	http://factordb.com/index.php?showid=1100000003850161943	http://factordb.com/helper.php?id=1100000003850161943	http://factordb.com/cert.php?id=1100000003850161943	http://factordb.com/certchain.php?fid=1100000003850161943&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282*28%5E%28n%2B2%29-383%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25496	C5A₂₇₃F	(9217×28²⁷⁴+125)/27	276	400	http://factordb.com/index.php?id=1100000003850161944&open=prime	http://factordb.com/index.php?showid=1100000003850161944&base=28	http://factordb.com/index.php?showid=1100000003850161944	http://factordb.com/helper.php?id=1100000003850161944	http://factordb.com/cert.php?id=1100000003850161944	http://factordb.com/certchain.php?fid=1100000003850161944&action=all&fr=0&to=100	http://factordb.com/index.php?query=%289217*28%5E%28n%2B1%29%2B125%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25497	J0₂₇₆IMB	19×28²⁷⁹+14739	280	406	http://factordb.com/index.php?id=1100000003850161945&open=prime	http://factordb.com/index.php?showid=1100000003850161945&base=28	http://factordb.com/index.php?showid=1100000003850161945	http://factordb.com/helper.php?id=1100000003850161945	http://factordb.com/cert.php?id=1100000003850161945	http://factordb.com/certchain.php?fid=1100000003850161945&action=all&fr=0&to=100	http://factordb.com/index.php?query=19*28%5E%28n%2B3%29%2B14739&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25498	F0₂₈₂QAP	15×28²⁸⁵+20689	286	414	http://factordb.com/index.php?id=1100000000840840006&open=prime	http://factordb.com/index.php?showid=1100000000840840006&base=28	http://factordb.com/index.php?showid=1100000000840840006	http://factordb.com/helper.php?id=1100000000840840006	http://factordb.com/cert.php?id=1100000000840840006	http://factordb.com/certchain.php?fid=1100000000840840006&action=all&fr=0&to=100	http://factordb.com/index.php?query=15*28%5E%28n%2B3%29%2B20689&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25499	M0₂₉₆KKN	22×28²⁹⁹+16263	300	435	http://factordb.com/index.php?id=1100000003850161946&open=prime	http://factordb.com/index.php?showid=1100000003850161946&base=28	http://factordb.com/index.php?showid=1100000003850161946	http://factordb.com/helper.php?id=1100000003850161946	http://factordb.com/cert.php?id=1100000003850161946	http://factordb.com/certchain.php?fid=1100000003850161946&action=all&fr=0&to=100	http://factordb.com/index.php?query=22*28%5E%28n%2B3%29%2B16263&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25500	C₃₁₀43	(4×28³¹²−2101)/9	312	452	http://factordb.com/index.php?id=1100000003850161947&open=prime	http://factordb.com/index.php?showid=1100000003850161947&base=28	http://factordb.com/index.php?showid=1100000003850161947	http://factordb.com/helper.php?id=1100000003850161947	http://factordb.com/cert.php?id=1100000003850161947	http://factordb.com/certchain.php?fid=1100000003850161947&action=all&fr=0&to=100	http://factordb.com/index.php?query=%284*28%5E%28n%2B2%29-2101%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25501	RN₃₁₉	(752×28³¹⁹−23)/27	320	464	http://factordb.com/index.php?id=1100000002611723967&open=prime	http://factordb.com/index.php?showid=1100000002611723967&base=28	http://factordb.com/index.php?showid=1100000002611723967	http://factordb.com/helper.php?id=1100000002611723967	http://factordb.com/cert.php?id=1100000002611723967	http://factordb.com/certchain.php?fid=1100000002611723967&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28752*28%5En-23%29%2F27&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25502	CA₃₂₀F	(334×28³²¹+125)/27	322	466	http://factordb.com/index.php?id=1100000000840839995&open=prime	http://factordb.com/index.php?showid=1100000000840839995&base=28	http://factordb.com/index.php?showid=1100000000840839995	http://factordb.com/helper.php?id=1100000000840839995	http://factordb.com/cert.php?id=1100000000840839995	http://factordb.com/certchain.php?fid=1100000000840839995&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28334*28%5E%28n%2B1%29%2B125%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25503	D6₃₂₆LR	(119×28³²⁸+3967)/9	329	476	http://factordb.com/index.php?id=1100000003850161948&open=prime	http://factordb.com/index.php?showid=1100000003850161948&base=28	http://factordb.com/index.php?showid=1100000003850161948	http://factordb.com/helper.php?id=1100000003850161948	http://factordb.com/cert.php?id=1100000003850161948	http://factordb.com/certchain.php?fid=1100000003850161948&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28119*28%5E%28n%2B2%29%2B3967%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25504	B₃₅₀AB	(11×28³⁵²−767)/27	352	510	http://factordb.com/index.php?id=1100000003850161949&open=prime	http://factordb.com/index.php?showid=1100000003850161949&base=28	http://factordb.com/index.php?showid=1100000003850161949	http://factordb.com/helper.php?id=1100000003850161949	http://factordb.com/cert.php?id=1100000003850161949	http://factordb.com/certchain.php?fid=1100000003850161949&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2811*28%5E%28n%2B2%29-767%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25505	GA0₃₅₅N	458×28³⁵⁶+23	358	518	http://factordb.com/index.php?id=1100000003850161950&open=prime	http://factordb.com/index.php?showid=1100000003850161950&base=28	http://factordb.com/index.php?showid=1100000003850161950	http://factordb.com/helper.php?id=1100000003850161950	http://factordb.com/cert.php?id=1100000003850161950	http://factordb.com/certchain.php?fid=1100000003850161950&action=all&fr=0&to=100	http://factordb.com/index.php?query=458*28%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25506	A0₃₅₆P7P	10×28³⁵⁹+19821	360	521	http://factordb.com/index.php?id=1100000003850161951&open=prime	http://factordb.com/index.php?showid=1100000003850161951&base=28	http://factordb.com/index.php?showid=1100000003850161951	http://factordb.com/helper.php?id=1100000003850161951	http://factordb.com/cert.php?id=1100000003850161951	http://factordb.com/certchain.php?fid=1100000003850161951&action=all&fr=0&to=100	http://factordb.com/index.php?query=10*28%5E%28n%2B3%29%2B19821&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25507	J₃₆₃H	(19×28³⁶⁴−73)/27	364	527	http://factordb.com/index.php?id=1100000002611724460&open=prime	http://factordb.com/index.php?showid=1100000002611724460&base=28	http://factordb.com/index.php?showid=1100000002611724460	http://factordb.com/helper.php?id=1100000002611724460	http://factordb.com/cert.php?id=1100000002611724460	http://factordb.com/certchain.php?fid=1100000002611724460&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*28%5E%28n%2B1%29-73%29%2F27&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25508	4B₃₈₁	(119×28³⁸¹−11)/27	382	553	http://factordb.com/index.php?id=1100000002611724588&open=prime	http://factordb.com/index.php?showid=1100000002611724588&base=28	http://factordb.com/index.php?showid=1100000002611724588	http://factordb.com/helper.php?id=1100000002611724588	http://factordb.com/cert.php?id=1100000002611724588	http://factordb.com/certchain.php?fid=1100000002611724588&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28119*28%5En-11%29%2F27&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25509	EB0₄₀₅1	403×28⁴⁰⁶+1	408	591	http://factordb.com/index.php?id=1100000001534442374&open=prime	http://factordb.com/index.php?showid=1100000001534442374&base=28	http://factordb.com/index.php?showid=1100000001534442374	http://factordb.com/helper.php?id=1100000001534442374	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is trivially fully factored	http://factordb.com/index.php?id=1100000001534442380&open=ecm	http://factordb.com/index.php?query=403*28%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25510	AN₄₆₁	(293×28⁴⁶¹−23)/27	462	669	http://factordb.com/index.php?id=1100000002611724556&open=prime	http://factordb.com/index.php?showid=1100000002611724556&base=28	http://factordb.com/index.php?showid=1100000002611724556	http://factordb.com/helper.php?id=1100000002611724556	http://factordb.com/cert.php?id=1100000002611724556	http://factordb.com/certchain.php?fid=1100000002611724556&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28293*28%5En-23%29%2F27&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25511	4O₆₁₄09	(44×28⁶¹⁶−6191)/9	617	893	http://factordb.com/index.php?id=1100000000840839989&open=prime	http://factordb.com/index.php?showid=1100000000840839989&base=28	http://factordb.com/index.php?showid=1100000000840839989	http://factordb.com/helper.php?id=1100000000840839989	http://factordb.com/cert.php?id=1100000000840839989	http://factordb.com/certchain.php?fid=1100000000840839989&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2844*28%5E%28n%2B2%29-6191%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25512	2D₆₄₁	(67×28⁶⁴¹−13)/27	642	929	http://factordb.com/index.php?id=1100000002611725341&open=prime	http://factordb.com/index.php?showid=1100000002611725341&base=28	http://factordb.com/index.php?showid=1100000002611725341	http://factordb.com/helper.php?id=1100000002611725341	http://factordb.com/cert.php?id=1100000002611725341	http://factordb.com/certchain.php?fid=1100000002611725341&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2867*28%5En-13%29%2F27&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25513	70₇₄₈M5	7×28⁷⁵⁰+621	751	1087	http://factordb.com/index.php?id=1100000003850161956&open=prime	http://factordb.com/index.php?showid=1100000003850161956&base=28	http://factordb.com/index.php?showid=1100000003850161956	http://factordb.com/helper.php?id=1100000003850161956	http://factordb.com/cert.php?id=1100000003850161956	http://factordb.com/certchain.php?fid=1100000003850161956&action=all&fr=0&to=100	http://factordb.com/index.php?query=7*28%5E%28n%2B2%29%2B621&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25514	4A0₈₀₄B	122×28⁸⁰⁵+11	807	1168	http://factordb.com/index.php?id=1100000003850161957&open=prime	http://factordb.com/index.php?showid=1100000003850161957&base=28	http://factordb.com/index.php?showid=1100000003850161957	http://factordb.com/helper.php?id=1100000003850161957	http://factordb.com/cert.php?id=1100000003850161957	http://factordb.com/certchain.php?fid=1100000003850161957&action=all&fr=0&to=100	http://factordb.com/index.php?query=122*28%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25515	LK₉₂₅F	(587×28⁹²⁶−155)/27	927	1342	http://factordb.com/index.php?id=1100000000840839978&open=prime	http://factordb.com/index.php?showid=1100000000840839978&base=28	http://factordb.com/index.php?showid=1100000000840839978	http://factordb.com/helper.php?id=1100000000840839978	http://factordb.com/cert.php?id=1100000000840839978	http://factordb.com/certchain.php?fid=1100000000840839978&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28587*28%5E%28n%2B1%29-155%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25516	J0₁₀₇₁AC5	19×28¹⁰⁷⁴+8181	1075	1556	http://factordb.com/index.php?id=1100000003850161959&open=prime	http://factordb.com/index.php?showid=1100000003850161959&base=28	http://factordb.com/index.php?showid=1100000003850161959	http://factordb.com/helper.php?id=1100000003850161959	http://factordb.com/cert.php?id=1100000003850161959	http://factordb.com/certchain.php?fid=1100000003850161959&action=all&fr=0&to=100	http://factordb.com/index.php?query=19*28%5E%28n%2B3%29%2B8181&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25517	J0₁₂₅₂J5	19×28¹²⁵⁴+537	1255	1817	http://factordb.com/index.php?id=1100000003850161963&open=prime	http://factordb.com/index.php?showid=1100000003850161963&base=28	http://factordb.com/index.php?showid=1100000003850161963	http://factordb.com/helper.php?id=1100000003850161963	http://factordb.com/cert.php?id=1100000003850161963	http://factordb.com/certchain.php?fid=1100000003850161963&action=all&fr=0&to=100	http://factordb.com/index.php?query=19*28%5E%28n%2B2%29%2B537&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25518	5₁₃₀₄6F	(5×28¹³⁰⁶+1021)/27	1306	1890	http://factordb.com/index.php?id=1100000003850161964&open=prime	http://factordb.com/index.php?showid=1100000003850161964&base=28	http://factordb.com/index.php?showid=1100000003850161964	http://factordb.com/helper.php?id=1100000003850161964	http://factordb.com/cert.php?id=1100000003850161964	http://factordb.com/certchain.php?fid=1100000003850161964&action=all&fr=0&to=100	http://factordb.com/index.php?query=%285*28%5E%28n%2B2%29%2B1021%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25519	5₁₃₃₂P8P	(5×28¹³³⁵+426163)/27	1335	1932	http://factordb.com/index.php?id=1100000003850161965&open=prime	http://factordb.com/index.php?showid=1100000003850161965&base=28	http://factordb.com/index.php?showid=1100000003850161965	http://factordb.com/helper.php?id=1100000003850161965	http://factordb.com/cert.php?id=1100000003850161965	http://factordb.com/certchain.php?fid=1100000003850161965&action=all&fr=0&to=100	http://factordb.com/index.php?query=%285*28%5E%28n%2B3%29%2B426163%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25520	5I₁₃₇₀F	(17×28¹³⁷¹−11)/3	1372	1985	http://factordb.com/index.php?id=1100000003850161972&open=prime	http://factordb.com/index.php?showid=1100000003850161972&base=28	http://factordb.com/index.php?showid=1100000003850161972	http://factordb.com/helper.php?id=1100000003850161972	http://factordb.com/cert.php?id=1100000003850161972	http://factordb.com/certchain.php?fid=1100000003850161972&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2817*28%5E%28n%2B1%29-11%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25521	A₁₄₂₃6F	(10×28¹⁴²⁵−2899)/27	1425	2062	http://factordb.com/index.php?id=1100000000840839947&open=prime	http://factordb.com/index.php?showid=1100000000840839947&base=28	http://factordb.com/index.php?showid=1100000000840839947	http://factordb.com/helper.php?id=1100000000840839947	http://factordb.com/cert.php?id=1100000000840839947	http://factordb.com/certchain.php?fid=1100000000840839947&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2810*28%5E%28n%2B2%29-2899%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25522	G0₁₈₉₉AN	16×28¹⁹⁰¹+303	1902	2753	http://factordb.com/index.php?id=1100000003850161973&open=prime	http://factordb.com/index.php?showid=1100000003850161973&base=28	http://factordb.com/index.php?showid=1100000003850161973	http://factordb.com/helper.php?id=1100000003850161973	http://factordb.com/cert.php?id=1100000003850161973	http://factordb.com/certchain.php?fid=1100000003850161973&action=all&fr=0&to=100	http://factordb.com/index.php?query=16*28%5E%28n%2B2%29%2B303&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25523	5₃₇₄₆8P	(5×28³⁷⁴⁸+2803)/27	3748	5424	http://factordb.com/index.php?id=1100000003850161974&open=prime	http://factordb.com/index.php?showid=1100000003850161974&base=28	http://factordb.com/index.php?showid=1100000003850161974	http://factordb.com/helper.php?id=1100000003850161974	http://factordb.com/cert.php?id=1100000003850161974	http://factordb.com/certchain.php?fid=1100000003850161974&action=all&fr=0&to=100	http://factordb.com/index.php?query=%285*28%5E%28n%2B2%29%2B2803%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25524	QO₄₂₃₉69	(242×28⁴²⁴¹−4679)/9	4242	6139	http://factordb.com/index.php?id=1100000000840839934&open=prime	http://factordb.com/index.php?showid=1100000000840839934&base=28	http://factordb.com/index.php?showid=1100000000840839934	http://factordb.com/helper.php?id=1100000000840839934	http://factordb.com/cert.php?id=1100000000840839934	http://factordb.com/certchain.php?fid=1100000000840839934&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28242*28%5E%28n%2B2%29-4679%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
28	25525	D0₅₂₆₇77D	13×28⁵²⁷⁰+5697	5271	7628	http://factordb.com/index.php?id=1100000003850151420&open=prime	http://factordb.com/index.php?showid=1100000003850151420&base=28	http://factordb.com/index.php?showid=1100000003850151420	http://factordb.com/helper.php?id=1100000003850151420	http://factordb.com/cert.php?id=1100000003850151420	http://factordb.com/certchain.php?fid=1100000003850151420&action=all&fr=0&to=100	http://factordb.com/index.php?query=13*28%5E%28n%2B3%29%2B5697&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
30	2613	AN₂₀₆	(313×30²⁰⁶−23)/29	207	306	http://factordb.com/index.php?id=1100000002327651073&open=prime	http://factordb.com/index.php?showid=1100000002327651073&base=30	http://factordb.com/index.php?showid=1100000002327651073	http://factordb.com/helper.php?id=1100000002327651073	http://factordb.com/cert.php?id=1100000002327651073	http://factordb.com/certchain.php?fid=1100000002327651073&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28313*30%5En-23%29%2F29&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
30	2614	M₂₄₁QB	(22×30²⁴³+3139)/29	243	359	http://factordb.com/index.php?id=1100000003593408295&open=prime	http://factordb.com/index.php?showid=1100000003593408295&base=30	http://factordb.com/index.php?showid=1100000003593408295	http://factordb.com/helper.php?id=1100000003593408295	http://factordb.com/cert.php?id=1100000003593408295	http://factordb.com/certchain.php?fid=1100000003593408295&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2822*30%5E%28n%2B2%29%2B3139%29%2F29&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
30	2615	M0₅₄₇SS7	22×30⁵⁵⁰+26047	551	814	http://factordb.com/index.php?id=1100000003593407988&open=prime	http://factordb.com/index.php?showid=1100000003593407988&base=30	http://factordb.com/index.php?showid=1100000003593407988	http://factordb.com/helper.php?id=1100000003593407988	http://factordb.com/cert.php?id=1100000003593407988	http://factordb.com/certchain.php?fid=1100000003593407988&action=all&fr=0&to=100	http://factordb.com/index.php?query=22*30%5E%28n%2B3%29%2B26047&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
30	2616	C0₁₀₂₂1	12×30¹⁰²³+1	1024	1513	http://factordb.com/index.php?id=1100000000785448736&open=prime	http://factordb.com/index.php?showid=1100000000785448736&base=30	http://factordb.com/index.php?showid=1100000000785448736	http://factordb.com/helper.php?id=1100000000785448736	proven prime by N−1 test (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=1), since N−1 is trivially fully factored	http://factordb.com/index.php?id=1100000000785448737&open=ecm	http://factordb.com/index.php?query=12*30%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
30	2617	5₄₈₈₂J	(5×30⁴⁸⁸³+401)/29	4883	7213	http://factordb.com/index.php?id=1100000002327649423&open=prime	http://factordb.com/index.php?showid=1100000002327649423&base=30	http://factordb.com/index.php?showid=1100000002327649423	http://factordb.com/helper.php?id=1100000002327649423	http://factordb.com/cert.php?id=1100000002327649423	http://factordb.com/certchain.php?fid=1100000002327649423&action=all&fr=0&to=100	http://factordb.com/index.php?query=%285*30%5E%28n%2B1%29%2B401%29%2F29&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
30	2619	OT₃₄₂₀₅	25×30³⁴²⁰⁵−1	34206	50527	http://factordb.com/index.php?id=1100000000800812865&open=prime	http://factordb.com/index.php?showid=1100000000800812865&base=30	http://factordb.com/index.php?showid=1100000000800812865	http://factordb.com/helper.php?id=1100000000800812865	proven prime by N+1 test (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2), since N+1 is trivially fully factored	http://factordb.com/index.php?id=1100000000819405041&open=ecm	http://factordb.com/index.php?query=25*30%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35212	Q₁₉₅77	(26×36¹⁹⁷−24631)/35	197	307	http://factordb.com/index.php?id=1100000003807362350&open=prime	http://factordb.com/index.php?showid=1100000003807362350&base=36	http://factordb.com/index.php?showid=1100000003807362350	http://factordb.com/helper.php?id=1100000003807362350	http://factordb.com/cert.php?id=1100000003807362350	http://factordb.com/certchain.php?fid=1100000003807362350&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2826*36%5E%28n%2B2%29-24631%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35213	W0₁₉₉ND	32×36²⁰¹+841	202	315	http://factordb.com/index.php?id=1100000002634136732&open=prime	http://factordb.com/index.php?showid=1100000002634136732&base=36	http://factordb.com/index.php?showid=1100000002634136732	http://factordb.com/helper.php?id=1100000002634136732	http://factordb.com/cert.php?id=1100000002634136732	http://factordb.com/certchain.php?fid=1100000002634136732&action=all&fr=0&to=100	http://factordb.com/index.php?query=32*36%5E%28n%2B2%29%2B841&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35214	G0₂₀₄YT	16×36²⁰⁶+1253	207	322	http://factordb.com/index.php?id=1100000002634137789&open=prime	http://factordb.com/index.php?showid=1100000002634137789&base=36	http://factordb.com/index.php?showid=1100000002634137789	http://factordb.com/helper.php?id=1100000002634137789	http://factordb.com/cert.php?id=1100000002634137789	http://factordb.com/certchain.php?fid=1100000002634137789&action=all&fr=0&to=100	http://factordb.com/index.php?query=16*36%5E%28n%2B2%29%2B1253&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35215	RHY₂₂₃H	(34649×36²²⁴−629)/35	226	352	http://factordb.com/index.php?id=1100000003807362353&open=prime	http://factordb.com/index.php?showid=1100000003807362353&base=36	http://factordb.com/index.php?showid=1100000003807362353	http://factordb.com/helper.php?id=1100000003807362353	http://factordb.com/cert.php?id=1100000003807362353	http://factordb.com/certchain.php?fid=1100000003807362353&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2834649*36%5E%28n%2B1%29-629%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35216	T0₂₂₃ST	29×36²²⁵+1037	226	352	http://factordb.com/index.php?id=1100000002634136882&open=prime	http://factordb.com/index.php?showid=1100000002634136882&base=36	http://factordb.com/index.php?showid=1100000002634136882	http://factordb.com/helper.php?id=1100000002634136882	http://factordb.com/cert.php?id=1100000002634136882	http://factordb.com/certchain.php?fid=1100000002634136882&action=all&fr=0&to=100	http://factordb.com/index.php?query=29*36%5E%28n%2B2%29%2B1037&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35217	J0₂₂₄U6V	19×36²²⁷+39127	228	355	http://factordb.com/index.php?id=1100000003807362355&open=prime	http://factordb.com/index.php?showid=1100000003807362355&base=36	http://factordb.com/index.php?showid=1100000003807362355	http://factordb.com/helper.php?id=1100000003807362355	http://factordb.com/cert.php?id=1100000003807362355	http://factordb.com/certchain.php?fid=1100000003807362355&action=all&fr=0&to=100	http://factordb.com/index.php?query=19*36%5E%28n%2B3%29%2B39127&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35218	BE0₂₃₅IV	410×36²³⁷+679	239	372	http://factordb.com/index.php?id=1100000003807362356&open=prime	http://factordb.com/index.php?showid=1100000003807362356&base=36	http://factordb.com/index.php?showid=1100000003807362356	http://factordb.com/helper.php?id=1100000003807362356	http://factordb.com/cert.php?id=1100000003807362356	http://factordb.com/certchain.php?fid=1100000003807362356&action=all&fr=0&to=100	http://factordb.com/index.php?query=410*36%5E%28n%2B2%29%2B679&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35219	E0₂₃₆KY1	14×36²³⁹+27145	240	374	http://factordb.com/index.php?id=1100000000840634520&open=prime	http://factordb.com/index.php?showid=1100000000840634520&base=36	http://factordb.com/index.php?showid=1100000000840634520	http://factordb.com/helper.php?id=1100000000840634520	http://factordb.com/cert.php?id=1100000000840634520	http://factordb.com/certchain.php?fid=1100000000840634520&action=all&fr=0&to=100	http://factordb.com/index.php?query=14*36%5E%28n%2B3%29%2B27145&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35220	JXV0₂₄₄B	25843×36²⁴⁵+11	248	386	http://factordb.com/index.php?id=1100000003807362357&open=prime	http://factordb.com/index.php?showid=1100000003807362357&base=36	http://factordb.com/index.php?showid=1100000003807362357	http://factordb.com/helper.php?id=1100000003807362357	http://factordb.com/cert.php?id=1100000003807362357	http://factordb.com/certchain.php?fid=1100000003807362357&action=all&fr=0&to=100	http://factordb.com/index.php?query=25843*36%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35221	5Q₂₄₉7	(201×36²⁵⁰−691)/35	251	390	http://factordb.com/index.php?id=1100000003807362359&open=prime	http://factordb.com/index.php?showid=1100000003807362359&base=36	http://factordb.com/index.php?showid=1100000003807362359	http://factordb.com/helper.php?id=1100000003807362359	http://factordb.com/cert.php?id=1100000003807362359	http://factordb.com/certchain.php?fid=1100000003807362359&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28201*36%5E%28n%2B1%29-691%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35222	N30₂₅₃H	831×36²⁵⁴+17	256	399	http://factordb.com/index.php?id=1100000002634137359&open=prime	http://factordb.com/index.php?showid=1100000002634137359&base=36	http://factordb.com/index.php?showid=1100000002634137359	http://factordb.com/helper.php?id=1100000002634137359	http://factordb.com/cert.php?id=1100000002634137359	http://factordb.com/certchain.php?fid=1100000002634137359&action=all&fr=0&to=100	http://factordb.com/index.php?query=831*36%5E%28n%2B1%29%2B17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35223	Y₂₆₁AH	(34×36²⁶³−30869)/35	263	410	http://factordb.com/index.php?id=1100000003807362360&open=prime	http://factordb.com/index.php?showid=1100000003807362360&base=36	http://factordb.com/index.php?showid=1100000003807362360	http://factordb.com/helper.php?id=1100000003807362360	http://factordb.com/cert.php?id=1100000003807362360	http://factordb.com/certchain.php?fid=1100000003807362360&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2834*36%5E%28n%2B2%29-30869%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35224	90₂₇₇VV	9×36²⁷⁹+1147	280	436	http://factordb.com/index.php?id=1100000002634138388&open=prime	http://factordb.com/index.php?showid=1100000002634138388&base=36	http://factordb.com/index.php?showid=1100000002634138388	http://factordb.com/helper.php?id=1100000002634138388	http://factordb.com/cert.php?id=1100000002634138388	http://factordb.com/certchain.php?fid=1100000002634138388&action=all&fr=0&to=100	http://factordb.com/index.php?query=9*36%5E%28n%2B2%29%2B1147&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35225	J0₂₈₁VB	19×36²⁸³+1127	284	442	http://factordb.com/index.php?id=1100000002634137683&open=prime	http://factordb.com/index.php?showid=1100000002634137683&base=36	http://factordb.com/index.php?showid=1100000002634137683	http://factordb.com/helper.php?id=1100000002634137683	http://factordb.com/cert.php?id=1100000002634137683	http://factordb.com/certchain.php?fid=1100000002634137683&action=all&fr=0&to=100	http://factordb.com/index.php?query=19*36%5E%28n%2B2%29%2B1127&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35226	J0₂₈₁WV	19×36²⁸³+1183	284	442	http://factordb.com/index.php?id=1100000002634137660&open=prime	http://factordb.com/index.php?showid=1100000002634137660&base=36	http://factordb.com/index.php?showid=1100000002634137660	http://factordb.com/helper.php?id=1100000002634137660	http://factordb.com/cert.php?id=1100000002634137660	http://factordb.com/certchain.php?fid=1100000002634137660&action=all&fr=0&to=100	http://factordb.com/index.php?query=19*36%5E%28n%2B2%29%2B1183&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35227	DE0₂₈₁61	482×36²⁸³+217	285	444	http://factordb.com/index.php?id=1100000003807362361&open=prime	http://factordb.com/index.php?showid=1100000003807362361&base=36	http://factordb.com/index.php?showid=1100000003807362361	http://factordb.com/helper.php?id=1100000003807362361	http://factordb.com/cert.php?id=1100000003807362361	http://factordb.com/certchain.php?fid=1100000003807362361&action=all&fr=0&to=100	http://factordb.com/index.php?query=482*36%5E%28n%2B2%29%2B217&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35228	9H₂₉₇	(332×36²⁹⁷−17)/35	298	464	http://factordb.com/index.php?id=1100000002332535884&open=prime	http://factordb.com/index.php?showid=1100000002332535884&base=36	http://factordb.com/index.php?showid=1100000002332535884	http://factordb.com/helper.php?id=1100000002332535884	http://factordb.com/cert.php?id=1100000002332535884	http://factordb.com/certchain.php?fid=1100000002332535884&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28332*36%5En-17%29%2F35&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35229	M70₂₉₇FD	799×36²⁹⁹+553	301	469	http://factordb.com/index.php?id=1100000003807362363&open=prime	http://factordb.com/index.php?showid=1100000003807362363&base=36	http://factordb.com/index.php?showid=1100000003807362363	http://factordb.com/helper.php?id=1100000003807362363	http://factordb.com/cert.php?id=1100000003807362363	http://factordb.com/certchain.php?fid=1100000003807362363&action=all&fr=0&to=100	http://factordb.com/index.php?query=799*36%5E%28n%2B2%29%2B553&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35230	9X₃₀₁B	(348×36³⁰²−803)/35	303	472	http://factordb.com/index.php?id=1100000003807362364&open=prime	http://factordb.com/index.php?showid=1100000003807362364&base=36	http://factordb.com/index.php?showid=1100000003807362364	http://factordb.com/helper.php?id=1100000003807362364	http://factordb.com/cert.php?id=1100000003807362364	http://factordb.com/certchain.php?fid=1100000003807362364&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28348*36%5E%28n%2B1%29-803%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35231	XE0₃₂₅7	1202×36³²⁶+7	328	511	http://factordb.com/index.php?id=1100000002634136674&open=prime	http://factordb.com/index.php?showid=1100000002634136674&base=36	http://factordb.com/index.php?showid=1100000002634136674	http://factordb.com/helper.php?id=1100000002634136674	http://factordb.com/cert.php?id=1100000002634136674	http://factordb.com/certchain.php?fid=1100000002634136674&action=all&fr=0&to=100	http://factordb.com/index.php?query=1202*36%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35232	KP₃₃₀SZ	(145×36³³²+821)/7	333	519	http://factordb.com/index.php?id=1100000000840634515&open=prime	http://factordb.com/index.php?showid=1100000000840634515&base=36	http://factordb.com/index.php?showid=1100000000840634515	http://factordb.com/helper.php?id=1100000000840634515	http://factordb.com/cert.php?id=1100000000840634515	http://factordb.com/certchain.php?fid=1100000000840634515&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28145*36%5E%28n%2B2%29%2B821%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35233	5₃₄₇QP	(36³⁴⁹+5431)/7	349	543	http://factordb.com/index.php?id=1100000003807362365&open=prime	http://factordb.com/index.php?showid=1100000003807362365&base=36	http://factordb.com/index.php?showid=1100000003807362365	http://factordb.com/helper.php?id=1100000003807362365	http://factordb.com/cert.php?id=1100000003807362365	http://factordb.com/certchain.php?fid=1100000003807362365&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2836%5E%28n%2B2%29%2B5431%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35234	E0₃₄₉6U1	14×36³⁵²+8857	353	549	http://factordb.com/index.php?id=1100000000840634509&open=prime	http://factordb.com/index.php?showid=1100000000840634509&base=36	http://factordb.com/index.php?showid=1100000000840634509	http://factordb.com/helper.php?id=1100000000840634509	http://factordb.com/cert.php?id=1100000000840634509	http://factordb.com/certchain.php?fid=1100000000840634509&action=all&fr=0&to=100	http://factordb.com/index.php?query=14*36%5E%28n%2B3%29%2B8857&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35235	K0₃₆₇E6T	20×36³⁷⁰+18389	371	578	http://factordb.com/index.php?id=1100000003807362367&open=prime	http://factordb.com/index.php?showid=1100000003807362367&base=36	http://factordb.com/index.php?showid=1100000003807362367	http://factordb.com/helper.php?id=1100000003807362367	http://factordb.com/cert.php?id=1100000003807362367	http://factordb.com/certchain.php?fid=1100000003807362367&action=all&fr=0&to=100	http://factordb.com/index.php?query=20*36%5E%28n%2B3%29%2B18389&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35236	U0₃₇₀WP	30×36³⁷²+1177	373	581	http://factordb.com/index.php?id=1100000000840634503&open=prime	http://factordb.com/index.php?showid=1100000000840634503&base=36	http://factordb.com/index.php?showid=1100000000840634503	http://factordb.com/helper.php?id=1100000000840634503	http://factordb.com/cert.php?id=1100000000840634503	http://factordb.com/certchain.php?fid=1100000000840634503&action=all&fr=0&to=100	http://factordb.com/index.php?query=30*36%5E%28n%2B2%29%2B1177&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35237	P8Z₃₉₀	909×36³⁹⁰−1	392	610	http://factordb.com/index.php?id=1100000000764100228&open=prime	http://factordb.com/index.php?showid=1100000000764100228&base=36	http://factordb.com/index.php?showid=1100000000764100228	http://factordb.com/helper.php?id=1100000000764100228	proven prime by N+1 test (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2), since N+1 is trivially fully factored	http://factordb.com/index.php?id=1100000000764100231&open=ecm	http://factordb.com/index.php?query=909*36%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35238	90₃₉₇4B	9×36³⁹⁹+155	400	622	http://factordb.com/index.php?id=1100000002634138490&open=prime	http://factordb.com/index.php?showid=1100000002634138490&base=36	http://factordb.com/index.php?showid=1100000002634138490	http://factordb.com/helper.php?id=1100000002634138490	http://factordb.com/cert.php?id=1100000002634138490	http://factordb.com/certchain.php?fid=1100000002634138490&action=all&fr=0&to=100	http://factordb.com/index.php?query=9*36%5E%28n%2B2%29%2B155&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35239	50₄₀₅WW5	5×36⁴⁰⁸+42629	409	636	http://factordb.com/index.php?id=1100000003807362369&open=prime	http://factordb.com/index.php?showid=1100000003807362369&base=36	http://factordb.com/index.php?showid=1100000003807362369	http://factordb.com/helper.php?id=1100000003807362369	http://factordb.com/cert.php?id=1100000003807362369	http://factordb.com/certchain.php?fid=1100000003807362369&action=all&fr=0&to=100	http://factordb.com/index.php?query=5*36%5E%28n%2B3%29%2B42629&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35240	V0₄₀₅EE4B	31×36⁴⁰⁹+671483	410	639	http://factordb.com/index.php?id=1100000003807362370&open=prime	http://factordb.com/index.php?showid=1100000003807362370&base=36	http://factordb.com/index.php?showid=1100000003807362370	http://factordb.com/helper.php?id=1100000003807362370	http://factordb.com/cert.php?id=1100000003807362370	http://factordb.com/certchain.php?fid=1100000003807362370&action=all&fr=0&to=100	http://factordb.com/index.php?query=31*36%5E%28n%2B4%29%2B671483&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35241	TTR0₄₃₄T	38655×36⁴³⁵+29	438	682	http://factordb.com/index.php?id=1100000003807362372&open=prime	http://factordb.com/index.php?showid=1100000003807362372&base=36	http://factordb.com/index.php?showid=1100000003807362372	http://factordb.com/helper.php?id=1100000003807362372	http://factordb.com/cert.php?id=1100000003807362372	http://factordb.com/certchain.php?fid=1100000003807362372&action=all&fr=0&to=100	http://factordb.com/index.php?query=38655*36%5E%28n%2B1%29%2B29&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35242	LK₄₄₃Z	(151×36⁴⁴⁴+101)/7	445	693	http://factordb.com/index.php?id=1100000000840634496&open=prime	http://factordb.com/index.php?showid=1100000000840634496&base=36	http://factordb.com/index.php?showid=1100000000840634496	http://factordb.com/helper.php?id=1100000000840634496	http://factordb.com/cert.php?id=1100000000840634496	http://factordb.com/certchain.php?fid=1100000000840634496&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28151*36%5E%28n%2B1%29%2B101%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35243	Q₄₅₄7	(26×36⁴⁵⁵−691)/35	455	708	http://factordb.com/index.php?id=1100000002332534290&open=prime	http://factordb.com/index.php?showid=1100000002332534290&base=36	http://factordb.com/index.php?showid=1100000002332534290	http://factordb.com/helper.php?id=1100000002332534290	http://factordb.com/cert.php?id=1100000002332534290	http://factordb.com/certchain.php?fid=1100000002332534290&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2826*36%5E%28n%2B1%29-691%29%2F35&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35244	R0₄₅₈7	27×36⁴⁵⁹+7	460	716	http://factordb.com/index.php?id=1100000002356257765&open=prime	http://factordb.com/index.php?showid=1100000002356257765&base=36	http://factordb.com/index.php?showid=1100000002356257765	http://factordb.com/helper.php?id=1100000002356257765	http://factordb.com/cert.php?id=1100000002356257765	http://factordb.com/certchain.php?fid=1100000002356257765&action=all&fr=0&to=100	http://factordb.com/index.php?query=27*36%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35245	50₄₆₀KGZ	5×36⁴⁶³+26531	464	722	http://factordb.com/index.php?id=1100000003807362374&open=prime	http://factordb.com/index.php?showid=1100000003807362374&base=36	http://factordb.com/index.php?showid=1100000003807362374	http://factordb.com/helper.php?id=1100000003807362374	http://factordb.com/cert.php?id=1100000003807362374	http://factordb.com/certchain.php?fid=1100000003807362374&action=all&fr=0&to=100	http://factordb.com/index.php?query=5*36%5E%28n%2B3%29%2B26531&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35246	K0₄₇₄OY1	20×36⁴⁷⁷+32329	478	744	http://factordb.com/index.php?id=1100000000840634488&open=prime	http://factordb.com/index.php?showid=1100000000840634488&base=36	http://factordb.com/index.php?showid=1100000000840634488	http://factordb.com/helper.php?id=1100000000840634488	http://factordb.com/cert.php?id=1100000000840634488	http://factordb.com/certchain.php?fid=1100000000840634488&action=all&fr=0&to=100	http://factordb.com/index.php?query=20*36%5E%28n%2B3%29%2B32329&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35247	B₄₇₈KB	(11×36⁴⁸⁰+11329)/35	480	747	http://factordb.com/index.php?id=1100000003807362381&open=prime	http://factordb.com/index.php?showid=1100000003807362381&base=36	http://factordb.com/index.php?showid=1100000003807362381	http://factordb.com/helper.php?id=1100000003807362381	http://factordb.com/cert.php?id=1100000003807362381	http://factordb.com/certchain.php?fid=1100000003807362381&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2811*36%5E%28n%2B2%29%2B11329%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35248	WY₅₀₇H	(1154×36⁵⁰⁸−629)/35	509	793	http://factordb.com/index.php?id=1100000003807362386&open=prime	http://factordb.com/index.php?showid=1100000003807362386&base=36	http://factordb.com/index.php?showid=1100000003807362386	http://factordb.com/helper.php?id=1100000003807362386	http://factordb.com/cert.php?id=1100000003807362386	http://factordb.com/certchain.php?fid=1100000003807362386&action=all&fr=0&to=100	http://factordb.com/index.php?query=%281154*36%5E%28n%2B1%29-629%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35249	G0₅₁₀USJ	16×36⁵¹³+39907	514	800	http://factordb.com/index.php?id=1100000003807362389&open=prime	http://factordb.com/index.php?showid=1100000003807362389&base=36	http://factordb.com/index.php?showid=1100000003807362389	http://factordb.com/helper.php?id=1100000003807362389	http://factordb.com/cert.php?id=1100000003807362389	http://factordb.com/certchain.php?fid=1100000003807362389&action=all&fr=0&to=100	http://factordb.com/index.php?query=16*36%5E%28n%2B3%29%2B39907&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35250	Z₅₂₇EX7	36⁵³⁰−27317	530	825	http://factordb.com/index.php?id=1100000003807362391&open=prime	http://factordb.com/index.php?showid=1100000003807362391&base=36	http://factordb.com/index.php?showid=1100000003807362391	http://factordb.com/helper.php?id=1100000003807362391	http://factordb.com/cert.php?id=1100000003807362391	http://factordb.com/certchain.php?fid=1100000003807362391&action=all&fr=0&to=100	http://factordb.com/index.php?query=36%5E%28n%2B3%29-27317&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35251	EY0₅₃₄A1	538×36⁵³⁶+361	538	837	http://factordb.com/index.php?id=1100000000840634482&open=prime	http://factordb.com/index.php?showid=1100000000840634482&base=36	http://factordb.com/index.php?showid=1100000000840634482	http://factordb.com/helper.php?id=1100000000840634482	http://factordb.com/cert.php?id=1100000000840634482	http://factordb.com/certchain.php?fid=1100000000840634482&action=all&fr=0&to=100	http://factordb.com/index.php?query=538*36%5E%28n%2B2%29%2B361&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35252	Z0₅₆₃995	35×36⁵⁶⁶+11993	567	883	http://factordb.com/index.php?id=1100000003807362394&open=prime	http://factordb.com/index.php?showid=1100000003807362394&base=36	http://factordb.com/index.php?showid=1100000003807362394	http://factordb.com/helper.php?id=1100000003807362394	http://factordb.com/cert.php?id=1100000003807362394	http://factordb.com/certchain.php?fid=1100000003807362394&action=all&fr=0&to=100	http://factordb.com/index.php?query=35*36%5E%28n%2B3%29%2B11993&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35253	F₅₉₀95	(3×36⁵⁹²−1585)/7	592	921	http://factordb.com/index.php?id=1100000003807362398&open=prime	http://factordb.com/index.php?showid=1100000003807362398&base=36	http://factordb.com/index.php?showid=1100000003807362398	http://factordb.com/helper.php?id=1100000003807362398	http://factordb.com/cert.php?id=1100000003807362398	http://factordb.com/certchain.php?fid=1100000003807362398&action=all&fr=0&to=100	http://factordb.com/index.php?query=%283*36%5E%28n%2B2%29-1585%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35254	990₅₉₁B	333×36⁵⁹²+11	594	924	http://factordb.com/index.php?id=1100000002634138415&open=prime	http://factordb.com/index.php?showid=1100000002634138415&base=36	http://factordb.com/index.php?showid=1100000002634138415	http://factordb.com/helper.php?id=1100000002634138415	http://factordb.com/cert.php?id=1100000002634138415	http://factordb.com/certchain.php?fid=1100000002634138415&action=all&fr=0&to=100	http://factordb.com/index.php?query=333*36%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35255	J₆₇₅T	(19×36⁶⁷⁶+331)/35	676	1052	http://factordb.com/index.php?id=1100000002332534943&open=prime	http://factordb.com/index.php?showid=1100000002332534943&base=36	http://factordb.com/index.php?showid=1100000002332534943	http://factordb.com/helper.php?id=1100000002332534943	http://factordb.com/cert.php?id=1100000002332534943	http://factordb.com/certchain.php?fid=1100000002332534943&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*36%5E%28n%2B1%29%2B331%29%2F35&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35256	FZ₇₀₈OEB	16×36⁷¹¹−15037	712	1108	http://factordb.com/index.php?id=1100000003807362403&open=prime	http://factordb.com/index.php?showid=1100000003807362403&base=36	http://factordb.com/index.php?showid=1100000003807362403	http://factordb.com/helper.php?id=1100000003807362403	http://factordb.com/cert.php?id=1100000003807362403	http://factordb.com/certchain.php?fid=1100000003807362403&action=all&fr=0&to=100	http://factordb.com/index.php?query=16*36%5E%28n%2B3%29-15037&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35257	EX₇₃₂B	(523×36⁷³³−803)/35	734	1142	http://factordb.com/index.php?id=1100000003807362408&open=prime	http://factordb.com/index.php?showid=1100000003807362408&base=36	http://factordb.com/index.php?showid=1100000003807362408	http://factordb.com/helper.php?id=1100000003807362408	http://factordb.com/cert.php?id=1100000003807362408	http://factordb.com/certchain.php?fid=1100000003807362408&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28523*36%5E%28n%2B1%29-803%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35258	M₇₆₄8B	(22×36⁷⁶⁶−18047)/35	766	1192	http://factordb.com/index.php?id=1100000003807362414&open=prime	http://factordb.com/index.php?showid=1100000003807362414&base=36	http://factordb.com/index.php?showid=1100000003807362414	http://factordb.com/helper.php?id=1100000003807362414	http://factordb.com/cert.php?id=1100000003807362414	http://factordb.com/certchain.php?fid=1100000003807362414&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2822*36%5E%28n%2B2%29-18047%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35259	3EG₇₇₇D	(4286×36⁷⁷⁸−121)/35	780	1213	http://factordb.com/index.php?id=1100000003807362419&open=prime	http://factordb.com/index.php?showid=1100000003807362419&base=36	http://factordb.com/index.php?showid=1100000003807362419	http://factordb.com/helper.php?id=1100000003807362419	http://factordb.com/cert.php?id=1100000003807362419	http://factordb.com/certchain.php?fid=1100000003807362419&action=all&fr=0&to=100	http://factordb.com/index.php?query=%284286*36%5E%28n%2B1%29-121%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35260	W₉₆₂7	(32×36⁹⁶³−907)/35	963	1499	http://factordb.com/index.php?id=1100000002332533447&open=prime	http://factordb.com/index.php?showid=1100000002332533447&base=36	http://factordb.com/index.php?showid=1100000002332533447	http://factordb.com/helper.php?id=1100000002332533447	http://factordb.com/cert.php?id=1100000002332533447	http://factordb.com/certchain.php?fid=1100000002332533447&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2832*36%5E%28n%2B1%29-907%29%2F35&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35261	G₉₇₉88D	(16×36⁹⁸²−373081)/35	982	1528	http://factordb.com/index.php?id=1100000003807362435&open=prime	http://factordb.com/index.php?showid=1100000003807362435&base=36	http://factordb.com/index.php?showid=1100000003807362435	http://factordb.com/helper.php?id=1100000003807362435	http://factordb.com/cert.php?id=1100000003807362435	http://factordb.com/certchain.php?fid=1100000003807362435&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2816*36%5E%28n%2B3%29-373081%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35262	70₁₀₅₀XQN	7×36¹⁰⁵³+43727	1054	1640	http://factordb.com/index.php?id=1100000003807362444&open=prime	http://factordb.com/index.php?showid=1100000003807362444&base=36	http://factordb.com/index.php?showid=1100000003807362444	http://factordb.com/helper.php?id=1100000003807362444	http://factordb.com/cert.php?id=1100000003807362444	http://factordb.com/certchain.php?fid=1100000003807362444&action=all&fr=0&to=100	http://factordb.com/index.php?query=7*36%5E%28n%2B3%29%2B43727&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35263	EB0₁₀₈₃UV	515×36¹⁰⁸⁵+1111	1087	1692	http://factordb.com/index.php?id=1100000003807362457&open=prime	http://factordb.com/index.php?showid=1100000003807362457&base=36	http://factordb.com/index.php?showid=1100000003807362457	http://factordb.com/helper.php?id=1100000003807362457	http://factordb.com/cert.php?id=1100000003807362457	http://factordb.com/certchain.php?fid=1100000003807362457&action=all&fr=0&to=100	http://factordb.com/index.php?query=515*36%5E%28n%2B2%29%2B1111&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35264	F02R0₁₂₃₇D	699939×36¹²³⁸+13	1242	1933	http://factordb.com/index.php?id=1100000003807362472&open=prime	http://factordb.com/index.php?showid=1100000003807362472&base=36	http://factordb.com/index.php?showid=1100000003807362472	http://factordb.com/helper.php?id=1100000003807362472	http://factordb.com/cert.php?id=1100000003807362472	http://factordb.com/certchain.php?fid=1100000003807362472&action=all&fr=0&to=100	http://factordb.com/index.php?query=699939*36%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35265	50₁₃₁₃WMN	5×36¹³¹⁶+42287	1317	2049	http://factordb.com/index.php?id=1100000003807362473&open=prime	http://factordb.com/index.php?showid=1100000003807362473&base=36	http://factordb.com/index.php?showid=1100000003807362473	http://factordb.com/helper.php?id=1100000003807362473	http://factordb.com/cert.php?id=1100000003807362473	http://factordb.com/certchain.php?fid=1100000003807362473&action=all&fr=0&to=100	http://factordb.com/index.php?query=5*36%5E%28n%2B3%29%2B42287&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35266	V0₁₃₂₈444B	31×36¹³³²+191963	1333	2075	http://factordb.com/index.php?id=1100000003807362474&open=prime	http://factordb.com/index.php?showid=1100000003807362474&base=36	http://factordb.com/index.php?showid=1100000003807362474	http://factordb.com/helper.php?id=1100000003807362474	http://factordb.com/cert.php?id=1100000003807362474	http://factordb.com/certchain.php?fid=1100000003807362474&action=all&fr=0&to=100	http://factordb.com/index.php?query=31*36%5E%28n%2B4%29%2B191963&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35267	SI0₁₇₁₂KH	1026×36¹⁷¹⁴+737	1716	2671	http://factordb.com/index.php?id=1100000003807362475&open=prime	http://factordb.com/index.php?showid=1100000003807362475&base=36	http://factordb.com/index.php?showid=1100000003807362475	http://factordb.com/helper.php?id=1100000003807362475	http://factordb.com/cert.php?id=1100000003807362475	http://factordb.com/certchain.php?fid=1100000003807362475&action=all&fr=0&to=100	http://factordb.com/index.php?query=1026*36%5E%28n%2B2%29%2B737&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35268	Z0₁₇₁₄387	35×36¹⁷¹⁷+4183	1718	2674	http://factordb.com/index.php?id=1100000003807362477&open=prime	http://factordb.com/index.php?showid=1100000003807362477&base=36	http://factordb.com/index.php?showid=1100000003807362477	http://factordb.com/helper.php?id=1100000003807362477	http://factordb.com/cert.php?id=1100000003807362477	http://factordb.com/certchain.php?fid=1100000003807362477&action=all&fr=0&to=100	http://factordb.com/index.php?query=35*36%5E%28n%2B3%29%2B4183&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35269	5₁₉₃₆3Z	(36¹⁹³⁸−295)/7	1938	3016	http://factordb.com/index.php?id=1100000003807362478&open=prime	http://factordb.com/index.php?showid=1100000003807362478&base=36	http://factordb.com/index.php?showid=1100000003807362478	http://factordb.com/helper.php?id=1100000003807362478	http://factordb.com/cert.php?id=1100000003807362478	http://factordb.com/certchain.php?fid=1100000003807362478&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2836%5E%28n%2B2%29-295%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35270	40₂₄₇₈RV	4×36²⁴⁸⁰+1003	2481	3861	http://factordb.com/index.php?id=1100000002634138559&open=prime	http://factordb.com/index.php?showid=1100000002634138559&base=36	http://factordb.com/index.php?showid=1100000002634138559	http://factordb.com/helper.php?id=1100000002634138559	http://factordb.com/cert.php?id=1100000002634138559	http://factordb.com/certchain.php?fid=1100000002634138559&action=all&fr=0&to=100	http://factordb.com/index.php?query=4*36%5E%28n%2B2%29%2B1003&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35271	IS0₂₆₈₄A0H	676×36²⁶⁸⁷+12977	2689	4185	http://factordb.com/index.php?id=1100000003807362479&open=prime	http://factordb.com/index.php?showid=1100000003807362479&base=36	http://factordb.com/index.php?showid=1100000003807362479	http://factordb.com/helper.php?id=1100000003807362479	http://factordb.com/cert.php?id=1100000003807362479	http://factordb.com/certchain.php?fid=1100000003807362479&action=all&fr=0&to=100	http://factordb.com/index.php?query=676*36%5E%28n%2B3%29%2B12977&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35272	5Z₂₈₅₉95	6×36²⁸⁶¹−967	2862	4454	http://factordb.com/index.php?id=1100000003807362480&open=prime	http://factordb.com/index.php?showid=1100000003807362480&base=36	http://factordb.com/index.php?showid=1100000003807362480	http://factordb.com/helper.php?id=1100000003807362480	http://factordb.com/cert.php?id=1100000003807362480	http://factordb.com/certchain.php?fid=1100000003807362480&action=all&fr=0&to=100	http://factordb.com/index.php?query=6*36%5E%28n%2B2%29-967&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35273	Q₂₉₄₂2D	(26×36²⁹⁴⁴−30721)/35	2944	4582	http://factordb.com/index.php?id=1100000003807362481&open=prime	http://factordb.com/index.php?showid=1100000003807362481&base=36	http://factordb.com/index.php?showid=1100000003807362481	http://factordb.com/helper.php?id=1100000003807362481	http://factordb.com/cert.php?id=1100000003807362481	http://factordb.com/certchain.php?fid=1100000003807362481&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2826*36%5E%28n%2B2%29-30721%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35274	D0₃₀₄₇6E01	13×36³⁰⁵¹+298081	3052	4750	http://factordb.com/index.php?id=1100000003807362482&open=prime	http://factordb.com/index.php?showid=1100000003807362482&base=36	http://factordb.com/index.php?showid=1100000003807362482	http://factordb.com/helper.php?id=1100000003807362482	http://factordb.com/cert.php?id=1100000003807362482	http://factordb.com/certchain.php?fid=1100000003807362482&action=all&fr=0&to=100	http://factordb.com/index.php?query=13*36%5E%28n%2B4%29%2B298081&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35275	CNS₃₄₂₄J	(2279×36³⁴²⁵−49)/5	3427	5333	http://factordb.com/index.php?id=1100000003807362483&open=prime	http://factordb.com/index.php?showid=1100000003807362483&base=36	http://factordb.com/index.php?showid=1100000003807362483	http://factordb.com/helper.php?id=1100000003807362483	http://factordb.com/cert.php?id=1100000003807362483	http://factordb.com/certchain.php?fid=1100000003807362483&action=all&fr=0&to=100	http://factordb.com/index.php?query=%282279*36%5E%28n%2B1%29-49%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35276	4₃₉₂₅V	(4×36³⁹²⁶+941)/35	3926	6110	http://factordb.com/index.php?id=1100000002332536659&open=prime	http://factordb.com/index.php?showid=1100000002332536659&base=36	http://factordb.com/index.php?showid=1100000002332536659	http://factordb.com/helper.php?id=1100000002332536659	http://factordb.com/cert.php?id=1100000002332536659	http://factordb.com/certchain.php?fid=1100000002332536659&action=all&fr=0&to=100	http://factordb.com/index.php?query=%284*36%5E%28n%2B1%29%2B941%29%2F35&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35277	OZ₃₉₃₂AZ	25×36³⁹³⁴−901	3935	6124	http://factordb.com/index.php?id=1100000000840634476&open=prime	http://factordb.com/index.php?showid=1100000000840634476&base=36	http://factordb.com/index.php?showid=1100000000840634476	http://factordb.com/helper.php?id=1100000000840634476	http://factordb.com/cert.php?id=1100000000840634476	http://factordb.com/certchain.php?fid=1100000000840634476&action=all&fr=0&to=100	http://factordb.com/index.php?query=25*36%5E%28n%2B2%29-901&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35278	RY₄₅₆₂H	(979×36⁴⁵⁶³−629)/35	4564	7103	http://factordb.com/index.php?id=1100000003807362485&open=prime	http://factordb.com/index.php?showid=1100000003807362485&base=36	http://factordb.com/index.php?showid=1100000003807362485	http://factordb.com/helper.php?id=1100000003807362485	http://factordb.com/cert.php?id=1100000003807362485	http://factordb.com/certchain.php?fid=1100000003807362485&action=all&fr=0&to=100	http://factordb.com/index.php?query=%28979*36%5E%28n%2B1%29-629%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35279	T09₄₆₁₈1	(36549×36⁴⁶¹⁹−289)/35	4621	7192	http://factordb.com/index.php?id=1100000003807362486&open=prime	http://factordb.com/index.php?showid=1100000003807362486&base=36	http://factordb.com/index.php?showid=1100000003807362486	http://factordb.com/helper.php?id=1100000003807362486	http://factordb.com/cert.php?id=1100000003807362486	http://factordb.com/certchain.php?fid=1100000003807362486&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2836549*36%5E%28n%2B1%29-289%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35280	FZ₅₇₇₇3P	16×36⁵⁷⁷⁹−1163	5780	8996	http://factordb.com/index.php?id=1100000003807362487&open=prime	http://factordb.com/index.php?showid=1100000003807362487&base=36	http://factordb.com/index.php?showid=1100000003807362487	http://factordb.com/helper.php?id=1100000003807362487	http://factordb.com/cert.php?id=1100000003807362487	http://factordb.com/certchain.php?fid=1100000003807362487&action=all&fr=0&to=100	http://factordb.com/index.php?query=16*36%5E%28n%2B2%29-1163&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35281	EO0₆₁₇₇V	528×36⁶¹⁷⁸+31	6180	9618	http://factordb.com/index.php?id=1100000003807362488&open=prime	http://factordb.com/index.php?showid=1100000003807362488&base=36	http://factordb.com/index.php?showid=1100000003807362488	http://factordb.com/helper.php?id=1100000003807362488	http://factordb.com/cert.php?id=1100000003807362488	http://factordb.com/certchain.php?fid=1100000003807362488&action=all&fr=0&to=100	http://factordb.com/index.php?query=528*36%5E%28n%2B1%29%2B31&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35282	VL0₇₂₅₈J	1137×36⁷²⁵⁹+19	7261	11301	http://factordb.com/index.php?id=1100000003807362489&open=prime	http://factordb.com/index.php?showid=1100000003807362489&base=36	http://factordb.com/index.php?showid=1100000003807362489	http://factordb.com/helper.php?id=1100000003807362489	http://factordb.com/cert.php?id=1100000003807362489	http://factordb.com/certchain.php?fid=1100000003807362489&action=all&fr=0&to=100	http://factordb.com/index.php?query=1137*36%5E%28n%2B1%29%2B19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show
36	35283	J₁₀₁₁₇LJ	(19×36¹⁰¹¹⁹+2501)/35	10119	15748	http://factordb.com/index.php?id=1100000003807362491&open=prime	http://factordb.com/index.php?showid=1100000003807362491&base=36	http://factordb.com/index.php?showid=1100000003807362491	http://factordb.com/helper.php?id=1100000003807362491	http://factordb.com/cert.php?id=1100000003807362491	http://factordb.com/certchain.php?fid=1100000003807362491&action=all&fr=0&to=100	http://factordb.com/index.php?query=%2819*36%5E%28n%2B2%29%2B2501%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show

Condensed table for bases 2 ≤ b ≤ 36: (the bases b = 11, 13, 16, 17, 19, 21~23, 25~36 data assumes the primality of the probable primes) (This data assumes that a number > 10²⁵⁰⁰⁰ which has passed the Miller–Rabin primality tests (https://t5k.org/prove/prove2_3.html, https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test, https://en.wikipedia.org/wiki/Strong_pseudoprime, https://t5k.org/glossary/xpage/MillersTest.html, https://t5k.org/glossary/xpage/StrongPRP.html, https://www.rieselprime.de/ziki/Miller-Rabin_pseudoprimality_test, https://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html, https://mathworld.wolfram.com/StrongPseudoprime.html, http://www.numericana.com/answer/pseudo.htm#rabin, http://www.numericana.com/answer/pseudo.htm#strong, http://www.javascripter.net/math/primes/millerrabinprimalitytest.htm, http://ntheory.org/data/spsps.txt, https://faculty.lynchburg.edu/~nicely/misc/mpzspsp.html, https://miller-rabin.appspot.com/, http://www.pi-e.de/Miller-Rabin-Pseudoprimzahlen.htm (in German), http://factordb.com/prooffailed.php, https://sites.google.com/view/strong-pseudoprime, https://sites.google.com/view/bases-strong-pseudoprime, https://oeis.org/A001262, https://oeis.org/A020229, https://oeis.org/A020231, https://oeis.org/A020233, https://oeis.org/A072276, https://oeis.org/A056915, https://oeis.org/A074773, https://oeis.org/A014233, https://oeis.org/A006945, https://oeis.org/A089825, https://oeis.org/A181782, https://oeis.org/A071294, https://oeis.org/A141768, https://oeis.org/A195328, https://oeis.org/A329759, https://oeis.org/A298756) to all prime bases p < 64 and has passed the Baillie–PSW primality test (https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test, https://mathworld.wolfram.com/Baillie-PSWPrimalityTest.html, http://pseudoprime.com/dopo.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_318.pdf)) and has trial factored (https://en.wikipedia.org/wiki/Trial_division, https://t5k.org/glossary/xpage/TrialDivision.html, https://www.rieselprime.de/ziki/Trial_factoring, https://mathworld.wolfram.com/TrialDivision.html, http://www.numericana.com/answer/factoring.htm#trial, https://www.mersenne.ca/tf1G/, https://www.mersenne.ca/tfmissed.php, https://oeis.org/A189172) to 10¹⁶ is in fact prime, since in some cases (e.g. b = 11) a candidate for minimal prime base b is too large to be proven prime rigorously, this candidate for minimal prime base 11 has 65263 decimal digits, while the top record ordinary prime (https://t5k.org/glossary/xpage/OrdinaryPrime.html) (i.e. neither N−1 (https://t5k.org/prove/prove3_1.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, https://en.wikipedia.org/wiki/Pocklington_primality_test, https://www.rieselprime.de/ziki/Pocklington%27s_theorem, https://mathworld.wolfram.com/PocklingtonsTheorem.html, https://stdkmd.net/nrr/pock/, http://factordb.com/nmoverview.php?method=1) nor N+1 (https://t5k.org/prove/prove3_2.html, http://bln.curtisbright.com/2013/10/09/the-n-1-and-n1-primality-tests/, http://irvinemclean.com/maths/pfaq4.htm, http://factordb.com/nmoverview.php?method=2) can be ≥ 1/4 factored (https://en.wikipedia.org/wiki/Integer_factorization, https://www.rieselprime.de/ziki/Factorization, https://mathworld.wolfram.com/PrimeFactorization.html, https://mathworld.wolfram.com/PrimeFactorizationAlgorithms.html, http://www.numericana.com/answer/factoring.htm)) has 86453 decimal digits (the entry of this prime in top definitely primes is https://t5k.org/primes/page.php?id=136044), see https://t5k.org/top20/page.php?id=27 and https://t5k.org/primes/search.php?Comment=ECPP&OnList=all&Number=1000000&Style=HTML and http://factordb.com/certoverview.php?digits=300&perpage=1000&skip=0&descending=on)

For every solved base b, we give the number of minimal primes (or probable prime, which is a minimal prime assuming its primality) and the top 10 minimal primes (or probable prime, which is a minimal prime assuming its primality) in the table below, and the minimal primes (or probable prime, which is a minimal prime assuming its primality) are exactly the elements in the "kernel b" file. For every unsolved base b, we give the current greatest lower bound (https://en.wikipedia.org/wiki/Greatest_lower_bound, https://mathworld.wolfram.com/GreatestLowerBound.html) and the current least upper bound (https://en.wikipedia.org/wiki/Least_upper_bound, https://mathworld.wolfram.com/LeastUpperBound.html) for the number of minimal primes (or probable prime, which is a minimal prime assuming its primality) and the top 10 known minimal primes (or probable prime, which is a minimal prime assuming its primality) and the number of families of the form x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b) which have no known prime (or strong probable prime) members > b, nor can be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them) in the table below, and the greatest lower bound (https://en.wikipedia.org/wiki/Greatest_lower_bound, https://mathworld.wolfram.com/GreatestLowerBound.html) for the number of minimal primes (or probable prime, which is a minimal prime assuming its primality) is exactly the number of the elements in the "kernel b" file (also, the currently known minimal primes (or probable prime, which is a minimal prime assuming its primality) are exactly the elements in the "kernel b" file), and the left families (i.e. families which have no known prime (or strong probable prime) members > b, nor can be ruled out as only containing composites (only count the numbers > b) (by covering congruence, algebraic factorization, or combine of them)) (all of them are linear families, i.e. of the form x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b)) are exactly the families in the "left b" file, since such linear families can contain at most one minimal prime (in fact, they must contain exactly one minimal prime if they are not covered by another left family (e.g. the base 19 left family 5{H}05 is covered by another base 19 left family 5{H}5, thus the base 19 left family 5{H}05 may contain no minimal primes) if we assume the heuristic argument (https://en.wikipedia.org/wiki/Heuristic_argument, https://t5k.org/glossary/xpage/Heuristic.html, https://mathworld.wolfram.com/Heuristic.html, https://web.archive.org/web/20230911032453/https://www.utm.edu/staff/caldwell/preprints/Heuristics.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_112.pdf), https://arxiv.org/pdf/2103.04483.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_113.pdf)) that all unsolved families have a prime, this is reasonable, references: https://t5k.org/mersenne/heuristic.html, https://t5k.org/notes/faq/NextMersenne.html, https://t5k.org/glossary/xpage/Repunit.html, https://web.archive.org/web/20100628035147/http://www.math.niu.edu/~rusin/known-math/98/exp_primes, https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906, https://mathoverflow.net/questions/268918/density-of-primes-in-sequences-of-the-form-anb, https://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Mathematics/2023_September_25#Are_there_infinitely_many_primes_of_the_form_1000%E2%80%A60007,_333%E2%80%A63331,_7111%E2%80%A6111,_or_3444%E2%80%A64447_in_base_10?, https://arxiv.org/pdf/2307.07894.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_203.pdf), https://web.archive.org/web/20231002020455/http://yves.gallot.pagesperso-orange.fr/papers/weight.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_216.pdf), https://www.mersenneforum.org/showthread.php?t=12327, https://oeis.org/A234285 (the comment by Farideh Firoozbakht, although this comment is not true, there is no prime for s = 509203 and s = −78557, s = 509203 has a covering set of {3, 5, 7, 13, 17, 241}, and s = −78557 has a covering set of {3, 5, 7, 13, 19, 37, 73}), https://www.mersenneforum.org/showpost.php?p=564786&postcount=3, https://www.mersenneforum.org/showpost.php?p=461665&postcount=7, https://www.mersenneforum.org/showpost.php?p=354505&postcount=5, https://www.mersenneforum.org/showpost.php?p=344985&postcount=293, https://www.mersenneforum.org/showpost.php?p=625978&postcount=1027, https://www.primegrid.com/forum_thread.php?id=5093&nowrap=true#66471, https://www.primegrid.com/forum_thread.php?id=4935&nowrap=true#63813, also the graphs https://t5k.org/gifs/lg_lg_Mn.gif (for the family {1} in base b = 2) and https://t5k.org/gifs/repunits.gif (for the family {1} in base b = 10) and https://www.mersenneforum.org/attachment.php?attachmentid=4010&d=1642088235 (for the family 2{0}1 in base b = 3)), the least upper bound (https://en.wikipedia.org/wiki/Least_upper_bound, https://mathworld.wolfram.com/LeastUpperBound.html) for the number of minimal primes (or probable prime, which is a minimal prime assuming its primality) is given by the sum of the greatest lower bound for the number of minimal primes (or probable prime, which is a minimal prime assuming its primality) (i.e. the number of elements in the "kernel b" file) and the number of left families (i.e. the number of families in the "left b" file), also, we give the searching limit of length for the linear families, if there are any more minimal primes (or probable prime, which is a minimal prime assuming its primality) base b they must have > this many digits in base b.

Four coincidences (https://en.wikipedia.org/wiki/Mathematical_coincidence, https://mathworld.wolfram.com/Coincidence.html):

The length of the largest minimal prime in bases b = 18 and b = 20 are both 6271 (in theory, b = 20 should be about 1.65 times as b = 18).
The length of the 10401st minimal prime in base b = 17 is exactly 10401.
Bases b = 20 and b = 23 have two same type of families which have the minimal prime with the same length: (b−1)×bⁿ+1 (both have length 15: J00000000000001 and M00000000000001, respectively) and bⁿ−(b−1) (both have length 17: JJJJJJJJJJJJJJJJ1 and MMMMMMMMMMMMMMMM1, respectively).
A minimal prime in base b = 34 has length exactly 100000 (it is GFGC₉₉₉₉₆5).

b	number of minimal primes (or probable prime, which is a minimal prime assuming its primality) base b	base-b form of the top 10 known minimal primes (or probable prime, which is a minimal prime assuming its primality) base b (write "d_n" if there are 5 or more (n) consecutive same digits d)	length of the top 10 known minimal primes (or probable prime, which is a minimal prime assuming its primality) base b	length of the top 10 known minimal primes (or probable prime, which is a minimal prime assuming its primality) base b in decimal	algebraic ((a×bⁿ+c)/gcd(a+c,b−1)) form of the top 10 known minimal primes (or probable prime, which is a minimal prime assuming its primality) base b	factordb entry of the top 10 known minimal primes (or probable prime, which is a minimal prime assuming its primality)	the top 10 known minimal primes (or probable prime, which is a minimal prime assuming its primality) written in base b (use lower case letters instead of upper case letters)	the top 10 known minimal primes (or probable prime, which is a minimal prime assuming its primality) written in decimal	factorization of the first 200 numbers in corresponding family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0) of the top 10 known minimal primes)	number of left families in base b (all of these left families are linear families)	searching limit of length for the left families in base b (if there are different searching limits for the left families in base b, choose the lowest searching limit)
2	1	11	2	1	3	http://factordb.com/index.php?id=3&open=ecm	http://factordb.com/index.php?showid=3&base=2	http://factordb.com/index.php?showid=3	–	0	–
3	3	111 21 12	3 2 2	2 1 1	13 7 5	http://factordb.com/index.php?id=13&open=ecm http://factordb.com/index.php?id=7&open=ecm http://factordb.com/index.php?id=5&open=ecm	http://factordb.com/index.php?showid=13&base=3 http://factordb.com/index.php?showid=7&base=3 http://factordb.com/index.php?showid=5&base=3	http://factordb.com/index.php?showid=13 http://factordb.com/index.php?showid=7 http://factordb.com/index.php?showid=5	– – –	0	–
4	5	221 31 23 13 11	3 2 2 2 2	2 2 2 1 1	41 13 11 7 5	http://factordb.com/index.php?id=41&open=ecm http://factordb.com/index.php?id=13&open=ecm http://factordb.com/index.php?id=11&open=ecm http://factordb.com/index.php?id=7&open=ecm http://factordb.com/index.php?id=5&open=ecm	http://factordb.com/index.php?showid=41&base=4 http://factordb.com/index.php?showid=13&base=4 http://factordb.com/index.php?showid=11&base=4 http://factordb.com/index.php?showid=7&base=4 http://factordb.com/index.php?showid=5&base=4	http://factordb.com/index.php?showid=41 http://factordb.com/index.php?showid=13 http://factordb.com/index.php?showid=11 http://factordb.com/index.php?showid=7 http://factordb.com/index.php?showid=5	– – – – –	0	–
5	22	10₉₃13 300031 44441 33331 33001 30301 14444 10103 3101 414	96 6 5 5 5 5 5 5 4 3	67 4 4 4 4 4 4 3 3 3	5⁹⁵+8 9391 3121 2341 2251 1951 1249 653 401 109	http://factordb.com/index.php?id=1100000000034686071&open=ecm http://factordb.com/index.php?id=9391&open=ecm http://factordb.com/index.php?id=3121&open=ecm http://factordb.com/index.php?id=2341&open=ecm http://factordb.com/index.php?id=2251&open=ecm http://factordb.com/index.php?id=1951&open=ecm http://factordb.com/index.php?id=1249&open=ecm http://factordb.com/index.php?id=653&open=ecm http://factordb.com/index.php?id=401&open=ecm http://factordb.com/index.php?id=109&open=ecm	http://factordb.com/index.php?showid=1100000000034686071&base=5 http://factordb.com/index.php?showid=9391&base=5 http://factordb.com/index.php?showid=3121&base=5 http://factordb.com/index.php?showid=2341&base=5 http://factordb.com/index.php?showid=2251&base=5 http://factordb.com/index.php?showid=1951&base=5 http://factordb.com/index.php?showid=1249&base=5 http://factordb.com/index.php?showid=653&base=5 http://factordb.com/index.php?showid=401&base=5 http://factordb.com/index.php?showid=109&base=5	http://factordb.com/index.php?showid=1100000000034686071 http://factordb.com/index.php?showid=9391 http://factordb.com/index.php?showid=3121 http://factordb.com/index.php?showid=2341 http://factordb.com/index.php?showid=2251 http://factordb.com/index.php?showid=1951 http://factordb.com/index.php?showid=1249 http://factordb.com/index.php?showid=653 http://factordb.com/index.php?showid=401 http://factordb.com/index.php?showid=109	http://factordb.com/index.php?query=5%5E%28n%2B2%29%2B8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show – – – – – – – – –	0	–
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7	71	3₁₆1 510₇1 3₆01 1100021 531101 351101 300053 150001 100121 40054	17 10 8 7 6 6 6 6 6 5	15 9 7 6 5 5 5 5 5 4	(7¹⁷−5)/2 36×7⁸+1 (7⁸−47)/2 134471 91631 62819 50459 28813 16871 9643	http://factordb.com/index.php?id=116315256993601&open=ecm http://factordb.com/index.php?id=207532837&open=ecm http://factordb.com/index.php?id=2882377&open=ecm http://factordb.com/index.php?id=134471&open=ecm http://factordb.com/index.php?id=91631&open=ecm http://factordb.com/index.php?id=62819&open=ecm http://factordb.com/index.php?id=50459&open=ecm http://factordb.com/index.php?id=28813&open=ecm http://factordb.com/index.php?id=16871&open=ecm http://factordb.com/index.php?id=9643&open=ecm	http://factordb.com/index.php?showid=116315256993601&base=7 http://factordb.com/index.php?showid=207532837&base=7 http://factordb.com/index.php?showid=2882377&base=7 http://factordb.com/index.php?showid=134471&base=7 http://factordb.com/index.php?showid=91631&base=7 http://factordb.com/index.php?showid=62819&base=7 http://factordb.com/index.php?showid=50459&base=7 http://factordb.com/index.php?showid=28813&base=7 http://factordb.com/index.php?showid=16871&base=7 http://factordb.com/index.php?showid=9643&base=7	http://factordb.com/index.php?showid=116315256993601 http://factordb.com/index.php?showid=207532837 http://factordb.com/index.php?showid=2882377 http://factordb.com/index.php?showid=134471 http://factordb.com/index.php?showid=91631 http://factordb.com/index.php?showid=62819 http://factordb.com/index.php?showid=50459 http://factordb.com/index.php?showid=28813 http://factordb.com/index.php?showid=16871 http://factordb.com/index.php?showid=9643	http://factordb.com/index.php?query=%287%5E%28n%2B1%29-5%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=36*7%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%287%5E%28n%2B2%29-47%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show – – – – – – –	0	–
8	75	4₂₂₀7 5₁₃25 7₁₂1 77774₆1 74₇1 4₈1 5₅025 5550525 5500525 4₅77	221 15 13 11 9 9 8 7 7 7	200 14 12 10 9 8 8 7 7 7	(4×8²²¹+17)/7 (5×8¹⁵−173)/7 8¹³−7 (28669×8⁷−25)/7 (53×8⁸−25)/7 (4×8⁹−25)/7 (5×8⁸−2413)/7 1495381 1474901 (4×8⁷+185)/7	http://factordb.com/index.php?id=1100000000416605822&open=ecm http://factordb.com/index.php?id=25131694349141&open=ecm http://factordb.com/index.php?id=549755813881&open=ecm http://factordb.com/index.php?id=8589035809&open=ecm http://factordb.com/index.php?id=127027489&open=ecm http://factordb.com/index.php?id=76695841&open=ecm http://factordb.com/index.php?id=11983381&open=ecm http://factordb.com/index.php?id=1495381&open=ecm http://factordb.com/index.php?id=1474901&open=ecm http://factordb.com/index.php?id=1198399&open=ecm	http://factordb.com/index.php?showid=1100000000416605822&base=8 http://factordb.com/index.php?showid=25131694349141&base=8 http://factordb.com/index.php?showid=549755813881&base=8 http://factordb.com/index.php?showid=8589035809&base=8 http://factordb.com/index.php?showid=127027489&base=8 http://factordb.com/index.php?showid=76695841&base=8 http://factordb.com/index.php?showid=11983381&base=8 http://factordb.com/index.php?showid=1495381&base=8 http://factordb.com/index.php?showid=1474901&base=8 http://factordb.com/index.php?showid=1198399&base=8	http://factordb.com/index.php?showid=1100000000416605822 http://factordb.com/index.php?showid=25131694349141 http://factordb.com/index.php?showid=549755813881 http://factordb.com/index.php?showid=8589035809 http://factordb.com/index.php?showid=127027489 http://factordb.com/index.php?showid=76695841 http://factordb.com/index.php?showid=11983381 http://factordb.com/index.php?showid=1495381 http://factordb.com/index.php?showid=1474901 http://factordb.com/index.php?showid=1198399	http://factordb.com/index.php?query=%2848%5E%28n%2B1%29%2B17%29%2F7&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2858%5E%28n%2B2%29-173%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=8%5E%28n%2B1%29-7&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28286698%5E%28n%2B1%29-25%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28538%5E%28n%2B1%29-25%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2848%5E%28n%2B1%29-25%29%2F7&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2858%5E%28n%2B3%29-2413%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show – – http://factordb.com/index.php?query=%284*8%5E%28n%2B2%29%2B185%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
9	151	30₁₁₅₈11 27₆₈₆07 76₃₂₉2 561₃₆ 10₂₅57 30₂₀51 8₁₉335 727₁₅07 51₁₃61 10₁₁507	1161 689 331 38 28 23 22 19 16 15	1108 657 316 37 26 22 21 19 16 14	3×9¹¹⁶⁰+10 (23×9⁶⁸⁸−511)/8 (31×9³³⁰−19)/4 (409×9³⁶−1)/8 9²⁷+52 3×9²²+46 9²²−454 (527×9¹⁷−511)/8 (41×9¹⁵+359)/8 9¹⁴+412	http://factordb.com/index.php?id=1100000002376318423&open=prime http://factordb.com/index.php?id=1100000002495467486&open=prime http://factordb.com/index.php?id=1100000002359003642&open=prime http://factordb.com/index.php?id=1100000001554010824&open=ecm http://factordb.com/index.php?id=1100000002512830927&open=ecm http://factordb.com/index.php?id=1100000000032261811&open=ecm http://factordb.com/index.php?id=1100000002495736583&open=ecm http://factordb.com/index.php?id=1100000003446800389&open=ecm http://factordb.com/index.php?id=1055192051985121&open=ecm http://factordb.com/index.php?id=22876792455373&open=ecm	http://factordb.com/index.php?showid=1100000002376318423&base=9 http://factordb.com/index.php?showid=1100000002495467486&base=9 http://factordb.com/index.php?showid=1100000002359003642&base=9 http://factordb.com/index.php?showid=1100000001554010824&base=9 http://factordb.com/index.php?showid=1100000002512830927&base=9 http://factordb.com/index.php?showid=1100000000032261811&base=9 http://factordb.com/index.php?showid=1100000002495736583&base=9 http://factordb.com/index.php?showid=1100000003446800389&base=9 http://factordb.com/index.php?showid=1055192051985121&base=9 http://factordb.com/index.php?showid=22876792455373&base=9	http://factordb.com/index.php?showid=1100000002376318423 http://factordb.com/index.php?showid=1100000002495467486 http://factordb.com/index.php?showid=1100000002359003642 http://factordb.com/index.php?showid=1100000001554010824 http://factordb.com/index.php?showid=1100000002512830927 http://factordb.com/index.php?showid=1100000000032261811 http://factordb.com/index.php?showid=1100000002495736583 http://factordb.com/index.php?showid=1100000003446800389 http://factordb.com/index.php?showid=1055192051985121 http://factordb.com/index.php?showid=22876792455373	http://factordb.com/index.php?query=39%5E%28n%2B2%29%2B10&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28239%5E%28n%2B2%29-511%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28319%5E%28n%2B1%29-19%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%284099%5En-1%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=9%5E%28n%2B2%29%2B52&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=39%5E%28n%2B2%29%2B46&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=9%5E%28n%2B3%29-454&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%285279%5E%28n%2B2%29-511%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2841*9%5E%28n%2B2%29%2B359%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=9%5E%28n%2B3%29%2B412&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
10	77	50₂₈27 5₁₁1 805₅1 66600049 66000049 60₅49 220₅1 5200007 946669 666649	31 12 8 8 8 8 8 7 6 6	31 12 8 8 8 8 8 7 6 6	5×10³⁰+27 (5×10¹²−41)/9 (725×10⁶−41)/9 66600049 66000049 6×10⁷+49 22×10⁶+1 5200007 946669 666649	http://factordb.com/index.php?id=1100000000204142046&open=ecm http://factordb.com/index.php?id=555555555551&open=ecm http://factordb.com/index.php?id=80555551&open=ecm http://factordb.com/index.php?id=66600049&open=ecm http://factordb.com/index.php?id=66000049&open=ecm http://factordb.com/index.php?id=60000049&open=ecm http://factordb.com/index.php?id=22000001&open=ecm http://factordb.com/index.php?id=5200007&open=ecm http://factordb.com/index.php?id=946669&open=ecm http://factordb.com/index.php?id=666649&open=ecm	http://factordb.com/index.php?showid=1100000000204142046&base=10 http://factordb.com/index.php?showid=555555555551&base=10 http://factordb.com/index.php?showid=80555551&base=10 http://factordb.com/index.php?showid=66600049&base=10 http://factordb.com/index.php?showid=66000049&base=10 http://factordb.com/index.php?showid=60000049&base=10 http://factordb.com/index.php?showid=22000001&base=10 http://factordb.com/index.php?showid=5200007&base=10 http://factordb.com/index.php?showid=946669&base=10 http://factordb.com/index.php?showid=666649&base=10	http://factordb.com/index.php?showid=1100000000204142046 http://factordb.com/index.php?showid=555555555551 http://factordb.com/index.php?showid=80555551 http://factordb.com/index.php?showid=66600049 http://factordb.com/index.php?showid=66000049 http://factordb.com/index.php?showid=60000049 http://factordb.com/index.php?showid=22000001 http://factordb.com/index.php?showid=5200007 http://factordb.com/index.php?showid=946669 http://factordb.com/index.php?showid=666649	http://factordb.com/index.php?query=510%5E%28n%2B2%29%2B27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28510%5E%28n%2B1%29-41%29%2F9&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2872510%5E%28n%2B1%29-41%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show – – http://factordb.com/index.php?query=610%5E%28n%2B2%29%2B49&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=22*10%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show – – –	0	–
11	1068	57₆₂₆₆₈ 557₁₀₁₁ 7₇₅₉44 A₇₁₃58 85₂₂₀05 507₂₀₆ 5₁₆₁2A 50₁₂₆57 10₁₂₅51 326₁₂₂	62669 1013 761 715 223 208 163 129 128 124	65263 1055 793 745 233 217 170 134 133 129	(57×11⁶²⁶⁶⁸−7)/10 (607×11¹⁰¹¹−7)/10 (7×11⁷⁶¹−367)/10 11⁷¹⁵−58 (17×11²²²−111)/2 (557×11²⁰⁶−7)/10 (11¹⁶³−57)/2 5×11¹²⁸+62 11¹²⁷+56 (178×11¹²²−3)/5	http://factordb.com/index.php?id=1100000003573679860&open=prime http://factordb.com/index.php?id=1100000002361376522&open=prime http://factordb.com/index.php?id=1100000002505568840&open=prime http://factordb.com/index.php?id=1100000003576826487&open=prime http://factordb.com/index.php?id=1100000003576826769&open=ecm http://factordb.com/index.php?id=1100000002518512744&open=ecm http://factordb.com/index.php?id=1100000002391585327&open=ecm http://factordb.com/index.php?id=1100000002632393378&open=ecm http://factordb.com/index.php?id=1100000002391531300&open=ecm http://factordb.com/index.php?id=1100000003576826781&open=ecm	http://factordb.com/index.php?showid=1100000003573679860&base=11 http://factordb.com/index.php?showid=1100000002361376522&base=11 http://factordb.com/index.php?showid=1100000002505568840&base=11 http://factordb.com/index.php?showid=1100000003576826487&base=11 http://factordb.com/index.php?showid=1100000003576826769&base=11 http://factordb.com/index.php?showid=1100000002518512744&base=11 http://factordb.com/index.php?showid=1100000002391585327&base=11 http://factordb.com/index.php?showid=1100000002632393378&base=11 http://factordb.com/index.php?showid=1100000002391531300&base=11 http://factordb.com/index.php?showid=1100000003576826781&base=11	http://factordb.com/index.php?showid=1100000003573679860 http://factordb.com/index.php?showid=1100000002361376522 http://factordb.com/index.php?showid=1100000002505568840 http://factordb.com/index.php?showid=1100000003576826487 http://factordb.com/index.php?showid=1100000003576826769 http://factordb.com/index.php?showid=1100000002518512744 http://factordb.com/index.php?showid=1100000002391585327 http://factordb.com/index.php?showid=1100000002632393378 http://factordb.com/index.php?showid=1100000002391531300 http://factordb.com/index.php?showid=1100000003576826781	http://factordb.com/index.php?query=%285711%5En-7%29%2F10&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2860711%5En-7%29%2F10&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28711%5E%28n%2B2%29-367%29%2F10&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=11%5E%28n%2B2%29-58&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281711%5E%28n%2B2%29-111%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2855711%5En-7%29%2F10&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2811%5E%28n%2B2%29-57%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=511%5E%28n%2B2%29%2B62&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=11%5E%28n%2B2%29%2B56&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28178*11%5En-3%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
12	106	40₃₉77 B0₂₇9B B₆99B AA0₅1 B00099B AAA0001 BBBAA1 A00065 44AAA1 BBBB1	42 30 9 8 7 7 6 6 6 5	45 33 10 9 8 8 7 7 7 6	4×12⁴¹+91 11×12²⁹+119 12⁹−313 130×12⁶+1 32847239 32555521 2985817 2488397 1097113 248821	http://factordb.com/index.php?id=1100000002375054575&open=ecm http://factordb.com/index.php?id=1100000002354113100&open=ecm http://factordb.com/index.php?id=5159780039&open=ecm http://factordb.com/index.php?id=388177921&open=ecm http://factordb.com/index.php?id=32847239&open=ecm http://factordb.com/index.php?id=32555521&open=ecm http://factordb.com/index.php?id=2985817&open=ecm http://factordb.com/index.php?id=2488397&open=ecm http://factordb.com/index.php?id=1097113&open=ecm http://factordb.com/index.php?id=248821&open=ecm	http://factordb.com/index.php?showid=1100000002375054575&base=12 http://factordb.com/index.php?showid=1100000002354113100&base=12 http://factordb.com/index.php?showid=5159780039&base=12 http://factordb.com/index.php?showid=388177921&base=12 http://factordb.com/index.php?showid=32847239&base=12 http://factordb.com/index.php?showid=32555521&base=12 http://factordb.com/index.php?showid=2985817&base=12 http://factordb.com/index.php?showid=2488397&base=12 http://factordb.com/index.php?showid=1097113&base=12 http://factordb.com/index.php?showid=248821&base=12	http://factordb.com/index.php?showid=1100000002375054575 http://factordb.com/index.php?showid=1100000002354113100 http://factordb.com/index.php?showid=5159780039 http://factordb.com/index.php?showid=388177921 http://factordb.com/index.php?showid=32847239 http://factordb.com/index.php?showid=32555521 http://factordb.com/index.php?showid=2985817 http://factordb.com/index.php?showid=2488397 http://factordb.com/index.php?showid=1097113 http://factordb.com/index.php?showid=248821	http://factordb.com/index.php?query=412%5E%28n%2B2%29%2B91&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1112%5E%28n%2B2%29%2B119&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=12%5E%28n%2B3%29-313&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=130*12%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show – – – – – –	0	–
13	3197	A3₅₉₂₁₉₇A 95₁₉₇₄₂₀ 80₃₂₀₁₇111 C5₂₃₇₅₅C C₁₀₆₃₁92 B0₆₅₄₀BBA 390₆₂₆₆1 1770₂₇₀₃17 720₂₂₉₇2 930₁₅₅₁1	592199 197421 32021 23757 10633 6544 6269 2708 2300 1554	659677 219916 35670 26464 11845 7290 6983 3016 2562 1731	(41×13⁵⁹²¹⁹⁸+27)/4 (113×13¹⁹⁷⁴²⁰−5)/12 8×13³²⁰²⁰+183 (149×13²³⁷⁵⁶+79)/12 13¹⁰⁶³³−50 11×13⁶⁵⁴³+2012 48×13⁶²⁶⁷+1 267×13²⁷⁰⁵+20 93×13²²⁹⁸+2 120×13¹⁵⁵²+1	http://factordb.com/index.php?id=1100000005489162806&open=prime http://factordb.com/index.php?id=1100000003943359311&open=prime http://factordb.com/index.php?id=1100000000490878060&open=prime http://factordb.com/index.php?id=1100000003590647776&open=prime http://factordb.com/index.php?id=1100000003590493750&open=prime http://factordb.com/index.php?id=1100000002616382906&open=prime http://factordb.com/index.php?id=1100000000765961441&open=prime http://factordb.com/index.php?id=1100000003590430825&open=prime http://factordb.com/index.php?id=1100000002632396910&open=prime http://factordb.com/index.php?id=1100000000765961452&open=prime	http://factordb.com/index.php?showid=1100000005489162806&base=13 http://factordb.com/index.php?showid=1100000003943359311&base=13 http://factordb.com/index.php?showid=1100000000490878060&base=13 http://factordb.com/index.php?showid=1100000003590647776&base=13 http://factordb.com/index.php?showid=1100000003590493750&base=13 http://factordb.com/index.php?showid=1100000002616382906&base=13 http://factordb.com/index.php?showid=1100000000765961441&base=13 http://factordb.com/index.php?showid=1100000003590430825&base=13 http://factordb.com/index.php?showid=1100000002632396910&base=13 http://factordb.com/index.php?showid=1100000000765961452&base=13	http://factordb.com/index.php?showid=1100000005489162806 http://factordb.com/index.php?showid=1100000003943359311 http://factordb.com/index.php?showid=1100000000490878060 http://factordb.com/index.php?showid=1100000003590647776 http://factordb.com/index.php?showid=1100000003590493750 http://factordb.com/index.php?showid=1100000002616382906 http://factordb.com/index.php?showid=1100000000765961441 http://factordb.com/index.php?showid=1100000003590430825 http://factordb.com/index.php?showid=1100000002632396910 http://factordb.com/index.php?showid=1100000000765961452	http://factordb.com/index.php?query=%284113%5E%28n%2B1%29%2B27%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2811313%5En-5%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=813%5E%28n%2B3%29%2B183&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2814913%5E%28n%2B1%29%2B79%29%2F12&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=13%5E%28n%2B2%29-50&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1113%5E%28n%2B3%29%2B2012&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=4813%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=26713%5E%28n%2B2%29%2B20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=9313%5E%28n%2B1%29%2B2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=120*13%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
14	650	4D₁₉₆₉₈ 34D₇₀₈ 8D₁₄₁85 8₈₆B 40₈₃49 8C₇₉3 18₇₉B 6B₇₇2B 4₆₃09 A₅₉3	19699 710 144 87 86 81 81 80 65 60	22578 814 165 100 99 93 92 92 74 69	5×14¹⁹⁶⁹⁸−1 47×14⁷⁰⁸−1 9×14¹⁴³−79 (8×14⁸⁷+31)/13 4×14⁸⁵+65 (116×14⁸⁰−129)/13 (21×14⁸⁰+31)/13 (89×14⁷⁹−1649)/13 (4×14⁶⁵−667)/13 (10×14⁶⁰−101)/13	http://factordb.com/index.php?id=1100000000884560233&open=prime http://factordb.com/index.php?id=1100000001540144903&open=prime http://factordb.com/index.php?id=1100000003575856650&open=ecm http://factordb.com/index.php?id=1100000002321014379&open=ecm http://factordb.com/index.php?id=1100000000823937973&open=ecm http://factordb.com/index.php?id=1100000002631073246&open=ecm http://factordb.com/index.php?id=1100000002384401372&open=ecm http://factordb.com/index.php?id=1100000002631077787&open=ecm http://factordb.com/index.php?id=1100000000840126683&open=ecm http://factordb.com/index.php?id=1100000002321038522&open=ecm	http://factordb.com/index.php?showid=1100000000884560233&base=14 http://factordb.com/index.php?showid=1100000001540144903&base=14 http://factordb.com/index.php?showid=1100000003575856650&base=14 http://factordb.com/index.php?showid=1100000002321014379&base=14 http://factordb.com/index.php?showid=1100000000823937973&base=14 http://factordb.com/index.php?showid=1100000002631073246&base=14 http://factordb.com/index.php?showid=1100000002384401372&base=14 http://factordb.com/index.php?showid=1100000002631077787&base=14 http://factordb.com/index.php?showid=1100000000840126683&base=14 http://factordb.com/index.php?showid=1100000002321038522&base=14	http://factordb.com/index.php?showid=1100000000884560233 http://factordb.com/index.php?showid=1100000001540144903 http://factordb.com/index.php?showid=1100000003575856650 http://factordb.com/index.php?showid=1100000002321014379 http://factordb.com/index.php?showid=1100000000823937973 http://factordb.com/index.php?showid=1100000002631073246 http://factordb.com/index.php?showid=1100000002384401372 http://factordb.com/index.php?showid=1100000002631077787 http://factordb.com/index.php?showid=1100000000840126683 http://factordb.com/index.php?showid=1100000002321038522	http://factordb.com/index.php?query=514%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=4714%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=914%5E%28n%2B2%29-79&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28814%5E%28n%2B1%29%2B31%29%2F13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=414%5E%28n%2B2%29%2B65&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2811614%5E%28n%2B1%29-129%29%2F13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%282114%5E%28n%2B1%29%2B31%29%2F13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%288914%5E%28n%2B2%29-1649%29%2F13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28414%5E%28n%2B2%29-667%29%2F13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281014%5E%28n%2B1%29-101%29%2F13&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
15	1284	7₁₅₅97 E₁₄₅397 96₁₀₄08 7₇₃CE 7₅₉CCE 50₃₃17 EB₃₁ 6330₂₆1 7050₂₄B B70₂₄1	157 148 107 75 62 36 32 30 28 27	185 175 126 88 73 42 38 35 33 32	(15¹⁵⁷+59)/2 15¹⁴⁸−2558 (66×15¹⁰⁶−619)/7 (15⁷⁵+163)/2 (15⁶²+2413)/2 5×15³⁵+22 (207×15³¹−11)/14 1398×15²⁷+1 1580×15²⁵+11 172×15²⁵+1	http://factordb.com/index.php?id=1100000002454891840&open=ecm http://factordb.com/index.php?id=1100000002454900849&open=ecm http://factordb.com/index.php?id=1100000000823937997&open=ecm http://factordb.com/index.php?id=1100000003588407143&open=ecm http://factordb.com/index.php?id=1100000003588407386&open=ecm http://factordb.com/index.php?id=1100000002632398579&open=ecm http://factordb.com/index.php?id=1100000002321033312&open=ecm http://factordb.com/index.php?id=1100000002391199877&open=ecm http://factordb.com/index.php?id=1100000003588407806&open=ecm http://factordb.com/index.php?id=1100000000851967288&open=ecm	http://factordb.com/index.php?showid=1100000002454891840&base=15 http://factordb.com/index.php?showid=1100000002454900849&base=15 http://factordb.com/index.php?showid=1100000000823937997&base=15 http://factordb.com/index.php?showid=1100000003588407143&base=15 http://factordb.com/index.php?showid=1100000003588407386&base=15 http://factordb.com/index.php?showid=1100000002632398579&base=15 http://factordb.com/index.php?showid=1100000002321033312&base=15 http://factordb.com/index.php?showid=1100000002391199877&base=15 http://factordb.com/index.php?showid=1100000003588407806&base=15 http://factordb.com/index.php?showid=1100000000851967288&base=15	http://factordb.com/index.php?showid=1100000002454891840 http://factordb.com/index.php?showid=1100000002454900849 http://factordb.com/index.php?showid=1100000000823937997 http://factordb.com/index.php?showid=1100000003588407143 http://factordb.com/index.php?showid=1100000003588407386 http://factordb.com/index.php?showid=1100000002632398579 http://factordb.com/index.php?showid=1100000002321033312 http://factordb.com/index.php?showid=1100000002391199877 http://factordb.com/index.php?showid=1100000003588407806 http://factordb.com/index.php?showid=1100000000851967288	http://factordb.com/index.php?query=%2815%5E%28n%2B2%29%2B59%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=15%5E%28n%2B3%29-2558&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%286615%5E%28n%2B2%29-619%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2815%5E%28n%2B2%29%2B163%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2815%5E%28n%2B3%29%2B2413%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=515%5E%28n%2B2%29%2B22&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2820715%5En-11%29%2F14&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=139815%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=158015%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=17215%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
16	2347	3₁₁₆₁₃₇AF 4₇₂₇₈₅DD DB₃₂₂₃₄ D0B₁₇₈₀₄ 5BC₃₇₀₀D 90₃₅₄₂91 300F₁₉₆₀AF 20₁₇₁₃321 F8₁₅₁₇F FAF₁₀₆₂45	116139 72787 32235 17806 3703 3545 1965 1717 1519 1066	139845 87644 38815 21441 4459 4269 2366 2067 1830 1284	(16¹¹⁶¹³⁹+619)/5 (4×16⁷²⁷⁸⁷+2291)/15 (206×16³²²³⁴−11)/15 (3131×16¹⁷⁸⁰⁴−11)/15 (459×16³⁷⁰¹+1)/5 9×16³⁵⁴⁴+145 769×16¹⁹⁶²−81 2×16¹⁷¹⁶+801 (233×16¹⁵¹⁸+97)/15 251×16¹⁰⁶⁴−187	http://factordb.com/index.php?id=1100000003851731988&open=prime http://factordb.com/index.php?id=1100000003615909841&open=prime http://factordb.com/index.php?id=1100000002383583629&open=prime http://factordb.com/index.php?id=1100000003589278511&open=prime http://factordb.com/index.php?id=1100000000993764322&open=prime http://factordb.com/index.php?id=1100000000633424191&open=prime http://factordb.com/index.php?id=1100000003588368750&open=prime http://factordb.com/index.php?id=1100000003588386735&open=prime http://factordb.com/index.php?id=1100000000633744824&open=prime http://factordb.com/index.php?id=1100000003588387610&open=prime	http://factordb.com/index.php?showid=1100000003851731988&base=16 http://factordb.com/index.php?showid=1100000003615909841&base=16 http://factordb.com/index.php?showid=1100000002383583629&base=16 http://factordb.com/index.php?showid=1100000003589278511&base=16 http://factordb.com/index.php?showid=1100000000993764322&base=16 http://factordb.com/index.php?showid=1100000000633424191&base=16 http://factordb.com/index.php?showid=1100000003588368750&base=16 http://factordb.com/index.php?showid=1100000003588386735&base=16 http://factordb.com/index.php?showid=1100000000633744824&base=16 http://factordb.com/index.php?showid=1100000003588387610&base=16	http://factordb.com/index.php?showid=1100000003851731988 http://factordb.com/index.php?showid=1100000003615909841 http://factordb.com/index.php?showid=1100000002383583629 http://factordb.com/index.php?showid=1100000003589278511 http://factordb.com/index.php?showid=1100000000993764322 http://factordb.com/index.php?showid=1100000000633424191 http://factordb.com/index.php?showid=1100000003588368750 http://factordb.com/index.php?showid=1100000003588386735 http://factordb.com/index.php?showid=1100000000633744824 http://factordb.com/index.php?showid=1100000003588387610	http://factordb.com/index.php?query=%2816%5E%28n%2B2%29%2B619%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28416%5E%28n%2B2%29%2B2291%29%2F15&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2820616%5En-11%29%2F15&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28313116%5En-11%29%2F15&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2845916%5E%28n%2B1%29%2B1%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=916%5E%28n%2B2%29%2B145&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=76916%5E%28n%2B2%29-81&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=216%5E%28n%2B3%29%2B801&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2823316%5E%28n%2B1%29%2B97%29%2F15&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=251*16%5E%28n%2B2%29-187&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
17	10409~10427	B₆₇₁₀₃2E 570₅₁₃₁₀1 E9B₄₄₇₃₂ D0GD₃₇₀₉₆ G7₃₂₀₇₂F 150₂₄₃₂₅D 347₁₆₀₇₄ B30₁₃₀₇₇D 9D0₁₀₃₉₈5 10₉₀₁₉1F	67105 51313 44734 37099 32074 24328 16076 13080 10401 9022	82570 63138 55043 45649 39466 29934 19780 16095 12798 11100	(11×17⁶⁷¹⁰⁵−2411)/16 92×17⁵¹³¹¹+1 (3963×17⁴⁴⁷³²−11)/16 (60381×17³⁷⁰⁹⁶−13)/16 (263×17³²⁰⁷³+121)/16 22×17²⁴³²⁶+13 (887×17¹⁶⁰⁷⁴−7)/16 190×17¹³⁰⁷⁸+13 166×17¹⁰³⁹⁹+5 17⁹⁰²¹+32	http://factordb.com/index.php?id=1100000003993647842&open=prime http://factordb.com/index.php?id=1100000000765961389&open=prime http://factordb.com/index.php?id=1100000003883765450&open=prime http://factordb.com/index.php?id=1100000003848346668&open=prime http://factordb.com/index.php?id=1100000003838755382&open=prime http://factordb.com/index.php?id=1100000003815568647&open=prime http://factordb.com/index.php?id=1100000003802992457&open=prime http://factordb.com/index.php?id=1100000003782940761&open=prime http://factordb.com/index.php?id=1100000003782940760&open=prime http://factordb.com/index.php?id=1100000001100010542&open=prime	http://factordb.com/index.php?showid=1100000003993647842&base=17 http://factordb.com/index.php?showid=1100000000765961389&base=17 http://factordb.com/index.php?showid=1100000003883765450&base=17 http://factordb.com/index.php?showid=1100000003848346668&base=17 http://factordb.com/index.php?showid=1100000003838755382&base=17 http://factordb.com/index.php?showid=1100000003815568647&base=17 http://factordb.com/index.php?showid=1100000003802992457&base=17 http://factordb.com/index.php?showid=1100000003782940761&base=17 http://factordb.com/index.php?showid=1100000003782940760&base=17 http://factordb.com/index.php?showid=1100000001100010542&base=17	http://factordb.com/index.php?showid=1100000003993647842 http://factordb.com/index.php?showid=1100000000765961389 http://factordb.com/index.php?showid=1100000003883765450 http://factordb.com/index.php?showid=1100000003848346668 http://factordb.com/index.php?showid=1100000003838755382 http://factordb.com/index.php?showid=1100000003815568647 http://factordb.com/index.php?showid=1100000003802992457 http://factordb.com/index.php?showid=1100000003782940761 http://factordb.com/index.php?showid=1100000003782940760 http://factordb.com/index.php?showid=1100000001100010542	http://factordb.com/index.php?query=%281117%5E%28n%2B2%29-2411%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=9217%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28396317%5En-11%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%286038117%5En-13%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2826317%5E%28n%2B1%29%2B121%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=2217%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2888717%5En-7%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=19017%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=166*17%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=17%5E%28n%2B2%29%2B32&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	18	100000
18	549	C0₆₂₆₈C5 H₇₆₆FH 80₂₉₈B C0₁₁₆F5 HD₉₃ GG0₃₀1 CF₃₀5 B₁₉6B CCF₁₄5 7₁₄G7	6271 768 300 119 94 33 32 21 17 16	7872 965 377 150 118 42 41 27 22 20	12×18⁶²⁷⁰+221 18⁷⁶⁸−37 8×18²⁹⁹+11 12×18¹¹⁸+275 (302×18⁹³−13)/17 304×18³¹+1 (219×18³¹−185)/17 (11×18²¹−1541)/17 (3891×18¹⁵−185)/17 (7×18¹⁶+2747)/17	http://factordb.com/index.php?id=1100000003590442437&open=prime http://factordb.com/index.php?id=1100000003590430490&open=prime http://factordb.com/index.php?id=1100000002355574745&open=prime http://factordb.com/index.php?id=1100000002632837015&open=ecm http://factordb.com/index.php?id=1100000002321052894&open=ecm http://factordb.com/index.php?id=1100000000819230161&open=ecm http://factordb.com/index.php?id=1100000002631240657&open=ecm http://factordb.com/index.php?id=1100000003590430474&open=ecm http://factordb.com/index.php?id=1100000003590430470&open=ecm http://factordb.com/index.php?id=1100000003590430465&open=ecm	http://factordb.com/index.php?showid=1100000003590442437&base=18 http://factordb.com/index.php?showid=1100000003590430490&base=18 http://factordb.com/index.php?showid=1100000002355574745&base=18 http://factordb.com/index.php?showid=1100000002632837015&base=18 http://factordb.com/index.php?showid=1100000002321052894&base=18 http://factordb.com/index.php?showid=1100000000819230161&base=18 http://factordb.com/index.php?showid=1100000002631240657&base=18 http://factordb.com/index.php?showid=1100000003590430474&base=18 http://factordb.com/index.php?showid=1100000003590430470&base=18 http://factordb.com/index.php?showid=1100000003590430465&base=18	http://factordb.com/index.php?showid=1100000003590442437 http://factordb.com/index.php?showid=1100000003590430490 http://factordb.com/index.php?showid=1100000002355574745 http://factordb.com/index.php?showid=1100000002632837015 http://factordb.com/index.php?showid=1100000002321052894 http://factordb.com/index.php?showid=1100000000819230161 http://factordb.com/index.php?showid=1100000002631240657 http://factordb.com/index.php?showid=1100000003590430474 http://factordb.com/index.php?showid=1100000003590430470 http://factordb.com/index.php?showid=1100000003590430465	http://factordb.com/index.php?query=1218%5E%28n%2B2%29%2B221&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=18%5E%28n%2B2%29-37&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=818%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1218%5E%28n%2B2%29%2B275&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2830218%5En-13%29%2F17&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=30418%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2821918%5E%28n%2B1%29-185%29%2F17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281118%5E%28n%2B2%29-1541%29%2F17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28389118%5E%28n%2B1%29-185%29%2F17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%287*18%5E%28n%2B2%29%2B2747%29%2F17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
19	31412~31435	H₈₆₂₉₁6 D90₇₃₀₄₆9 4F0₄₉₈₄₇6 2₄₈₂₂₄7 2₄₅₈₈₆7A 90₄₂₉₉₄G DB₃₆₂₇₂ 3335₃₁₀₈₈ B₂₆₅₈₈FG 10₂₂₇₉₀7717	86292 73049 49850 48225 45888 42996 36273 31091 26590 22795	110347 93412 63746 61667 58679 54981 46385 39757 34002 29148	(17×19⁸⁶²⁹²−215)/18 256×19⁷³⁰⁴⁷+9 91×19⁴⁹⁸⁴⁸+6 (19⁴⁸²²⁵+44)/9 (19⁴⁵⁸⁸⁸+926)/9 9×19⁴²⁹⁹⁵+16 (245×19³⁶²⁷²−11)/18 (20579×19³¹⁰⁸⁸−5)/18 (11×19²⁶⁵⁹⁰+1447)/18 19²²⁷⁹⁴+50566	http://factordb.com/index.php?id=1100000004163040839&open=prime http://factordb.com/index.php?id=1100000003998413751&open=prime http://factordb.com/index.php?id=1100000000808118332&open=prime http://factordb.com/index.php?id=1100000003949188041&open=prime http://factordb.com/index.php?id=1100000003949189035&open=prime http://factordb.com/index.php?id=1100000000808118328&open=prime http://factordb.com/index.php?id=1100000003968090004&open=prime http://factordb.com/index.php?id=1100000003949189435&open=prime http://factordb.com/index.php?id=1100000003968087931&open=prime http://factordb.com/index.php?id=1100000003949187975&open=prime	http://factordb.com/index.php?showid=1100000004163040839&base=19 http://factordb.com/index.php?showid=1100000003998413751&base=19 http://factordb.com/index.php?showid=1100000000808118332&base=19 http://factordb.com/index.php?showid=1100000003949188041&base=19 http://factordb.com/index.php?showid=1100000003949189035&base=19 http://factordb.com/index.php?showid=1100000000808118328&base=19 http://factordb.com/index.php?showid=1100000003968090004&base=19 http://factordb.com/index.php?showid=1100000003949189435&base=19 http://factordb.com/index.php?showid=1100000003968087931&base=19 http://factordb.com/index.php?showid=1100000003949187975&base=19	http://factordb.com/index.php?showid=1100000004163040839 http://factordb.com/index.php?showid=1100000003998413751 http://factordb.com/index.php?showid=1100000000808118332 http://factordb.com/index.php?showid=1100000003949188041 http://factordb.com/index.php?showid=1100000003949189035 http://factordb.com/index.php?showid=1100000000808118328 http://factordb.com/index.php?showid=1100000003968090004 http://factordb.com/index.php?showid=1100000003949189435 http://factordb.com/index.php?showid=1100000003968087931 http://factordb.com/index.php?showid=1100000003949187975	http://factordb.com/index.php?query=%281719%5E%28n%2B1%29-215%29%2F18&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=25619%5E%28n%2B1%29%2B9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=9119%5E%28n%2B1%29%2B6&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2819%5E%28n%2B1%29%2B44%29%2F9&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2819%5E%28n%2B2%29%2B926%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=919%5E%28n%2B1%29%2B16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2824519%5En-11%29%2F18&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%282057919%5En-5%29%2F18&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2811*19%5E%28n%2B2%29%2B1447%29%2F18&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=19%5E%28n%2B4%29%2B50566&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	23	100000
20	3314	G0₆₂₆₉D CD₂₄₄₉ 50₁₁₆₃AJ J₆₅₅05J JCJ₆₂₉ E₅₆₆C7 3A₅₂₇3 G₄₄₇99 EC0₄₂₉7 40₃₈₇404B	6271 2450 1166 658 631 568 529 449 432 392	8159 3188 1517 857 821 739 688 585 562 510	16×20⁶²⁷⁰+13 (241×20²⁴⁴⁹−13)/19 5×20¹¹⁶⁵+219 20⁶⁵⁸−7881 393×20⁶²⁹−1 (14×20⁵⁶⁸−907)/19 (67×20⁵²⁸−143)/19 (16×20⁴⁴⁹−2809)/19 292×20⁴³⁰+7 4×20³⁹¹+32091	http://factordb.com/index.php?id=1100000003590539457&open=prime http://factordb.com/index.php?id=1100000002325393915&open=prime http://factordb.com/index.php?id=1100000003590502412&open=prime http://factordb.com/index.php?id=1100000003590502490&open=prime http://factordb.com/index.php?id=1100000001559454258&open=prime http://factordb.com/index.php?id=1100000003590502516&open=prime http://factordb.com/index.php?id=1100000003590502531&open=prime http://factordb.com/index.php?id=1100000000840126753&open=prime http://factordb.com/index.php?id=1100000002633348702&open=prime http://factordb.com/index.php?id=1100000003590502563&open=prime	http://factordb.com/index.php?showid=1100000003590539457&base=20 http://factordb.com/index.php?showid=1100000002325393915&base=20 http://factordb.com/index.php?showid=1100000003590502412&base=20 http://factordb.com/index.php?showid=1100000003590502490&base=20 http://factordb.com/index.php?showid=1100000001559454258&base=20 http://factordb.com/index.php?showid=1100000003590502516&base=20 http://factordb.com/index.php?showid=1100000003590502531&base=20 http://factordb.com/index.php?showid=1100000000840126753&base=20 http://factordb.com/index.php?showid=1100000002633348702&base=20 http://factordb.com/index.php?showid=1100000003590502563&base=20	http://factordb.com/index.php?showid=1100000003590539457 http://factordb.com/index.php?showid=1100000002325393915 http://factordb.com/index.php?showid=1100000003590502412 http://factordb.com/index.php?showid=1100000003590502490 http://factordb.com/index.php?showid=1100000001559454258 http://factordb.com/index.php?showid=1100000003590502516 http://factordb.com/index.php?showid=1100000003590502531 http://factordb.com/index.php?showid=1100000000840126753 http://factordb.com/index.php?showid=1100000002633348702 http://factordb.com/index.php?showid=1100000003590502563	http://factordb.com/index.php?query=1620%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2824120%5En-13%29%2F19&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=520%5E%28n%2B2%29%2B219&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=20%5E%28n%2B3%29-7881&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=39320%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281420%5E%28n%2B2%29-907%29%2F19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%286720%5E%28n%2B1%29-143%29%2F19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281620%5E%28n%2B2%29-2809%29%2F19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=29220%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=4*20%5E%28n%2B4%29%2B32091&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
21	13382~13394	40₄₇₃₃₃9G B90₄₅₀₁₉E5 HD₃₇₄₁₄ BD₃₅₀₂₇B 990₃₃₂₃₉99H 5₃₀₆₀₆FEK 43₂₉₂₃₆B J₂₃₃₀₄6J 9₂₁₁₂₆0D 5D0₁₉₈₄₈1	47336 45023 37415 35029 33244 30609 29238 23306 21128 19851	62588 59531 49471 46316 43956 40472 38659 30816 27936 26247	4×21⁴⁷³³⁵+205 240×21⁴⁵⁰²¹+299 (353×21³⁷⁴¹⁴−13)/20 (233×21³⁵⁰²⁸−53)/20 198×21³³²⁴²+4175 (21³⁰⁶⁰⁹+18455)/4 (83×21²⁹²³⁷+157)/20 (19×21²³³⁰⁶−5479)/20 (9×21²¹¹²⁸−3709)/20 118×21¹⁹⁸⁴⁹+1	http://factordb.com/index.php?id=1100000000808118331&open=prime http://factordb.com/index.php?id=1100000003996110311&open=prime http://factordb.com/index.php?id=1100000003996110479&open=prime http://factordb.com/index.php?id=1100000003996110718&open=prime http://factordb.com/index.php?id=1100000003996110944&open=prime http://factordb.com/index.php?id=1100000003996111130&open=prime http://factordb.com/index.php?id=1100000003996112263&open=prime http://factordb.com/index.php?id=1100000003996112521&open=prime http://factordb.com/index.php?id=1100000003996112710&open=prime http://factordb.com/index.php?id=1100000000777265872&open=prime	http://factordb.com/index.php?showid=1100000000808118331&base=21 http://factordb.com/index.php?showid=1100000003996110311&base=21 http://factordb.com/index.php?showid=1100000003996110479&base=21 http://factordb.com/index.php?showid=1100000003996110718&base=21 http://factordb.com/index.php?showid=1100000003996110944&base=21 http://factordb.com/index.php?showid=1100000003996111130&base=21 http://factordb.com/index.php?showid=1100000003996112263&base=21 http://factordb.com/index.php?showid=1100000003996112521&base=21 http://factordb.com/index.php?showid=1100000003996112710&base=21 http://factordb.com/index.php?showid=1100000000777265872&base=21	http://factordb.com/index.php?showid=1100000000808118331 http://factordb.com/index.php?showid=1100000003996110311 http://factordb.com/index.php?showid=1100000003996110479 http://factordb.com/index.php?showid=1100000003996110718 http://factordb.com/index.php?showid=1100000003996110944 http://factordb.com/index.php?showid=1100000003996111130 http://factordb.com/index.php?showid=1100000003996112263 http://factordb.com/index.php?showid=1100000003996112521 http://factordb.com/index.php?showid=1100000003996112710 http://factordb.com/index.php?showid=1100000000777265872	http://factordb.com/index.php?query=421%5E%28n%2B2%29%2B205&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=24021%5E%28n%2B2%29%2B299&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2835321%5En-13%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2823321%5E%28n%2B1%29-53%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=19821%5E%28n%2B3%29%2B4175&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2821%5E%28n%2B3%29%2B18455%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%288321%5E%28n%2B1%29%2B157%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281921%5E%28n%2B2%29-5479%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28921%5E%28n%2B2%29-3709%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=118*21%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	12	100000
22	8003	BK₂₂₀₀₁5 7₃₈₁₅2L L₂₃₈₅KE7 7₉₅₉K7 J0₇₆₇IGGJ K0₇₆₀EC1 I₆₂₆AF E60₄₉₆L L₄₈₃G3 L0₄₅₄B63	22003 3817 2388 961 772 764 628 499 485 458	29538 5124 3206 1290 1037 1026 843 670 652 615	(251×22²²⁰⁰²−335)/21 (22³⁸¹⁷−289)/3 22²³⁸⁸−653 (22⁹⁶¹+857)/3 19×22⁷⁷¹+199779 20×22⁷⁶³+7041 (6×22⁶²⁸−1259)/7 314×22⁴⁹⁷+21 22⁴⁸⁵−129 21×22⁴⁵⁷+5459	http://factordb.com/index.php?id=1100000003594696838&open=prime http://factordb.com/index.php?id=1100000003591359839&open=prime http://factordb.com/index.php?id=1100000003591360774&open=prime http://factordb.com/index.php?id=1100000003591361817&open=prime http://factordb.com/index.php?id=1100000003591362567&open=prime http://factordb.com/index.php?id=1100000000632724415&open=prime http://factordb.com/index.php?id=1100000000632724334&open=prime http://factordb.com/index.php?id=1100000000632703239&open=prime http://factordb.com/index.php?id=1100000003591364730&open=prime http://factordb.com/index.php?id=1100000003591365331&open=prime	http://factordb.com/index.php?showid=1100000003594696838&base=22 http://factordb.com/index.php?showid=1100000003591359839&base=22 http://factordb.com/index.php?showid=1100000003591360774&base=22 http://factordb.com/index.php?showid=1100000003591361817&base=22 http://factordb.com/index.php?showid=1100000003591362567&base=22 http://factordb.com/index.php?showid=1100000000632724415&base=22 http://factordb.com/index.php?showid=1100000000632724334&base=22 http://factordb.com/index.php?showid=1100000000632703239&base=22 http://factordb.com/index.php?showid=1100000003591364730&base=22 http://factordb.com/index.php?showid=1100000003591365331&base=22	http://factordb.com/index.php?showid=1100000003594696838 http://factordb.com/index.php?showid=1100000003591359839 http://factordb.com/index.php?showid=1100000003591360774 http://factordb.com/index.php?showid=1100000003591361817 http://factordb.com/index.php?showid=1100000003591362567 http://factordb.com/index.php?showid=1100000000632724415 http://factordb.com/index.php?showid=1100000000632724334 http://factordb.com/index.php?showid=1100000000632703239 http://factordb.com/index.php?showid=1100000003591364730 http://factordb.com/index.php?showid=1100000003591365331	http://factordb.com/index.php?query=%2825122%5E%28n%2B1%29-335%29%2F21&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2822%5E%28n%2B2%29-289%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=22%5E%28n%2B3%29-653&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2822%5E%28n%2B2%29%2B857%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1922%5E%28n%2B4%29%2B199779&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=2022%5E%28n%2B3%29%2B7041&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28622%5E%28n%2B2%29-1259%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=31422%5E%28n%2B1%29%2B21&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=22%5E%28n%2B2%29-129&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=2122%5E%28n%2B3%29%2B5459&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
23	65178~65265	B0₉₃₀₄₆FB L₈₆₄₄₄D AJ₈₁₀₆₅4 20₇₃₅₆₀98 J₆₈₂₁₇G4 D70₆₆₇₇₀B 5F₆₂₃₄₀6 A7M7₆₁₅₃₂ B30₆₁₁₃₆5 EJ₅₂₁₆₉	93049 86445 81067 73563 68219 66773 62342 61535 61139 52170	126708 117715 110391 100172 92896 90927 84893 83794 83255 71042	11×23⁹³⁰⁴⁸+356 (21×23⁸⁶⁴⁴⁵−197)/22 (239×23⁸¹⁰⁶⁶−349)/22 2×23⁷³⁵⁶²+215 (19×23⁶⁸²¹⁹−1867)/22 306×23⁶⁶⁷⁷¹+11 (125×23⁶²³⁴¹−213)/22 (120413×23⁶¹⁵³²−7)/22 256×23⁶¹¹³⁷+5 (327×23⁵²¹⁶⁹−19)/22	http://factordb.com/index.php?id=1100000004691540361&open=prime http://factordb.com/index.php?id=1100000004691546739&open=prime http://factordb.com/index.php?id=1100000004691548070&open=prime http://factordb.com/index.php?id=1100000004691548569&open=prime http://factordb.com/index.php?id=1100000004691549462&open=prime http://factordb.com/index.php?id=1100000004691549803&open=prime http://factordb.com/index.php?id=1100000004691551005&open=prime http://factordb.com/index.php?id=1100000004691556967&open=prime http://factordb.com/index.php?id=1100000004691557254&open=prime http://factordb.com/index.php?id=1100000004691557548&open=prime	http://factordb.com/index.php?showid=1100000004691540361&base=23 http://factordb.com/index.php?showid=1100000004691546739&base=23 http://factordb.com/index.php?showid=1100000004691548070&base=23 http://factordb.com/index.php?showid=1100000004691548569&base=23 http://factordb.com/index.php?showid=1100000004691549462&base=23 http://factordb.com/index.php?showid=1100000004691549803&base=23 http://factordb.com/index.php?showid=1100000004691551005&base=23 http://factordb.com/index.php?showid=1100000004691556967&base=23 http://factordb.com/index.php?showid=1100000004691557254&base=23 http://factordb.com/index.php?showid=1100000004691557548&base=23	http://factordb.com/index.php?showid=1100000004691540361 http://factordb.com/index.php?showid=1100000004691546739 http://factordb.com/index.php?showid=1100000004691548070 http://factordb.com/index.php?showid=1100000004691548569 http://factordb.com/index.php?showid=1100000004691549462 http://factordb.com/index.php?showid=1100000004691549803 http://factordb.com/index.php?showid=1100000004691551005 http://factordb.com/index.php?showid=1100000004691556967 http://factordb.com/index.php?showid=1100000004691557254 http://factordb.com/index.php?showid=1100000004691557548	http://factordb.com/index.php?query=1123%5E%28n%2B2%29%2B356&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%282123%5E%28n%2B1%29-197%29%2F22&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2823923%5E%28n%2B1%29-349%29%2F22&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=223%5E%28n%2B2%29%2B215&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281923%5E%28n%2B2%29-1867%29%2F22&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=30623%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2812523%5E%28n%2B1%29-213%29%2F22&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2812041323%5En-7%29%2F22&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=25623%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2832723%5En-19%29%2F22&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	87	100000
24	3409	N00N₈₁₂₉LN 88N₅₉₅₁ A0₂₉₅₁8ID D₂₆₉₈LD N₂₆₄₄LLN BC0₃₃₁B 20₃₁₃7 C7₂₉₈ D0₂₅₉KKD I0₂₄₁I5	8134 5953 2955 2700 2647 334 315 299 263 244	11227 8216 4079 3727 3654 461 434 413 363 337	13249×24⁸¹³¹−49 201×24⁵⁹⁵¹−1 10×24²⁹⁵⁴+5053 (13×24²⁷⁰⁰+4403)/23 24²⁶⁴⁷−1201 276×24³³²+11 2×24³¹⁴+7 (283×24²⁹⁸−7)/23 13×24²⁶²+12013 18×24²⁴³+437	http://factordb.com/index.php?id=1100000003593391606&open=prime http://factordb.com/index.php?id=1100000003593275880&open=prime http://factordb.com/index.php?id=1100000003593269654&open=prime http://factordb.com/index.php?id=1100000003593269876&open=prime http://factordb.com/index.php?id=1100000003593270089&open=prime http://factordb.com/index.php?id=1100000002633359842&open=prime http://factordb.com/index.php?id=1100000002355610241&open=prime http://factordb.com/index.php?id=1100000002326181235&open=prime http://factordb.com/index.php?id=1100000003593270725&open=prime http://factordb.com/index.php?id=1100000002633360037&open=prime	http://factordb.com/index.php?showid=1100000003593391606&base=24 http://factordb.com/index.php?showid=1100000003593275880&base=24 http://factordb.com/index.php?showid=1100000003593269654&base=24 http://factordb.com/index.php?showid=1100000003593269876&base=24 http://factordb.com/index.php?showid=1100000003593270089&base=24 http://factordb.com/index.php?showid=1100000002633359842&base=24 http://factordb.com/index.php?showid=1100000002355610241&base=24 http://factordb.com/index.php?showid=1100000002326181235&base=24 http://factordb.com/index.php?showid=1100000003593270725&base=24 http://factordb.com/index.php?showid=1100000002633360037&base=24	http://factordb.com/index.php?showid=1100000003593391606 http://factordb.com/index.php?showid=1100000003593275880 http://factordb.com/index.php?showid=1100000003593269654 http://factordb.com/index.php?showid=1100000003593269876 http://factordb.com/index.php?showid=1100000003593270089 http://factordb.com/index.php?showid=1100000002633359842 http://factordb.com/index.php?showid=1100000002355610241 http://factordb.com/index.php?showid=1100000002326181235 http://factordb.com/index.php?showid=1100000003593270725 http://factordb.com/index.php?showid=1100000002633360037	http://factordb.com/index.php?query=1324924%5E%28n%2B2%29-49&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=20124%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1024%5E%28n%2B3%29%2B5053&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281324%5E%28n%2B2%29%2B4403%29%2F23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=24%5E%28n%2B3%29-1201&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=27624%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=224%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2828324%5En-7%29%2F23&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1324%5E%28n%2B3%29%2B12013&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=18*24%5E%28n%2B2%29%2B437&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
25	133639~133724	E₉₈₃₉₆FOO 1J710₉₆₂₇₂1 NB0₈₅₅₉₈5NH D70₈₁₅₈₁JJ7 F0₈₀₀₅₄HL J010₇₅₉₄₃E7 K₆₇₇₇₁5I LO₆₆₃₇₇KC KJD0₆₃₃₉₉1 70₆₀₈₉₂D711	98399 96277 85603 81586 80057 75948 67773 66380 63403 60897	137556 134589 119668 114053 111915 106171 94743 92796 88634 85130	(7×25⁹⁸³⁹⁹+10613)/12 27676×25⁹⁶²⁷³+1 586×25⁸⁵⁶⁰¹+3717 332×25⁸¹⁵⁸⁴+12357 15×25⁸⁰⁰⁵⁶+446 11876×25⁷⁵⁹⁴⁵+357 (5×25⁶⁷⁷⁷³−2267)/6 22×25⁶⁶³⁷⁹−113 12988×25⁶³⁴⁰⁰+1 7×25⁶⁰⁸⁹⁶+207526	http://factordb.com/index.php?id=1100000000808118215&open=prime http://factordb.com/index.php?id=1100000003983674902&open=prime http://factordb.com/index.php?id=1100000004909706420&open=prime http://factordb.com/index.php?id=1100000004909733266&open=prime http://factordb.com/index.php?id=1100000004909750102&open=prime http://factordb.com/index.php?id=1100000004909770736&open=prime http://factordb.com/index.php?id=1100000004586986394&open=prime http://factordb.com/index.php?id=1100000000808118270&open=prime http://factordb.com/index.php?id=1100000004586986664&open=prime http://factordb.com/index.php?id=1100000004586986798&open=prime	http://factordb.com/index.php?showid=1100000000808118215&base=25 http://factordb.com/index.php?showid=1100000003983674902&base=25 http://factordb.com/index.php?showid=1100000004909706420&base=25 http://factordb.com/index.php?showid=1100000004909733266&base=25 http://factordb.com/index.php?showid=1100000004909750102&base=25 http://factordb.com/index.php?showid=1100000004909770736&base=25 http://factordb.com/index.php?showid=1100000004586986394&base=25 http://factordb.com/index.php?showid=1100000000808118270&base=25 http://factordb.com/index.php?showid=1100000004586986664&base=25 http://factordb.com/index.php?showid=1100000004586986798&base=25	http://factordb.com/index.php?showid=1100000000808118215 http://factordb.com/index.php?showid=1100000003983674902 http://factordb.com/index.php?showid=1100000004909706420 http://factordb.com/index.php?showid=1100000004909733266 http://factordb.com/index.php?showid=1100000004909750102 http://factordb.com/index.php?showid=1100000004909770736 http://factordb.com/index.php?showid=1100000004586986394 http://factordb.com/index.php?showid=1100000000808118270 http://factordb.com/index.php?showid=1100000004586986664 http://factordb.com/index.php?showid=1100000004586986798	http://factordb.com/index.php?query=%28725%5E%28n%2B3%29%2B10613%29%2F12&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=2767625%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=58625%5E%28n%2B3%29%2B3717&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=33225%5E%28n%2B3%29%2B12357&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1525%5E%28n%2B2%29%2B446&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1187625%5E%28n%2B2%29%2B357&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28525%5E%28n%2B2%29-2267%29%2F6&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=2225%5E%28n%2B2%29-113&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1298825%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=725%5E%28n%2B4%29%2B207526&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	85	100000
26	25255~25259	M0₆₁₁₈₆2BB J0₄₄₃₀₃KCB 6K₂₃₃₀₀5 LD0₂₀₉₇₅7 7₂₀₂₇₉OL 5₁₉₃₉₁6F 9GDK₁₅₉₂₀P M₈₇₇₂P K0₄₃₆₄I5 J₄₂₂₂P	61190 44307 23302 20978 20281 19393 15924 8773 4367 4223	86583 62694 32972 29684 28697 27440 22532 12414 6180 5976	22×26⁶¹¹⁸⁹+1649 19×26⁴⁴³⁰⁶+13843 (34×26²³³⁰¹−79)/5 559×26²⁰⁹⁷⁶+7 (7×26²⁰²⁸¹+11393)/25 (26¹⁹³⁹³+179)/5 (32569×26¹⁵⁹²¹+21)/5 (22×26⁸⁷⁷³+53)/25 20×26⁴³⁶⁶+473 (19×26⁴²²³+131)/25	http://factordb.com/index.php?id=1100000003968169875&open=prime http://factordb.com/index.php?id=1100000003968156595&open=prime http://factordb.com/index.php?id=1100000003892628745&open=prime http://factordb.com/index.php?id=1100000003892628658&open=prime http://factordb.com/index.php?id=1100000003892628605&open=prime http://factordb.com/index.php?id=1100000003850151202&open=prime http://factordb.com/index.php?id=1100000003850155316&open=prime http://factordb.com/index.php?id=1100000000758011195&open=prime http://factordb.com/index.php?id=1100000002634136508&open=prime http://factordb.com/index.php?id=1100000002328056865&open=prime	http://factordb.com/index.php?showid=1100000003968169875&base=26 http://factordb.com/index.php?showid=1100000003968156595&base=26 http://factordb.com/index.php?showid=1100000003892628745&base=26 http://factordb.com/index.php?showid=1100000003892628658&base=26 http://factordb.com/index.php?showid=1100000003892628605&base=26 http://factordb.com/index.php?showid=1100000003850151202&base=26 http://factordb.com/index.php?showid=1100000003850155316&base=26 http://factordb.com/index.php?showid=1100000000758011195&base=26 http://factordb.com/index.php?showid=1100000002634136508&base=26 http://factordb.com/index.php?showid=1100000002328056865&base=26	http://factordb.com/index.php?showid=1100000003968169875 http://factordb.com/index.php?showid=1100000003968156595 http://factordb.com/index.php?showid=1100000003892628745 http://factordb.com/index.php?showid=1100000003892628658 http://factordb.com/index.php?showid=1100000003892628605 http://factordb.com/index.php?showid=1100000003850151202 http://factordb.com/index.php?showid=1100000003850155316 http://factordb.com/index.php?showid=1100000000758011195 http://factordb.com/index.php?showid=1100000002634136508 http://factordb.com/index.php?showid=1100000002328056865	http://factordb.com/index.php?query=2226%5E%28n%2B3%29%2B1649&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1926%5E%28n%2B3%29%2B13843&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%283426%5E%28n%2B1%29-79%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=55926%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28726%5E%28n%2B2%29%2B11393%29%2F25&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2826%5E%28n%2B2%29%2B179%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%283256926%5E%28n%2B1%29%2B21%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%282226%5E%28n%2B1%29%2B53%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=2026%5E%28n%2B2%29%2B473&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2819*26%5E%28n%2B1%29%2B131%29%2F25&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	4	100000
27	102852~102896	CA0F₈₈₈₈₃A GNN0₇₈₇₉₅N O44L₆₆₀₁₆7 NJ0₆₄₃₆₉H ME₄₉₆₄₀9G PH0₄₇₈₉₀1 QF₄₇₁₆₅AF5 J0₄₀₇₉₁PD 510₃₉₁₆₄I07 NGN0₃₆₃₂₉N	88887 78799 66020 64372 49643 47893 47169 40794 39169 36333	127230 112790 94499 92140 71058 68553 67516 58391 56065 52006	(234483×27⁸⁸⁸⁸⁴−145)/26 12308×27⁷⁸⁷⁹⁶+23 (457829×27⁶⁶⁰¹⁷−385)/26 640×27⁶⁴³⁷⁰+17 (293×27⁴⁹⁶⁴²−1736)/13 692×27⁴⁷⁸⁹¹+1 (691×27⁴⁷¹⁶⁸−95045)/26 19×27⁴⁰⁷⁹³+688 136×27³⁹¹⁶⁷+13129 17222×27³⁶³³⁰+23	http://factordb.com/index.php?id=1100000000808118233&open=prime http://factordb.com/index.php?id=1100000004681348398&open=prime http://factordb.com/index.php?id=1100000004374140861&open=prime http://factordb.com/index.php?id=1100000004374138999&open=prime http://factordb.com/index.php?id=1100000000819229859&open=prime http://factordb.com/index.php?id=1100000004102754118&open=prime http://factordb.com/index.php?id=1100000004102755880&open=prime http://factordb.com/index.php?id=1100000004102758254&open=prime http://factordb.com/index.php?id=1100000004102875088&open=prime http://factordb.com/index.php?id=1100000004103372866&open=prime	http://factordb.com/index.php?showid=1100000000808118233&base=27 http://factordb.com/index.php?showid=1100000004681348398&base=27 http://factordb.com/index.php?showid=1100000004374140861&base=27 http://factordb.com/index.php?showid=1100000004374138999&base=27 http://factordb.com/index.php?showid=1100000000819229859&base=27 http://factordb.com/index.php?showid=1100000004102754118&base=27 http://factordb.com/index.php?showid=1100000004102755880&base=27 http://factordb.com/index.php?showid=1100000004102758254&base=27 http://factordb.com/index.php?showid=1100000004102875088&base=27 http://factordb.com/index.php?showid=1100000004103372866&base=27	http://factordb.com/index.php?showid=1100000000808118233 http://factordb.com/index.php?showid=1100000004681348398 http://factordb.com/index.php?showid=1100000004374140861 http://factordb.com/index.php?showid=1100000004374138999 http://factordb.com/index.php?showid=1100000000819229859 http://factordb.com/index.php?showid=1100000004102754118 http://factordb.com/index.php?showid=1100000004102755880 http://factordb.com/index.php?showid=1100000004102758254 http://factordb.com/index.php?showid=1100000004102875088 http://factordb.com/index.php?showid=1100000004103372866	http://factordb.com/index.php?query=%2823448327%5E%28n%2B1%29-145%29%2F26&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1230827%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2845782927%5E%28n%2B1%29-385%29%2F26&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=64027%5E%28n%2B1%29%2B17&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2829327%5E%28n%2B2%29-1736%29%2F13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=69227%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2869127%5E%28n%2B3%29-95045%29%2F26&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1927%5E%28n%2B2%29%2B688&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=13627%5E%28n%2B3%29%2B13129&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1722227%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	44	100000
28	25528~25529	O4O₉₄₅₃₅9 5OA₃₁₂₃₈F N6₂₄₀₅₁LR D0₅₂₆₇77D QO₄₂₃₉69 5₃₇₄₆8P G0₁₈₉₉AN A₁₄₂₃6F 5I₁₃₇₀F 5₁₃₃₂P8P	94538 31241 24054 5271 4242 3748 1902 1425 1372 1335	136812 45210 34810 7628 6139 5424 2753 2062 1985 1932	(6092×28⁹⁴⁵³⁶−143)/9 (4438×28³¹²³⁹+125)/27 (209×28²⁴⁰⁵³+3967)/9 13×28⁵²⁷⁰+5697 (242×28⁴²⁴¹−4679)/9 (5×28³⁷⁴⁸+2803)/27 16×28¹⁹⁰¹+303 (10×28¹⁴²⁵−2899)/27 (17×28¹³⁷¹−11)/3 (5×28¹³³⁵+426163)/27	http://factordb.com/index.php?id=1100000000808118231&open=prime http://factordb.com/index.php?id=1100000003880455200&open=prime http://factordb.com/index.php?id=1100000003879667576&open=prime http://factordb.com/index.php?id=1100000003850151420&open=prime http://factordb.com/index.php?id=1100000000840839934&open=prime http://factordb.com/index.php?id=1100000003850161974&open=prime http://factordb.com/index.php?id=1100000003850161973&open=prime http://factordb.com/index.php?id=1100000000840839947&open=prime http://factordb.com/index.php?id=1100000003850161972&open=prime http://factordb.com/index.php?id=1100000003850161965&open=prime	http://factordb.com/index.php?showid=1100000000808118231&base=28 http://factordb.com/index.php?showid=1100000003880455200&base=28 http://factordb.com/index.php?showid=1100000003879667576&base=28 http://factordb.com/index.php?showid=1100000003850151420&base=28 http://factordb.com/index.php?showid=1100000000840839934&base=28 http://factordb.com/index.php?showid=1100000003850161974&base=28 http://factordb.com/index.php?showid=1100000003850161973&base=28 http://factordb.com/index.php?showid=1100000000840839947&base=28 http://factordb.com/index.php?showid=1100000003850161972&base=28 http://factordb.com/index.php?showid=1100000003850161965&base=28	http://factordb.com/index.php?showid=1100000000808118231 http://factordb.com/index.php?showid=1100000003880455200 http://factordb.com/index.php?showid=1100000003879667576 http://factordb.com/index.php?showid=1100000003850151420 http://factordb.com/index.php?showid=1100000000840839934 http://factordb.com/index.php?showid=1100000003850161974 http://factordb.com/index.php?showid=1100000003850161973 http://factordb.com/index.php?showid=1100000000840839947 http://factordb.com/index.php?showid=1100000003850161972 http://factordb.com/index.php?showid=1100000003850161965	http://factordb.com/index.php?query=%28609228%5E%28n%2B1%29-143%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28443828%5E%28n%2B1%29%2B125%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2820928%5E%28n%2B2%29%2B3967%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1328%5E%28n%2B3%29%2B5697&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2824228%5E%28n%2B2%29-4679%29%2F9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28528%5E%28n%2B2%29%2B2803%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1628%5E%28n%2B2%29%2B303&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281028%5E%28n%2B2%29-2899%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281728%5E%28n%2B1%29-11%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28528%5E%28n%2B3%29%2B426163%29%2F27&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	1	543202
29	355205~355367	H0₄₉₉₄₉IDL BP0₄₇₈₆₀7 R0J₄₆₅₈₃OR 40O₄₅₀₇₄3 6B₄₄₈₁₉LF 5250₄₄₇₈₇5 PF3₄₃₅₈₁ G0J₄₃₅₂₈P D3DP₄₃₂₀₆ 3₄₂₃₄₇8S	49953 47863 46587 45077 44822 44791 43583 43531 43209 42349	73051 69995 68129 65920 65547 65502 63736 63660 63189 61931	17×29⁴⁹⁹⁵²+15536 344×29⁴⁷⁸⁶¹+7 (21943×29⁴⁶⁵⁸⁵+4265)/28 (818×29⁴⁵⁰⁷⁵−153)/7 (179×29⁴⁴⁸²¹+8221)/28 4268×29⁴⁴⁷⁸⁸+5 (20723×29⁴³⁵⁸¹−3)/28 (13011×29⁴³⁵²⁹+149)/28 (308949×29⁴³²⁰⁶−25)/28 (3×29⁴²³⁴⁹+4757)/28	http://factordb.com/index.php?id=1100000005145379508&open=prime http://factordb.com/index.php?id=1100000005145388777&open=prime http://factordb.com/index.php?id=1100000005145401955&open=prime http://factordb.com/index.php?id=1100000005145412940&open=prime http://factordb.com/index.php?id=1100000005146692934&open=prime http://factordb.com/index.php?id=1100000005146963940&open=prime http://factordb.com/index.php?id=1100000005147140656&open=prime http://factordb.com/index.php?id=1100000005186782527&open=prime http://factordb.com/index.php?id=1100000005186784294&open=prime http://factordb.com/index.php?id=1100000005186785258&open=prime	http://factordb.com/index.php?showid=1100000005145379508&base=29 http://factordb.com/index.php?showid=1100000005145388777&base=29 http://factordb.com/index.php?showid=1100000005145401955&base=29 http://factordb.com/index.php?showid=1100000005145412940&base=29 http://factordb.com/index.php?showid=1100000005146692934&base=29 http://factordb.com/index.php?showid=1100000005146963940&base=29 http://factordb.com/index.php?showid=1100000005147140656&base=29 http://factordb.com/index.php?showid=1100000005186782527&base=29 http://factordb.com/index.php?showid=1100000005186784294&base=29 http://factordb.com/index.php?showid=1100000005186785258&base=29	http://factordb.com/index.php?showid=1100000005145379508 http://factordb.com/index.php?showid=1100000005145388777 http://factordb.com/index.php?showid=1100000005145401955 http://factordb.com/index.php?showid=1100000005145412940 http://factordb.com/index.php?showid=1100000005146692934 http://factordb.com/index.php?showid=1100000005146963940 http://factordb.com/index.php?showid=1100000005147140656 http://factordb.com/index.php?showid=1100000005186782527 http://factordb.com/index.php?showid=1100000005186784294 http://factordb.com/index.php?showid=1100000005186785258	http://factordb.com/index.php?query=1729%5E%28n%2B3%29%2B15536&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=34429%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%282194329%5E%28n%2B2%29%2B4265%29%2F28&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2881829%5E%28n%2B1%29-153%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2817929%5E%28n%2B2%29%2B8221%29%2F28&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=426829%5E%28n%2B1%29%2B5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%282072329%5En-3%29%2F28&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281301129%5E%28n%2B1%29%2B149%29%2F28&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2830894929%5En-25%29%2F28&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28329%5E%28n%2B2%29%2B4757%29%2F28&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	162	50000
30	2619	OT₃₄₂₀₅ I0₂₄₆₀₈D 5₄₈₈₂J C0₁₀₂₂1 M0₅₄₇SS7 M₂₄₁QB AN₂₀₆ 50₁₆₄B J₁₅₃QJ J₉₄QQJ	34206 24610 4883 1024 551 243 207 166 155 97	50527 36352 7213 1513 814 359 306 245 229 144	25×30³⁴²⁰⁵−1 18×30²⁴⁶⁰⁹+13 (5×30⁴⁸⁸³+401)/29 12×30¹⁰²³+1 22×30⁵⁵⁰+26047 (22×30²⁴³+3139)/29 (313×30²⁰⁶−23)/29 5×30¹⁶⁵+11 (19×30¹⁵⁵+6071)/29 (19×30⁹⁷+188771)/29	http://factordb.com/index.php?id=1100000000800812865&open=prime http://factordb.com/index.php?id=1100000003593967511&open=prime http://factordb.com/index.php?id=1100000002327649423&open=prime http://factordb.com/index.php?id=1100000000785448736&open=prime http://factordb.com/index.php?id=1100000003593407988&open=prime http://factordb.com/index.php?id=1100000003593408295&open=prime http://factordb.com/index.php?id=1100000002327651073&open=prime http://factordb.com/index.php?id=1100000002356282476&open=ecm http://factordb.com/index.php?id=1100000003593409109&open=ecm http://factordb.com/index.php?id=1100000003593409165&open=ecm	http://factordb.com/index.php?showid=1100000000800812865&base=30 http://factordb.com/index.php?showid=1100000003593967511&base=30 http://factordb.com/index.php?showid=1100000002327649423&base=30 http://factordb.com/index.php?showid=1100000000785448736&base=30 http://factordb.com/index.php?showid=1100000003593407988&base=30 http://factordb.com/index.php?showid=1100000003593408295&base=30 http://factordb.com/index.php?showid=1100000002327651073&base=30 http://factordb.com/index.php?showid=1100000002356282476&base=30 http://factordb.com/index.php?showid=1100000003593409109&base=30 http://factordb.com/index.php?showid=1100000003593409165&base=30	http://factordb.com/index.php?showid=1100000000800812865 http://factordb.com/index.php?showid=1100000003593967511 http://factordb.com/index.php?showid=1100000002327649423 http://factordb.com/index.php?showid=1100000000785448736 http://factordb.com/index.php?showid=1100000003593407988 http://factordb.com/index.php?showid=1100000003593408295 http://factordb.com/index.php?showid=1100000002327651073 http://factordb.com/index.php?showid=1100000002356282476 http://factordb.com/index.php?showid=1100000003593409109 http://factordb.com/index.php?showid=1100000003593409165	http://factordb.com/index.php?query=2530%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1830%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28530%5E%28n%2B1%29%2B401%29%2F29&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1230%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=2230%5E%28n%2B3%29%2B26047&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%282230%5E%28n%2B2%29%2B3139%29%2F29&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2831330%5En-23%29%2F29&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=530%5E%28n%2B1%29%2B11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281930%5E%28n%2B2%29%2B6071%29%2F29&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281930%5E%28n%2B3%29%2B188771%29%2F29&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	0	–
31	569323~569400	2IIF₉₁₈₀₅ B0₈₈₃₀₉APO9 J0T₇₇₅₁₆ J090₇₇₁₂₈NNN D₆₉₈₆₁QO 9MH0₆₈₆₃₇D J₆₇₁₆₂D N0₆₆₉₇₁32P DDDQ0₆₄₀₈₈TD U₆₃₈₆₁CM3	91808 88314 77518 77134 69863 68641 67163 66975 64094 63864	136918 131708 115608 115035 104191 102369 100165 99884 95587 95245	(4997×31⁹¹⁸⁰⁵−1)/2 11×31⁸⁸³¹³+322688 (17699×31⁷⁷⁵¹⁶−29)/30 18268×31⁷⁷¹³¹+22839 (13×31⁶⁹⁸⁶³+12407)/30 9348×31⁶⁸⁶³⁸+13 (19×31⁶⁷¹⁶³−199)/30 23×31⁶⁶⁹⁷⁴+2970 400205×31⁶⁴⁰⁹⁰+912 31⁶³⁸⁶⁴−17574	http://factordb.com/index.php?id=1100000007050395732&open=prime http://factordb.com/index.php?id=1100000007050397309&open=prime http://factordb.com/index.php?id=1100000007050398940&open=prime http://factordb.com/index.php?id=1100000007050400178&open=prime http://factordb.com/index.php?id=1100000006965878559&open=prime http://factordb.com/index.php?id=1100000006965875678&open=prime http://factordb.com/index.php?id=1100000006965873668&open=prime http://factordb.com/index.php?id=1100000006965870538&open=prime http://factordb.com/index.php?id=1100000006965868103&open=prime http://factordb.com/index.php?id=1100000006965865343&open=prime	http://factordb.com/index.php?showid=1100000007050395732&base=31 http://factordb.com/index.php?showid=1100000007050397309&base=31 http://factordb.com/index.php?showid=1100000007050398940&base=31 http://factordb.com/index.php?showid=1100000007050400178&base=31 http://factordb.com/index.php?showid=1100000006965878559&base=31 http://factordb.com/index.php?showid=1100000006965875678&base=31 http://factordb.com/index.php?showid=1100000006965873668&base=31 http://factordb.com/index.php?showid=1100000006965870538&base=31 http://factordb.com/index.php?showid=1100000006965868103&base=31 http://factordb.com/index.php?showid=1100000006965865343&base=31	http://factordb.com/index.php?showid=1100000007050395732 http://factordb.com/index.php?showid=1100000007050397309 http://factordb.com/index.php?showid=1100000007050398940 http://factordb.com/index.php?showid=1100000007050400178 http://factordb.com/index.php?showid=1100000006965878559 http://factordb.com/index.php?showid=1100000006965875678 http://factordb.com/index.php?showid=1100000006965873668 http://factordb.com/index.php?showid=1100000006965870538 http://factordb.com/index.php?showid=1100000006965868103 http://factordb.com/index.php?showid=1100000006965865343	http://factordb.com/index.php?query=%28499731%5En-1%29%2F2&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1131%5E%28n%2B4%29%2B322688&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281769931%5En-29%29%2F30&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1826831%5E%28n%2B3%29%2B22839&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281331%5E%28n%2B2%29%2B12407%29%2F30&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=934831%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281931%5E%28n%2B1%29-199%29%2F30&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=2331%5E%28n%2B3%29%2B2970&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=400205*31%5E%28n%2B2%29%2B912&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=31%5E%28n%2B3%29-17574&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	77	100000
32	168882~169002	V₉₉₅₈₃63 6₈₉₀₇₄AF 8₇₇₇₀₀H Q₇₇₄₀₁EQQQ3 8₇₇₂₄₉3 JM₇₆₀₂₈L E₇₂₉₁₉IL B0₆₇₆₈₀CB GK₆₆₀₇₆F KN₆₅₀₂₂	99585 89076 77701 77406 77250 76030 72921 67683 66078 65023	149891 134073 116952 116508 116273 114437 109757 101873 99458 97870	32⁹⁹⁵⁸⁵−829 (6×32⁸⁹⁰⁷⁶+4241)/31 (8×32⁷⁷⁷⁰¹+271)/31 (26×32⁷⁷⁴⁰⁶−390071011)/31 (8×32⁷⁷²⁵⁰−163)/31 (611×32⁷⁶⁰²⁹−53)/31 (14×32⁷²⁹²¹+4171)/31 11×32⁶⁷⁶⁸²+395 (516×32⁶⁶⁰⁷⁷−175)/31 (643×32⁶⁵⁰²²−23)/31	http://factordb.com/index.php?id=1100000005514892191&open=prime http://factordb.com/index.php?id=1100000005514897129&open=prime http://factordb.com/index.php?id=1100000005514901700&open=prime http://factordb.com/index.php?id=1100000005514915338&open=prime http://factordb.com/index.php?id=1100000005514918574&open=prime http://factordb.com/index.php?id=1100000005514922523&open=prime http://factordb.com/index.php?id=1100000004591654373&open=prime http://factordb.com/index.php?id=1100000004591654467&open=prime http://factordb.com/index.php?id=1100000004591654632&open=prime http://factordb.com/index.php?id=1100000004591654952&open=prime	http://factordb.com/index.php?showid=1100000005514892191&base=32 http://factordb.com/index.php?showid=1100000005514897129&base=32 http://factordb.com/index.php?showid=1100000005514901700&base=32 http://factordb.com/index.php?showid=1100000005514915338&base=32 http://factordb.com/index.php?showid=1100000005514918574&base=32 http://factordb.com/index.php?showid=1100000005514922523&base=32 http://factordb.com/index.php?showid=1100000004591654373&base=32 http://factordb.com/index.php?showid=1100000004591654467&base=32 http://factordb.com/index.php?showid=1100000004591654632&base=32 http://factordb.com/index.php?showid=1100000004591654952&base=32	http://factordb.com/index.php?showid=1100000005514892191 http://factordb.com/index.php?showid=1100000005514897129 http://factordb.com/index.php?showid=1100000005514901700 http://factordb.com/index.php?showid=1100000005514915338 http://factordb.com/index.php?showid=1100000005514918574 http://factordb.com/index.php?showid=1100000005514922523 http://factordb.com/index.php?showid=1100000004591654373 http://factordb.com/index.php?showid=1100000004591654467 http://factordb.com/index.php?showid=1100000004591654632 http://factordb.com/index.php?showid=1100000004591654952	http://factordb.com/index.php?query=32%5E%28n%2B2%29-829&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28632%5E%28n%2B2%29%2B4241%29%2F31&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28832%5E%28n%2B1%29%2B271%29%2F31&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%282632%5E%28n%2B5%29-390071011%29%2F31&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28832%5E%28n%2B1%29-163%29%2F31&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2861132%5E%28n%2B1%29-53%29%2F31&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281432%5E%28n%2B2%29%2B4171%29%2F31&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1132%5E%28n%2B2%29%2B395&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2851632%5E%28n%2B1%29-175%29%2F31&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28643*32%5En-23%29%2F31&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	120	100000
33	280012~280093	DP₉₅₀₉₃M5 HJ0₉₄₂₉₅J 90₉₃₅₉₇Q 9F0₉₃₁₅₇N 7₈₉₄₄₉333H K3₈₀₇₅₁6K D₈₀₁₀₇9UD VFU₇₂₂₀₄FK J₆₈₇₁₅2BJ DF0₆₈₃₆₇J	95096 94298 93599 93160 89453 80754 80110 72208 68718 68370	144405 143193 142131 141465 135835 122626 121648 109649 104350 103821	(441×33⁹⁵⁰⁹⁵−3833)/32 580×33⁹⁴²⁹⁶+19 9×33⁹³⁵⁹⁸+26 312×33⁹³¹⁵⁸+23 (7×33⁸⁹⁴⁵³−4743239)/32 (643×33⁸⁰⁷⁵³+3709)/32 (13×33⁸⁰¹¹⁰−121453)/32 (16623×33⁷²²⁰⁶−8095)/16 (19×33⁶⁸⁷¹⁸−600883)/32 444×33⁶⁸³⁶⁸+19	http://factordb.com/index.php?id=1100000005652348775&open=prime http://factordb.com/index.php?id=1100000005652362811&open=prime http://factordb.com/index.php?id=1100000005652375073&open=prime http://factordb.com/index.php?id=1100000005652389776&open=prime http://factordb.com/index.php?id=1100000005652430746&open=prime http://factordb.com/index.php?id=1100000005652446200&open=prime http://factordb.com/index.php?id=1100000005652461592&open=prime http://factordb.com/index.php?id=1100000004614764298&open=prime http://factordb.com/index.php?id=1100000004614770536&open=prime http://factordb.com/index.php?id=1100000004614784274&open=prime	http://factordb.com/index.php?showid=1100000005652348775&base=33 http://factordb.com/index.php?showid=1100000005652362811&base=33 http://factordb.com/index.php?showid=1100000005652375073&base=33 http://factordb.com/index.php?showid=1100000005652389776&base=33 http://factordb.com/index.php?showid=1100000005652430746&base=33 http://factordb.com/index.php?showid=1100000005652446200&base=33 http://factordb.com/index.php?showid=1100000005652461592&base=33 http://factordb.com/index.php?showid=1100000004614764298&base=33 http://factordb.com/index.php?showid=1100000004614770536&base=33 http://factordb.com/index.php?showid=1100000004614784274&base=33	http://factordb.com/index.php?showid=1100000005652348775 http://factordb.com/index.php?showid=1100000005652362811 http://factordb.com/index.php?showid=1100000005652375073 http://factordb.com/index.php?showid=1100000005652389776 http://factordb.com/index.php?showid=1100000005652430746 http://factordb.com/index.php?showid=1100000005652446200 http://factordb.com/index.php?showid=1100000005652461592 http://factordb.com/index.php?showid=1100000004614764298 http://factordb.com/index.php?showid=1100000004614770536 http://factordb.com/index.php?showid=1100000004614784274	http://factordb.com/index.php?query=%2844133%5E%28n%2B2%29-3833%29%2F32&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=58033%5E%28n%2B1%29%2B19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=933%5E%28n%2B1%29%2B26&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=31233%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28733%5E%28n%2B4%29-4743239%29%2F32&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2864333%5E%28n%2B2%29%2B3709%29%2F32&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281333%5E%28n%2B3%29-121453%29%2F32&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281662333%5E%28n%2B2%29-8095%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281933%5E%28n%2B3%29-600883%29%2F32&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=44433%5E%28n%2B1%29%2B19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	81	100000
34	184785~184832	GFGC₉₉₉₉₆5 90₉₇₉₅₀FJ NM0₈₅₂₁₈KX F₈₃₁₈₉H2HP P₇₉₄₄₁444P 6₇₇₀₂₇8X XQIQ₇₂₂₄₁D T₆₆₅₃₀IF 4₆₆₁₅₂B 2EEC₆₆₀₃₉7	100000 97953 85222 83193 79445 77029 72245 66532 66153 66043	153148 150013 130516 127408 121669 117968 110642 101893 101312 101143	(209246×34⁹⁹⁹⁹⁷−81)/11 9×34⁹⁷⁹⁵²+529 804×34⁸⁵²²⁰+713 (5×34⁸³¹⁹³+700233)/11 (25×34⁷⁹⁴⁴⁵−28062367)/33 (2×34⁷⁷⁰²⁹+1043)/11 (1288676×34⁷²²⁴²−455)/33 (29×34⁶⁶⁵³²−12833)/33 (4×34⁶⁶¹⁵³+227)/33 (30826×34⁶⁶⁰⁴⁰−59)/11	http://factordb.com/index.php?id=1100000004702891268&open=prime http://factordb.com/index.php?id=1100000004702894713&open=prime http://factordb.com/index.php?id=1100000004702900996&open=prime http://factordb.com/index.php?id=1100000004702910376&open=prime http://factordb.com/index.php?id=1100000004702913746&open=prime http://factordb.com/index.php?id=1100000004702918600&open=prime http://factordb.com/index.php?id=1100000004399656529&open=prime http://factordb.com/index.php?id=1100000004399657696&open=prime http://factordb.com/index.php?id=1100000004399658651&open=prime http://factordb.com/index.php?id=1100000004399659716&open=prime	http://factordb.com/index.php?showid=1100000004702891268&base=34 http://factordb.com/index.php?showid=1100000004702894713&base=34 http://factordb.com/index.php?showid=1100000004702900996&base=34 http://factordb.com/index.php?showid=1100000004702910376&base=34 http://factordb.com/index.php?showid=1100000004702913746&base=34 http://factordb.com/index.php?showid=1100000004702918600&base=34 http://factordb.com/index.php?showid=1100000004399656529&base=34 http://factordb.com/index.php?showid=1100000004399657696&base=34 http://factordb.com/index.php?showid=1100000004399658651&base=34 http://factordb.com/index.php?showid=1100000004399659716&base=34	http://factordb.com/index.php?showid=1100000004702891268 http://factordb.com/index.php?showid=1100000004702894713 http://factordb.com/index.php?showid=1100000004702900996 http://factordb.com/index.php?showid=1100000004702910376 http://factordb.com/index.php?showid=1100000004702913746 http://factordb.com/index.php?showid=1100000004702918600 http://factordb.com/index.php?showid=1100000004399656529 http://factordb.com/index.php?showid=1100000004399657696 http://factordb.com/index.php?showid=1100000004399658651 http://factordb.com/index.php?showid=1100000004399659716	http://factordb.com/index.php?query=%2820924634%5E%28n%2B1%29-81%29%2F11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=934%5E%28n%2B2%29%2B529&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=80434%5E%28n%2B2%29%2B713&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28534%5E%28n%2B4%29%2B700233%29%2F11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%282534%5E%28n%2B4%29-28062367%29%2F33&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28234%5E%28n%2B2%29%2B1043%29%2F11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28128867634%5E%28n%2B1%29-455%29%2F33&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%282934%5E%28n%2B2%29-12833%29%2F33&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%28434%5E%28n%2B1%29%2B227%29%2F33&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%283082634%5E%28n%2B1%29-59%29%2F11&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	47	100000
35	≥713502									(239 linear left families and 134 non-linear left families, totally 373 left families)
36	35286~35290	P₈₁₉₉₃SZ S0₇₅₀₀₇8H 7K₂₆₅₆₇Z J₁₀₁₁₇LJ VL0₇₂₅₈J EO0₆₁₇₇V FZ₅₇₇₇3P T09₄₆₁₈1 RY₄₅₆₂H OZ₃₉₃₂AZ	81995 75010 26569 10119 7261 6180 5780 4621 4564 3935	127609 116739 41349 15748 11301 9618 8996 7192 7103 6124	(5×36⁸¹⁹⁹⁵+821)/7 28×36⁷⁵⁰⁰⁹+305 (53×36²⁶⁵⁶⁸+101)/7 (19×36¹⁰¹¹⁹+2501)/35 1137×36⁷²⁵⁹+19 528×36⁶¹⁷⁸+31 16×36⁵⁷⁷⁹−1163 (36549×36⁴⁶¹⁹−289)/35 (979×36⁴⁵⁶³−629)/35 25×36³⁹³⁴−901	http://factordb.com/index.php?id=1100000002394962083&open=prime http://factordb.com/index.php?id=1100000004020085177&open=prime http://factordb.com/index.php?id=1100000003896952461&open=prime http://factordb.com/index.php?id=1100000003807362491&open=prime http://factordb.com/index.php?id=1100000003807362489&open=prime http://factordb.com/index.php?id=1100000003807362488&open=prime http://factordb.com/index.php?id=1100000003807362487&open=prime http://factordb.com/index.php?id=1100000003807362486&open=prime http://factordb.com/index.php?id=1100000003807362485&open=prime http://factordb.com/index.php?id=1100000000840634476&open=prime	http://factordb.com/index.php?showid=1100000002394962083&base=36 http://factordb.com/index.php?showid=1100000004020085177&base=36 http://factordb.com/index.php?showid=1100000003896952461&base=36 http://factordb.com/index.php?showid=1100000003807362491&base=36 http://factordb.com/index.php?showid=1100000003807362489&base=36 http://factordb.com/index.php?showid=1100000003807362488&base=36 http://factordb.com/index.php?showid=1100000003807362487&base=36 http://factordb.com/index.php?showid=1100000003807362486&base=36 http://factordb.com/index.php?showid=1100000003807362485&base=36 http://factordb.com/index.php?showid=1100000000840634476&base=36	http://factordb.com/index.php?showid=1100000002394962083 http://factordb.com/index.php?showid=1100000004020085177 http://factordb.com/index.php?showid=1100000003896952461 http://factordb.com/index.php?showid=1100000003807362491 http://factordb.com/index.php?showid=1100000003807362489 http://factordb.com/index.php?showid=1100000003807362488 http://factordb.com/index.php?showid=1100000003807362487 http://factordb.com/index.php?showid=1100000003807362486 http://factordb.com/index.php?showid=1100000003807362485 http://factordb.com/index.php?showid=1100000000840634476	http://factordb.com/index.php?query=%28536%5E%28n%2B2%29%2B821%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=2836%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%285336%5E%28n%2B1%29%2B101%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%281936%5E%28n%2B2%29%2B2501%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=113736%5E%28n%2B1%29%2B19&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=52836%5E%28n%2B1%29%2B31&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=1636%5E%28n%2B2%29-1163&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%283654936%5E%28n%2B1%29-289%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=%2897936%5E%28n%2B1%29-629%29%2F35&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show http://factordb.com/index.php?query=2536%5E%28n%2B2%29-901&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	4	100000

These "unsolved" families in fact have larger (probable) primes (found by other projects), but since the length of these (probable) primes are larger than the search limit of the corresponding bases b, and they are not in the kernel files (nor counted in the condensed table above) since they may not be the next minimal primes in base b, and the indices of these minimal primes in base b are unknown: (since the family {L}G in base b = 27 covers two other unsolved families {L}0G and N9{L}G in base b = 27, thus the family {L}0G only needs to search to length 101106 and the family N9{L}G only needs to search to length 101107)

b (2 ≤ b ≤ 36)	family	algebraic form	base-b form of the smallest (probable) prime in this family (write "d_n" if there are 5 or more (n) consecutive same digits d)	length of the smallest (probable) prime in this family	length of the smallest (probable) prime in this family in decimal	algebraic ((a×bⁿ+c)/gcd(a+c,b−1)) form of the smallest (probable) prime in this family	factordb entry of the smallest (probable) prime in this family	the smallest (probable) prime in this family written in base b (use lower case letters instead of upper case letters)	the smallest (probable) prime in this family written in decimal	factorization of the first 200 numbers in corresponding family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0))	the entry of the smallest (probable) prime in this family in the top definitely primes page or the top probable primes page	the process which the smallest (probable) prime in this family is found in	reference of searching the (probable) primes in this family
17	4{9}	(73×17ⁿ−9)/16 (n ≥ 1)	49₁₁₁₃₃₃	111334	136991	(73×17¹¹¹³³³−9)/16	http://factordb.com/index.php?id=1100000000808118219&open=prime	http://factordb.com/index.php?showid=1100000000808118219&base=17	http://factordb.com/index.php?showid=1100000000808118219	http://factordb.com/index.php?query=%2873*17%5En-9%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%2873*17%5E111333-9%29%2F16&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 17	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.17.txt
17	97{0}1	160×17ⁿ⁺¹+1 (n ≥ 0)	970₁₆₆₀₄₇1	166050	204316	160×17¹⁶⁶⁰⁴⁸+1	http://factordb.com/index.php?id=1100000000765961411&open=prime	http://factordb.com/index.php?showid=1100000000765961411&base=17	http://factordb.com/index.php?showid=1100000000765961411	http://factordb.com/index.php?query=160*17%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	https://t5k.org/primes/page.php?id=85139	solving the Sierpinski conjecture in base b = 17	http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm#S17
17	F7{0}1	262×17ⁿ⁺¹+1 (n ≥ 0)	F70₁₈₆₇₆₇1	186770	229811	262×17¹⁸⁶⁷⁶⁸+1	http://factordb.com/index.php?id=1100000000765961429&open=prime	http://factordb.com/index.php?showid=1100000000765961429&base=17	http://factordb.com/index.php?showid=1100000000765961429	http://factordb.com/index.php?query=262*17%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	https://t5k.org/primes/page.php?id=85256	solving the Sierpinski conjecture in base b = 17	http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm#S17
19	1E7{0}1	634×19ⁿ⁺¹+1 (n ≥ 0)	1E70₁₂₂₈₉₆1	122899	157158	634×19¹²²⁸⁹⁷+1	http://factordb.com/index.php?id=1100000001582289581&open=prime	http://factordb.com/index.php?showid=1100000001582289581&base=19	http://factordb.com/index.php?showid=1100000001582289581	http://factordb.com/index.php?query=634*19%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	(too small for the top primes page)	solving the Sierpinski conjecture in base b = 19	http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm#S19
19	FG{6}	(904×19ⁿ−1)/3 (n ≥ 0)	FG6₁₁₀₉₈₄	110986	141924	(904×19¹¹⁰⁹⁸⁴−1)/3	http://factordb.com/index.php?id=1100000000808118212&open=prime	http://factordb.com/index.php?showid=1100000000808118212&base=19	http://factordb.com/index.php?showid=1100000000808118212	http://factordb.com/index.php?query=%28904*19%5En-1%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%28904*19%5E110984-1%29%2F3&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 19	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.19.txt
21	C{F}0K	(51×21ⁿ⁺²−1243)/4 (n ≥ 0)	CF₄₇₉₁₄₇0K	479150	633542	(51×21⁴⁷⁹¹⁴⁹−1243)/4	http://factordb.com/index.php?id=1100000000805209046&open=prime	http://factordb.com/index.php?showid=1100000000805209046&base=21	http://factordb.com/index.php?showid=1100000000805209046	http://factordb.com/index.php?query=%2851*21%5E%28n%2B2%29-1243%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%2851*21%5E479149-1243%29%2F4&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 21	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.21.txt
23	8{0}1	8×23ⁿ⁺¹+1 (n ≥ 0)	80₁₁₉₂₁₄1	119216	162340	8×23¹¹⁹²¹⁵+1	http://factordb.com/index.php?id=1100000000634720609&open=prime	http://factordb.com/index.php?showid=1100000000634720609&base=23	http://factordb.com/index.php?showid=1100000000634720609	http://factordb.com/index.php?query=8*23%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	https://t5k.org/primes/page.php?id=85951	solving the Sierpinski conjecture in base b = 23	http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm#S23
23	9{E}	(106×23ⁿ−7)/11 (n ≥ 1)	9E₈₀₀₈₇₃	800874	1090573	(106×23⁸⁰⁰⁸⁷³−7)/11	http://factordb.com/index.php?id=1100000000782858648&open=prime	http://factordb.com/index.php?showid=1100000000782858648&base=23	http://factordb.com/index.php?showid=1100000000782858648	http://factordb.com/index.php?query=%28106*23%5En-7%29%2F11&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%28106*23%5E800873-7%29%2F11&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 23	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.23.txt
25	71JD{0}1	110488×25ⁿ⁺¹+1 (n ≥ 0)	71JD0₄₅₈₅₄₉1	458554	641031	110488×25⁴⁵⁸⁵⁵⁰+1	http://factordb.com/index.php?id=1100000002341496334&open=prime	http://factordb.com/index.php?showid=1100000002341496334&base=25	http://factordb.com/index.php?showid=1100000002341496334	http://factordb.com/index.php?query=110488*25%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	https://t5k.org/primes/page.php?id=111834	solving the Sierpinski conjecture in base b = 5 (110488×5^r+1 can be prime only if r is even, thus can be converted to 110488×25^r/2+1)	https://www.primegrid.com/forum_thread.php?id=5087&nowrap=true#66386
25	9{6}M	(37×25ⁿ⁺¹+63)/4 (n ≥ 0)	96₁₃₆₉₆₅M	136967	191472	(37×25¹³⁶⁹⁶⁶+63)/4	http://factordb.com/index.php?id=1100000000808118185&open=prime	http://factordb.com/index.php?showid=1100000000808118185&base=25	http://factordb.com/index.php?showid=1100000000808118185	http://factordb.com/index.php?query=%2837*25%5E%28n%2B1%29%2B63%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%2837*25%5E136966%2B63%29%2F4&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 25	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.25.txt
25	DKJ{0}1	8644×25ⁿ⁺¹+1 (n ≥ 0)	DKJ0₂₄₆₈₀₈1	246812	345029	8644×25²⁴⁶⁸⁰⁹+1	http://factordb.com/index.php?id=1100000003983678207&open=prime	http://factordb.com/index.php?showid=1100000003983678207&base=25	http://factordb.com/index.php?showid=1100000003983678207	http://factordb.com/index.php?query=8644*25%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	https://t5k.org/primes/page.php?id=94113	solving the Sierpinski conjecture in base b = 5 (8644×5^r+1 can be prime only if r is even, thus can be converted to 8644×25^r/2+1)	https://www.mersenneforum.org/showpost.php?p=224809&postcount=24
25	M{F}0F6	(181×25ⁿ⁺³−75077)/8 (n ≥ 0)	MF₁₀₉₉₈₈0F6	109992	153763	(181×25¹⁰⁹⁹⁹¹−75077)/8	http://factordb.com/index.php?id=1100000000808118206&open=prime	http://factordb.com/index.php?showid=1100000000808118206&base=25	http://factordb.com/index.php?showid=1100000000808118206	http://factordb.com/index.php?query=%28181*25%5E%28n%2B3%29-75077%29%2F8&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%28181*25%5E109991-75077%29%2F8&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 25	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.25.txt
27	A{0}PM	10×27ⁿ⁺²+697 (n ≥ 0)	A0₁₀₉₀₀₃PM	109006	156027	10×27¹⁰⁹⁰⁰⁵+697	http://factordb.com/index.php?id=1100000000808118203&open=prime	http://factordb.com/index.php?showid=1100000000808118203&base=27	http://factordb.com/index.php?showid=1100000000808118203	http://factordb.com/index.php?query=10*27%5E%28n%2B2%29%2B697&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=10*27%5E109005%2B697&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 27	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.27.txt
27	{L}G	(21×27ⁿ⁺¹−151)/26 (n ≥ 1)	L₁₀₁₁₀₅G	101106	144720	(21×27¹⁰¹¹⁰⁶−151)/26	http://factordb.com/index.php?id=1100000000808118209&open=prime	http://factordb.com/index.php?showid=1100000000808118209&base=27	http://factordb.com/index.php?showid=1100000000808118209	http://factordb.com/index.php?query=%2821*27%5E%28n%2B1%29-151%29%2F26&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%2821*27%5E101106-151%29%2F26&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 27	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.27.txt
29	47D{0}1	3580×29ⁿ⁺¹+1 (n ≥ 0)	47D0₁₃₄₂₅₃1	134257	196337	3580×29¹³⁴²⁵⁴+1	http://factordb.com/index.php?id=1100000005145366749&open=prime	http://factordb.com/index.php?showid=1100000005145366749&base=29	http://factordb.com/index.php?showid=1100000005145366749	http://factordb.com/index.php?query=3580*29%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	(too small for the top primes page)	solving the Sierpinski conjecture in base b = 841 (3580×29ⁿ⁺¹+1 can be prime only if n+1 is even, thus can be converted to 3580×841^(n+1)/2+1)	http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm#S841
29	E9{C}	(2908×29ⁿ−3)/7 (n ≥ 0)	E9C₆₁₅₀₁	61503	89942	(2908×29⁶¹⁵⁰¹−3)/7	http://factordb.com/index.php?id=1100000000808118274&open=prime	http://factordb.com/index.php?showid=1100000000808118274&base=29	http://factordb.com/index.php?showid=1100000000808118274	http://factordb.com/index.php?query=%282908*29%5En-3%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%282908*29%5E61501-3%29%2F7&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	{F}IK	(15×29ⁿ⁺²+2561)/28 (n ≥ 0)	F₅₇₂₄₉IK	57251	83724	(15×29⁵⁷²⁵¹+2561)/28	http://factordb.com/index.php?id=1100000000819229872&open=prime	http://factordb.com/index.php?showid=1100000000819229872&base=29	http://factordb.com/index.php?showid=1100000000819229872	http://factordb.com/index.php?query=%2815*29%5E%28n%2B2%29%2B2561%29%2F28&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%2815*29%5E57251%2B2561%29%2F28&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	{I}FK	(9×29ⁿ⁺²−1199)/14 (n ≥ 0)	I₁₁₀₇₂₅FK	110727	161927	(9×29¹¹⁰⁷²⁷−1199)/14	http://factordb.com/index.php?id=1100000000808118200&open=prime	http://factordb.com/index.php?showid=1100000000808118200&base=29	http://factordb.com/index.php?showid=1100000000808118200	http://factordb.com/index.php?query=%289*29%5E%28n%2B2%29-1199%29%2F14&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%289*29%5E110727-1199%29%2F14&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	{L}CE	(3×29ⁿ⁺²−1075)/4 (n ≥ 0)	L₇₂₀₈₇CE	72089	105423	(3×29⁷²⁰⁸⁹−1075)/4	http://factordb.com/index.php?id=1100000000808118245&open=prime	http://factordb.com/index.php?showid=1100000000808118245&base=29	http://factordb.com/index.php?showid=1100000000808118245	http://factordb.com/index.php?query=%283*29%5E%28n%2B2%29-1075%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%283*29%5E72089-1075%29%2F4&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	LO{G}	(4435×29ⁿ−4)/7 (n ≥ 0)	LOG₆₆₀₈₁	66083	96640	(4435×29⁶⁶⁰⁸¹−4)/7	http://factordb.com/index.php?id=1100000000808118256&open=prime	http://factordb.com/index.php?showid=1100000000808118256&base=29	http://factordb.com/index.php?showid=1100000000808118256	http://factordb.com/index.php?query=%284435*29%5En-4%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%284435*29%5E66081-4%29%2F7&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	LP{C}9	(4441×29ⁿ⁺¹−24)/7 (n ≥ 0)	LPC₇₅₁₅₁9	75154	109905	(4441×29⁷⁵¹⁵²−24)/7	http://factordb.com/index.php?id=1100000000808118236&open=prime	http://factordb.com/index.php?showid=1100000000808118236&base=29	http://factordb.com/index.php?showid=1100000000808118236	http://factordb.com/index.php?query=%284441*29%5E%28n%2B1%29-24%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%284441*29%5E75152-24%29%2F7&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	O{0}FPL	24×29ⁿ⁺³+13361 (n ≥ 0)	O0₁₇₄₂₃₆FPL	174240	254809	24×29¹⁷⁴²³⁹+13361	http://factordb.com/index.php?id=1100000000808118178&open=prime	http://factordb.com/index.php?showid=1100000000808118178&base=29	http://factordb.com/index.php?showid=1100000000808118178	http://factordb.com/index.php?query=24*29%5E%28n%2B3%29%2B13361&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=24*29%5E174239%2B13361&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	P{0}OPR	25×29ⁿ⁺³+20936 (n ≥ 0)	P0₅₉₁₄₄OPR	59148	86498	25×29⁵⁹¹⁴⁷+20936	http://factordb.com/index.php?id=1100000000808118282&open=prime	http://factordb.com/index.php?showid=1100000000808118282&base=29	http://factordb.com/index.php?showid=1100000000808118282	http://factordb.com/index.php?query=25*29%5E%28n%2B3%29%2B20936&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=25*29%5E59147%2B20936&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	PC{L}	(2951×29ⁿ−3)/4 (n ≥ 0)	PCL₁₂₃₄₁₈	123420	180490	(2951×29¹²³⁴¹⁸−3)/4	http://factordb.com/index.php?id=1100000000808118196&open=prime	http://factordb.com/index.php?showid=1100000000808118196&base=29	http://factordb.com/index.php?showid=1100000000808118196	http://factordb.com/index.php?query=%282951*29%5En-3%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%282951*29%5E123418-3%29%2F4&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	P{L}C	(103×29ⁿ⁺¹−39)/4 (n ≥ 0)	PL₅₄₁₇₈C	54180	79233	(103×29⁵⁴¹⁷⁹−39)/4	http://factordb.com/index.php?id=1100000000819229869&open=prime	http://factordb.com/index.php?showid=1100000000819229869&base=29	http://factordb.com/index.php?showid=1100000000819229869	http://factordb.com/index.php?query=%28103*29%5E%28n%2B1%29-39%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%28103*29%5E54179-39%29%2F4&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	PO{L}0O	(2999×29ⁿ⁺²−2427)/4 (n ≥ 0)	POL₆₄₅₅₄0O	64558	94410	(2999×29⁶⁴⁵⁵⁶−2427)/4	http://factordb.com/index.php?id=1100000000808118259&open=prime	http://factordb.com/index.php?showid=1100000000808118259&base=29	http://factordb.com/index.php?showid=1100000000808118259	http://factordb.com/index.php?query=%282999*29%5E%28n%2B2%29-2427%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=%282999*29%5E64556-2427%29%2F4&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
29	Q9R{0}9	22154×29ⁿ⁺¹+9 (n ≥ 0)	Q9R0₅₂₀₄₉9	52053	76123	22154×29⁵²⁰⁵⁰+9	http://factordb.com/index.php?id=1100000000819229865&open=prime	http://factordb.com/index.php?showid=1100000000819229865&base=29	http://factordb.com/index.php?showid=1100000000819229865	http://factordb.com/index.php?query=22154*29%5E%28n%2B1%29%2B9&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	http://www.primenumbers.net/prptop/searchform.php?form=22154*29%5E52050%2B9&action=Search	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 29	https://github.com/curtisbright/mepn-data/blob/master/data/minimal.29.txt
32	NU{0}1	766×32ⁿ⁺¹+1 (n ≥ 0)	NU0₆₆₁₈₆₃1	661866	996208	766×32⁶⁶¹⁸⁶⁴+1	http://factordb.com/index.php?id=1100000003813355148&open=prime	http://factordb.com/index.php?showid=1100000003813355148&base=32	http://factordb.com/index.php?showid=1100000003813355148	http://factordb.com/index.php?query=766*32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	https://t5k.org/primes/page.php?id=134216	finding the Proth primes k×2^r+1 for k = 383	http://www.prothsearch.com/riesel1a.html 3309321 is the smallest exponent r == 1 mod 5 (≥ 6) for k = 383 (since 766×32ⁿ⁺¹+1 = 383×2^5×(n+1)+1+1, thus we need an exponent r == 1 mod 5 for 383×2^r+1, i.e. the Proth number for k = 383, and since n ≥ 0, 5×(n+1)+1 must be ≥ 5×1+1 = 6)
33	N7{0}1	766×33ⁿ⁺¹+1 (n ≥ 0)	N70₆₁₀₄₁₁1	610414	926923	766×33⁶¹⁰⁴¹²+1	http://factordb.com/index.php?id=1100000000838755581&open=prime	http://factordb.com/index.php?showid=1100000000838755581&base=33	http://factordb.com/index.php?showid=1100000000838755581	http://factordb.com/index.php?query=766*33%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	https://t5k.org/primes/page.php?id=121575	solving the Sierpinski conjecture in base b = 33	http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm#S33
35	1B{0}1	46×35ⁿ⁺¹+1 (n ≥ 0)	1B0₅₆₀₆₁1	56064	86566	46×35⁵⁶⁰⁶²+1	http://factordb.com/index.php?id=1100000000885460611&open=prime	http://factordb.com/index.php?showid=1100000000885460611&base=35	http://factordb.com/index.php?showid=1100000000885460611	http://factordb.com/index.php?query=46*35%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	(too small for the top primes page)	solving the Sierpinski conjecture in base b = 35	http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm#S35

These unsolved families in fact have larger search limit of lengths (searched by other projects) than the search limit of the corresponding bases b:

b (2 ≤ b ≤ 36)	family	algebraic form	true search limit of length for this family	factorization of the first 200 numbers in this family (n is the number of digits in the "{}", start with the smallest n making the number > b (if n = 0 already makes the number > b, then start with n = 0))	the process of searching the (probable) primes in this family	reference of searching the (probable) primes in this family
17	F1{9}	(4105×17ⁿ−9)/16 (n ≥ 0)	1000000	http://factordb.com/index.php?query=%284105*17%5En-9%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 17	https://github.com/curtisbright/mepn-data/blob/master/data/sieve.17.txt
19	EE1{6}	(15964×19ⁿ−1)/3 (n ≥ 0)	707350	http://factordb.com/index.php?query=%2815964*19%5En-1%29%2F3&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 19	https://github.com/curtisbright/mepn-data/blob/master/data/sieve.19.txt
21	G{0}FK	16×21ⁿ⁺²+335 (n ≥ 0)	506722	http://factordb.com/index.php?query=16*21%5E%28n%2B2%29%2B335&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	solving the original minimal prime problem (i.e. prime > b is not required) in base b = 21	https://github.com/curtisbright/mepn-data/blob/master/data/sieve.21.txt
23	H3{0}1	394×23ⁿ⁺¹+1 (n ≥ 0)	800000	http://factordb.com/index.php?query=394*23%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	solving the Sierpinski conjecture in base b = 529 (394×23ⁿ⁺¹+1 can be prime only if n+1 is even, thus can be converted to 394×529^(n+1)/2+1)	http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm#S529
23	JH{0}1	454×23ⁿ⁺¹+1 (n ≥ 0)	800000	http://factordb.com/index.php?query=454*23%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	solving the Sierpinski conjecture in base b = 529 (454×23ⁿ⁺¹+1 can be prime only if n+1 is even, thus can be converted to 454×529^(n+1)/2+1)	http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm#S529
25	D71J{0}1	207544×25ⁿ⁺¹+1 (n ≥ 0)	350000	http://factordb.com/index.php?query=207544*25%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	solving the Sierpinski conjecture in base b = 25	http://www.noprimeleftbehind.net/crus/Sierp-conjecture-base25-reserve.htm
25	EF{O}	366×25ⁿ−1 (n ≥ 0)	300000	http://factordb.com/index.php?query=366*25%5En-1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	solving the Riesel conjecture in base b = 25	http://www.noprimeleftbehind.net/crus/Riesel-conjecture-base25-reserve.htm
31	{F}G	(31ⁿ⁺¹+1)/2 (n ≥ 1)	16777215	http://factordb.com/index.php?query=%2831%5E%28n%2B1%29%2B1%29%2F2&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	finding the generalized half Fermat primes (b^{2^r}+1)/2 in base b = 31 ((bⁿ⁺¹+1)/2 can be prime only if n+1 is power of 2, thus can be converted to (b^{2^r}+1)/2)	for n+1 ≤ 2¹⁹ = 524288 see http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt, and the numbers with n+1 = 2²⁰ = 1048576, 2²¹ = 2097152, 2²² = 4194304, 2²³ = 8388608 are divisible by 37339791361, 5138022401, 998244353, 2121143418881, respectively (these four prime factors are found by trial division), but the number with n+1 = 2²⁴ = 16777216 has no prime factor < 2⁴⁸ (also use trial division to show this), thus the smallest prime candidate is n+1 = 2²⁴ = 16777216, and its length is 16777216
32	4{0}1	4×32ⁿ⁺¹+1 (n ≥ 0)	1717986918	http://factordb.com/index.php?query=4*32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	finding the Fermat primes 2^{2^r}+1 (4×32ⁿ⁺¹+1 = 2^5×n+7+1, and 2^5×n+7+1 can be prime only if 5×n+7 is a power of 2, thus can be converted to 2^{2^r}+1)	http://www.prothsearch.com/fermat.html, 2^r == 2 mod 5 if and only if r == 1 mod 4, and the smallest r == 1 mod 4 (and r > 2) such that 2^{2^r}+1 may be prime is r = 33, and thus the smallest possible prime is n+1 = (2³³−2)/5 = 1717986918, and its length is 1717986919 (since 4×32ⁿ⁺¹+1 = 2^5×(n+1)+2+1, thus we need an exponent s == 2 mod 5 for 2^s+1 = 2^{2^r}+1 (if 2^s+1 is prime, then s is a power of 2, thus we can let s = 2^r), and 2^r == 2 mod 5 if and only if r == 1 mod 4, and since n ≥ 0, 5×(n+1)+2 must be ≥ 5×1+2 = 7, thus r = log₂(5×(n+1)+2) must be > 2)
32	G{0}1	16×32ⁿ⁺¹+1 (n ≥ 0)	3435973836	http://factordb.com/index.php?query=16*32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	finding the Fermat primes 2^{2^r}+1 (16×32ⁿ⁺¹+1 = 2^5×n+9+1, and 2^5×n+9+1 can be prime only if 5×n+9 is a power of 2, thus can be converted to 2^{2^r}+1)	http://www.prothsearch.com/fermat.html, 2^r == 4 mod 5 if and only if r == 2 mod 4, and the smallest r == 2 mod 4 (and r > 3) such that 2^{2^r}+1 may be prime is r = 34, and thus the smallest possible prime is n+1 = (2³⁴−4)/5 = 3435973836, and its length is 3435973837 (since 16×32ⁿ⁺¹+1 = 2^5×(n+1)+4+1, thus we need an exponent s == 4 mod 5 for 2^s+1 = 2^{2^r}+1 (if 2^s+1 is prime, then s is a power of 2, thus we can let s = 2^r), and 2^r == 4 mod 5 if and only if r == 2 mod 4, and since n ≥ 0, 5×(n+1)+4 must be ≥ 5×1+4 = 9, thus r = log₂(5×(n+1)+4) must be > 3)
32	NG{0}1	752×32ⁿ⁺¹+1 (n ≥ 0)	1800000	http://factordb.com/index.php?query=752*32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	finding the Proth primes k×2^r+1 for k = 47	http://www.prothsearch.com/riesel1.html k = 47 is searched to exponent 9000000 with no exponent == 4 mod 5 (≥ 9) has been found (since 752×32ⁿ⁺¹+1 = 47×2^5×(n+1)+4+1, thus we need an exponent r == 4 mod 5 for 47×2^r+1, i.e. the Proth number for k = 47, and since n ≥ 0, 5×(n+1)+4 must be ≥ 5×1+4 = 9)
32	UG{0}1	976×32ⁿ⁺¹+1 (n ≥ 0)	1000000	http://factordb.com/index.php?query=976*32%5E%28n%2B1%29%2B1&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	finding the Proth primes k×2^r+1 for k = 61	http://www.prothsearch.com/riesel1.html k = 61 is searched to exponent 5000000 with no exponent == 4 mod 5 (≥ 9) has been found (since 976×32ⁿ⁺¹+1 = 61×2^5×(n+1)+4+1, thus we need an exponent r == 4 mod 5 for 61×2^r+1, i.e. the Proth number for k = 61, and since n ≥ 0, 5×(n+1)+4 must be ≥ 5×1+4 = 9)
32	S{V}	29×32ⁿ−1 (n ≥ 1)	2000000	http://factordb.com/index.php?query=29*32%5En-1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show	solving the Riesel conjecture in base b = 1024 (29×32ⁿ−1 can be prime only if n is even, thus can be converted to 29×1024^n/2−1)	http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm#R1024 (note: the composite number SV_1745576 = 29×32^1745576−1 was submitted to top definitely primes in 2016 (it is a false prime and definitely composite) and had been deleted from top definitely primes, see https://web.archive.org/web/20211102171448/http://primes.utm.edu/primes/page.php?id=122375&deleted=1 and https://www.mersenneforum.org/showpost.php?p=445097&postcount=539 and https://www.mersenneforum.org/showpost.php?p=445118&postcount=543 and https://www.mersenneforum.org/showpost.php?p=445137&postcount=559 and https://www.mersenneforum.org/showpost.php?p=445153&postcount=561)

Also, the minimal primes in the families in the table "This problem covers finding the smallest prime in these families in the same base b (or proving that such prime does not exist), since the smallest prime in these families (if exists) must be a minimal prime in base b" in this "README" file for bases 2 ≤ b ≤ 36 and their lengths (in base b) and their indices in the set of the minimal primes base b are (according to this "README" file, the smallest prime in these families (if exists) must be a minimal prime in base b):

b (2 ≤ b ≤ 36)	(bⁿ−1)/(b−1) (n ≥ 2)	bⁿ+1 (n ≥ 1)	(bⁿ+1)/2 (odd b, n ≥ 2)	2×bⁿ+1 (b ≥ 3, n ≥ 1)	2×bⁿ−1 (b ≥ 3, n ≥ 1)	bⁿ+2 (b ≥ 3, n ≥ 1)	bⁿ−2 (b ≥ 3, n ≥ 2)	3×bⁿ+1 (b ≥ 4, n ≥ 1)	3×bⁿ−1 (b ≥ 4, n ≥ 1)	bⁿ+3 (b ≥ 4, n ≥ 1)	bⁿ−3 (b ≥ 4, n ≥ 2)	4×bⁿ+1 (b ≥ 5, n ≥ 1)	4×bⁿ−1 (b ≥ 5, n ≥ 1)	bⁿ+4 (b ≥ 5, n ≥ 1)	bⁿ−4 (b ≥ 5, n ≥ 2)	5×bⁿ+1 (b ≥ 6, n ≥ 1)	5×bⁿ−1 (b ≥ 6, n ≥ 1)	6×bⁿ+1 (b ≥ 7, n ≥ 1)	6×bⁿ−1 (b ≥ 7, n ≥ 1)	7×bⁿ+1 (b ≥ 8, n ≥ 1)	7×bⁿ−1 (b ≥ 8, n ≥ 1)	8×bⁿ+1 (b ≥ 9, n ≥ 1)	8×bⁿ−1 (b ≥ 9, n ≥ 1)	9×bⁿ+1 (b ≥ 10, n ≥ 1)	9×bⁿ−1 (b ≥ 10, n ≥ 1)	10×bⁿ+1 (b ≥ 11, n ≥ 1)	10×bⁿ−1 (b ≥ 11, n ≥ 1)	11×bⁿ+1 (b ≥ 12, n ≥ 1)	11×bⁿ−1 (b ≥ 12, n ≥ 1)	12×bⁿ+1 (b ≥ 13, n ≥ 1)	12×bⁿ−1 (b ≥ 13, n ≥ 1)	(b−1)×bⁿ+1 (n ≥ 1)	(b−1)×bⁿ−1 (n ≥ 1)	bⁿ+(b−1) (n ≥ 1)	bⁿ−(b−1) (n ≥ 2)
corresponding form ({x} or x{y} or {x}y or x{0}y)	{x}	x{0}y	{x}y	x{0}y	x{y}	x{0}y	{x}y	x{0}y	x{y}	x{0}y	{x}y	x{0}y	x{y}	x{0}y	{x}y	x{0}y	x{y}	x{0}y	x{y}	x{0}y	x{y}	x{0}y	x{y}	x{0}y	x{y}	x{0}y	x{y}	x{0}y	x{y}	x{0}y	x{y}	x{0}y	x{y}	x{0}y	{x}y
the value of x	1	1	(b−1)/2	2	1	1	b−1	3	2	1	b−1	4	3	1	b−1	5	4	6	5	7	6	8	7	9	8	10	9	11	10	12	11	b−1	b−2	1	b−1
the value of y	–	1	(b+1)/2	1	b−1	2	b−2	1	b−1	3	b−3	1	b−1	4	b−4	1	b−1	1	b−1	1	b−1	1	b−1	1	b−1	1	b−1	1	b−1	1	b−1	1	b−1	b−1	1
2	11 = 3 (length 2, index 1)	11 = 3 (length 2, index 1)	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	11 = 3 (length 2, index 1)	11 = 3 (length 2, index 1)	11 = 3 (length 2, index 1)	11 = 3 (length 2, index 1)
3	111 = 13 (length 3, index 3)	always divisible by 2	12 = 5 (length 2, index 1)	21 = 7 (length 2, index 2)	12 = 5 (length 2, index 1)	12 = 5 (length 2, index 1)	21 = 7 (length 2, index 2)	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	21 = 7 (length 2, index 2)	12 = 5 (length 2, index 1)	12 = 5 (length 2, index 1)	21 = 7 (length 2, index 2)
4	11 = 5 (length 2, index 1)	11 = 5 (length 2, index 1)	–	always divisible by 3	13 = 7 (length 2, index 2)	always divisible by 2	always divisible by 2	31 = 13 (length 2, index 4)	23 = 11 (length 2, index 3)	13 = 7 (length 2, index 2)	31 = 13 (length 2, index 4)	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	31 = 13 (length 2, index 4)	23 = 11 (length 2, index 3)	13 = 7 (length 2, index 2)	31 = 13 (length 2, index 4)
5	111 = 31 (length 3, index 8)	always divisible by 2	23 = 13 (length 2, index 3)	21 = 11 (length 2, index 2)	14444 = 1249 (length 5, index 16)	12 = 7 (length 2, index 1)	43 = 23 (length 2, index 6)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2	401 = 101 (length 3, index 12)	34 = 19 (length 2, index 5)	104 = 29 (length 3, index 7)	44441 = 3121 (length 5, index 20)	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	–	401 = 101 (length 3, index 12)	34 = 19 (length 2, index 5)	104 = 29 (length 3, index 7)	44441 = 3121 (length 5, index 20)
6	11 = 7 (length 2, index 1)	11 = 7 (length 2, index 1)	–	21 = 13 (length 2, index 3)	15 = 11 (length 2, index 2)	always divisible by 2	always divisible by 2	31 = 19 (length 2, index 5)	25 = 17 (length 2, index 4)	always divisible by 3	always divisible by 3	always divisible by 5	35 = 23 (length 2, index 6)	always divisible by 2 (in fact, always divisible by 4 for n ≥ 2)	always divisible by 2 (in fact, always divisible by 4)	51 = 31 (length 2, index 8)	45 = 29 (length 2, index 7)	–	–	–	–	–	–	–	–	–	–	–	–	–	–	51 = 31 (length 2, index 8)	45 = 29 (length 2, index 7)	15 = 11 (length 2, index 2)	51 = 31 (length 2, index 8)
7	11111 = 2801 (length 5, index 53)	always divisible by 2	3334 = 1201 (length 4, index 41)	always divisible by 3	16 = 13 (length 2, index 2)	always divisible by 3	65 = 47 (length 2, index 11)	always divisible by 2	always divisible by 2	always divisible by 2	always divisible by 2	41 = 29 (length 2, index 6)	always divisible by 3	14 = 11 (length 2, index 1)	always divisible by 3	always divisible by 2 (in fact, always divisible by 6)	always divisible by 2	always divisible by 2 (in fact, always divisible by 6)	always divisible by 2	61 = 43 (length 2, index 10)	56 = 41 (length 2, index 9)	–	–	–	–	–	–	–	–	–	–	–	–	61 = 43 (length 2, index 10)	56 = 41 (length 2, index 9)
8	111 = 73 (length 3, index 16)	sum-of-two-cubes factorization 8ⁿ+1 = (2ⁿ+1) × (4ⁿ−2ⁿ+1)	–	21 = 17 (length 2, index 3)	177 = 127 (length 3, index 21)	always divisible by 2	always divisible by 2	301 = 193 (length 3, index 24)	27 = 23 (length 2, index 5)	13 = 11 (length 2, index 1)	75 = 61 (length 2, index 14)	401 = 257 (length 3, index 27)	37 = 31 (length 2, index 7)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2 (in fact, always divisible by 4)	51 = 41 (length 2, index 9)	47777 = 20479 (length 5, index 58)	always divisible by 7	57 = 47 (length 2, index 11)	701 = 449 (length 3, index 39)	6777 = 3583 (length 4, index 55)	–	–	–	–	–	–	–	–	–	–	701 = 449 (length 3, index 39)	6777 = 3583 (length 4, index 55)	107 = 71 (length 3, index 15)	7₁₂1 = 8¹³−7 (length 13, index 73)
9	difference-of-two-squares factorization (9ⁿ−1)/8 = (3ⁿ−1) × (3ⁿ+1) / 8	always divisible by 2	45 = 41 (length 2, index 9)	21 = 19 (length 2, index 4)	18 = 17 (length 2, index 3)	12 = 11 (length 2, index 1)	87 = 79 (length 2, index 18)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2	always divisible by 2 (in fact, always divisible by 12)	always divisible by 2 (in fact, always divisible by 6)	41 = 37 (length 2, index 8)	difference-of-two-squares factorization 4×9ⁿ−1 = (2×3ⁿ−1) × (2×3ⁿ+1)	14 = 13 (length 2, index 2)	difference-of-two-squares factorization 9ⁿ−4 = (3ⁿ−2) × (3ⁿ+2)	always divisible by 2	always divisible by 2 (in fact, always divisible by 4)	601 = 487 (length 3, index 44)	58 = 53 (length 2, index 12)	always divisible by 2 (in fact, always divisible by 8)	always divisible by 2	81 = 73 (length 2, index 17)	78 = 71 (length 2, index 16)	–	–	–	–	–	–	–	–	81 = 73 (length 2, index 17)	78 = 71 (length 2, index 16)	18 = 17 (length 2, index 3)	81 = 73 (length 2, index 17)
10	11 = 11 (length 2, index 1)	11 = 11 (length 2, index 1)	–	always divisible by 3	19 = 19 (length 2, index 4)	always divisible by 2 (in fact, always divisible by 6)	always divisible by 2	31 = 31 (length 2, index 7)	29 = 29 (length 2, index 6)	13 = 13 (length 2, index 2)	97 = 97 (length 2, index 21)	41 = 41 (length 2, index 9)	always divisible by 3	always divisible by 2 (in fact, always divisible by 4 for n ≥ 2)	always divisible by 2 (in fact, always divisible by 12)	always divisible by 3	499 = 499 (length 3, index 30)	61 = 61 (length 2, index 14)	59 = 59 (length 2, index 13)	71 = 71 (length 2, index 16)	always divisible by 3	always divisible by 3 (in fact, always divisible by 9)	79 = 79 (length 2, index 18)	9001 = 9001 (length 4, index 56)	89 = 89 (length 2, index 20)	–	–	–	–	–	–	9001 = 9001 (length 4, index 56)	89 = 89 (length 2, index 20)	19 = 19 (length 2, index 4)	991 = 991 (length 3, index 44)
11	1₁₇ = (11¹⁷−1)/10 (length 17, index 975)	always divisible by 2	56 = 61 (length 2, index 13)	21 = 23 (length 2, index 4)	1AA = 241 (length 3, index 37)	12 = 13 (length 2, index 1)	AAA9 = 14639 (length 4, index 227)	always divisible by 2	always divisible by 2	always divisible by 2	always divisible by 2	always divisible by 5	3A = 43 (length 2, index 9)	always divisible by 5	AA7 = 1327 (length 3, index 112)	always divisible by 2 (in fact, always divisible by some element of {2²,2×3}) divisible by 2×3 if n is even, divisible by 2² if n is odd	always divisible by 2 (in fact, always divisible by some element of {2²,2×3}) divisible by 2² if n is even, divisible by 2×3 if n is odd	61 = 67 (length 2, index 14)	always divisible by 5	always divisible by 2 (in fact, always divisible by some element of {2²,2×3}) divisible by 2² if n is even, divisible by 2×3 if n is odd	always divisible by 2 (in fact, always divisible by some element of {2²,2×3}) divisible by 2×3 if n is even, divisible by 2² if n is odd	81 = 89 (length 2, index 19)	7AA = 967 (length 3, index 88)	always divisible by 2 (in fact, always divisible by 10)	always divisible by 2	A0₉1 = 10×11¹⁰+1 (length 11, index 905)	9A = 109 (length 2, index 24)	–	–	–	–	A0₉1 = 10×11¹⁰+1 (length 11, index 905)	9A = 109 (length 2, index 24)	10A = 131 (length 3, index 26)	AA1 = 1321 (length 3, index 111)
12	11 = 13 (length 2, index 1)	11 = 13 (length 2, index 1)	–	2001 = 3456 (length 4, index 58)	1B = 23 (length 2, index 4)	always divisible by 2	always divisible by 2	31 = 37 (length 2, index 7)	2BB = 431 (length 3, index 34)	always divisible by 3	always divisible by 3	401 = 577 (length 3, index 35)	3B = 47 (length 2, index 10)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2 (in fact, always divisible by 4)	51 = 61 (length 2, index 13)	4B = 59 (length 2, index 12)	61 = 73 (length 2, index 16)	5B = 71 (length 2, index 15)	701 = 1009 (length 3, index 43)	6B = 83 (length 2, index 18)	81 = 97 (length 2, index 20)	7BB = 1151 (length 3, index 51)	91 = 109 (length 2, index 24)	8B = 107 (length 2, index 23)	always divisible by 11	9BB = 1439 (length 3, index 54)	B001 = 19009 (length 4, index 84)	AB = 131 (length 2, index 27)	–	–	B001 = 19009 (length 4, index 84)	AB = 131 (length 2, index 27)	1B = 23 (length 2, index 4)	BBBB1 = 248821 (length 5, index 97)
13	11111 = 30941 (length 5, index 494)	always divisible by 2	6667 = 14281 (length 4, index 305)	always divisible by 3	1CC = 337 (length 3, index 48)	always divisible by 3	CB = 167 (length 2, index 33)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2	41 = 53 (length 2, index 10)	always divisible by 3	14 = 17 (length 2, index 1)	always divisible by 3	always divisible by 2 (in fact, always divisible by 6)	always divisible by 2 (in fact, always divisible by 4)	61 = 79 (length 2, index 16)	5CC = 1013 (length 3, index 101)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2 (in fact, always divisible by 6)	always divisible by 3	7C = 103 (length 2, index 21)	always divisible by 2	always divisible by 2 (in fact, always divisible by 4)	A1 = 131 (length 2, index 26)	always divisible by 3	always divisible by 2 (in fact, always divisible by 12)	always divisible by 2	C1 = 157 (length 2, index 31)	BCC = 2027 (length 3, index 176)	C1 = 157 (length 2, index 31)	BCC = 2027 (length 3, index 176)	10C = 181 (length 3, index 34)	CB = 167 (length 2, index 33)
14	111 = 211 (length 3, index 40)	101 = 197 (length 3, index 39)	–	21 = 29 (length 2, index 4)	1DDDD = 76831 (length 5, index 233)	always divisible by 2	always divisible by 2	31 = 43 (length 2, index 8)	2D = 41 (length 2, index 7)	13 = 17 (length 2, index 1)	DB = 193 (length 2, index 38)	always divisible by some element of {3,5} divisible by 3 if n is odd, divisible by 5 if n is even	always divisible by some element of {3,5} divisible by 3 if n is even, divisible by 5 if n is odd	always divisible by 2 (in fact, always divisible by 4 for n ≥ 2) (in fact, also always divisible by some element of {2²×3,2²×5} for n ≥ 2) divisible by 2²×3 if n ≥ 2 is odd, divisible by 2²×5 if n ≥ 2 is even	always divisible by 2 (in fact, always divisible by 4) (in fact, also always divisible by some element of {2²×3,2²×5}) divisible by 2²×3 if n is even, divisible by 2²×5 if n is odd	51 = 71 (length 2, index 14)	4D₁₉₆₉₈ = 5×14¹⁹⁶⁹⁸−1 (length 19699, index 650)	60₅1 = 6×14⁶+1 (length 7, index 468)	5D = 83 (length 2, index 17)	701 = 1373 (length 3, index 78)	6D = 97 (length 2, index 19)	81 = 113 (length 2, index 24)	7DD = 1567 (length 3, index 83)	91 = 127 (length 2, index 25)	combine of factor 5 and difference-of-two-squares factorization divisible by 5 if n is odd, 9×14ⁿ−1 = (3×14^n/2−1) × (3×14^n/2+1) if n is even	A0₅1 = 10×14⁶+1 (length 7, index 488)	9D = 139 (length 2, index 28)	always divisible by some element of {3,5} divisible by 3 if n is even, divisible by 5 if n is odd	always divisible by some element of {3,5} divisible by 3 if n is odd, divisible by 5 if n is even	always divisible by 13	BD = 167 (length 2, index 33)	D01 = 2549 (length 3, index 120)	CD = 181 (length 2, index 36)	10₁₅D = 14¹⁶+13 (length 17, index 606)	DD1 = 2731 (length 3, index 131)
15	111 = 241 (length 3, index 43)	always divisible by 2	78 = 113 (length 2, index 24)	21 = 31 (length 2, index 5)	1E = 29 (length 2, index 4)	12 = 17 (length 2, index 1)	ED = 223 (length 2, index 42)	always divisible by 2	always divisible by 2	always divisible by 2 (in fact, always divisible by 6)	always divisible by 2 (in fact, always divisible by 6)	41 = 61 (length 2, index 12)	3E = 59 (length 2, index 11)	14 = 19 (length 2, index 2)	EEB = 3371 (length 3, index 175)	always divisible by 2	always divisible by 2	always divisible by 7	5E = 89 (length 2, index 18)	always divisible by 2	always divisible by 2	801 = 1801 (length 3, index 118)	always divisible by 7	always divisible by 2	always divisible by 2	A1 = 151 (length 2, index 30)	9E = 149 (length 2, index 29)	always divisible by 2	always divisible by 2	C1 = 181 (length 2, index 36)	BE = 179 (length 2, index 35)	E1 = 211 (length 2, index 41)	DE₁₄ = 14×15¹⁴−1 (length 15, index 1252)	1E = 29 (length 2, index 4)	E1 = 211 (length 2, index 41)
16	11 = 17 (length 2, index 1)	11 = 17 (length 2, index 1)	–	always divisible by 3	1F = 31 (length 2, index 5)	always divisible by 2	always divisible by 2	301 = 769 (length 3, index 69)	2F = 47 (length 2, index 9)	13 = 19 (length 2, index 2)	FFD = 4093 (length 3, index 197)	always divisible by 5 (in fact, also Aurifeuillean factorization of x⁴+4×y⁴) 4×16ⁿ+1 = (2×4ⁿ−2×2ⁿ+1) × (2×4ⁿ+2×2ⁿ+1)	always divisible by 3 (in fact, also difference-of-two-squares factorization 4×16ⁿ−1 = (2×4ⁿ−1) × (2×4ⁿ+1)	always divisible by 2 (in fact, always divisible by 20) (in fact, also Aurifeuillean factorization of x⁴+4×y⁴) 16ⁿ+4 = (4ⁿ−2×2ⁿ+2) × (4ⁿ+2×2ⁿ+2)	always divisible by 2 (in fact, always divisible by 12) (in fact, also difference-of-two-squares factorization 16ⁿ−4 = (4ⁿ−2) × (4ⁿ+2)	always divisible by 3	4F = 79 (length 2, index 16)	61 = 97 (length 2, index 19)	always divisible by 5	71 = 113 (length 2, index 24)	always divisible by 3	always divisible by 3	7F = 127 (length 2, index 25)	always divisible by 5	difference-of-two-squares factorization 9×16ⁿ−1 = (3×4ⁿ−1) × (3×4ⁿ+1)	A001 = 40961 (length 4, index 364)	always divisible by 3	always divisible by 3	always divisible by 5	C1 = 193 (length 2, index 38)	BF = 191 (length 2, index 37)	F1 = 241 (length 2, index 47)	EF = 239 (length 2, index 46)	1F = 31 (length 2, index 5)	F1 = 241 (length 2, index 47)
17	111 = 307 (length 3, index 56)	always divisible by 2	8889 = 41761 (length 4, index 811)	20₄₆1 = 2×17⁴⁷+1 (length 48, index 10094)	1GG = 577 (length 3, index 86)	12 = 19 (length 2, index 1)	GGGGGF = 24137567 (length 6, index 4999)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2	4000001 = 96550277 (length 7, index 5138)	3G = 67 (length 2, index 12)	104 = 293 (length 3, index 55)	GGD = 4909 (length 3, index 378)	always divisible by 2	always divisible by 2 (in fact, always divisible by 4)	61 = 103 (length 2, index 20)	5G = 101 (length 2, index 19)	always divisible by 2 (in fact, always divisible by 8)	always divisible by 2	81 = 137 (length 2, index 26)	7GG = 2311 (length 3, index 209)	always divisible by 2	always divisible by 2 (in fact, always divisible by 8)	A0₁₃₅₅1 = 10×17¹³⁵⁶+1 (length 1357, index 10370)	9G₁₁₇ = 10×17¹¹⁷−1 (length 118, index 10239)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2	C01 = 3469 (length 3, index 292)	BGG = 3467 (length 3, index 291)	G0001 = 1336337 (length 5, index 3039)	FG = 271 (length 2, index 51)	1000G = 83537 (length 5, index 1348)	G₁₀F = 17¹¹−16 (length 11, index 8834)
18	11 = 19 (length 2, index 1)	11 = 19 (length 2, index 1)	–	21 = 37 (length 2, index 5)	1HH = 647 (length 3, index 66)	always divisible by 2	always divisible by 2	3001 = 17497 (length 4, index 195)	2H = 53 (length 2, index 9)	always divisible by 3	always divisible by 3	41 = 73 (length 2, index 14)	3H = 71 (length 2, index 13)	always divisible by 2 (in fact, always divisible by 4 for n ≥ 2)	always divisible by 2 (in fact, always divisible by 4)	501 = 1621 (length 3, index 83)	4H = 89 (length 2, index 17)	61 = 109 (length 2, index 22)	5H = 107 (length 2, index 21)	71 = 127 (length 2, index 24)	6HH = 2267 (length 3, index 99)	801 = 2593 (length 3, index 105)	7HH = 2591 (length 3, index 104)	91 = 163 (length 2, index 31)	8H₁₁ = 9×18¹¹−1 (length 12, index 532)	A1 = 181 (length 2, index 35)	9H = 179 (length 2, index 34)	B1 = 199 (length 2, index 39)	AH = 197 (length 2, index 38)	C01 = 3889 (length 3, index 135)	BH₈ = 12×18⁸−1 (length 9, index 517)	H1 = 307 (length 2, index 56)	GHH = 5507 (length 3, index 178)	100H = 5849 (length 4, index 185)	H1 = 307 (length 2, index 56)
19	1₁₉ = (19¹⁹−1)/18 (length 19, index 29382)	always divisible by 2	9A = 181 (length 2, index 34)	always divisible by 3	1I = 37 (length 2, index 4)	always divisible by 3	IH = 359 (length 2, index 64)	always divisible by 2	always divisible by 2	always divisible by 2	always divisible by 2	4001 = 27437 (length 4, index 748)	always divisible by 3 (in fact, also combine of factor 5 and difference-of-two-squares factorization) divisible by 5 if n is odd, 4×19ⁿ−1 = (2×19^n/2−1) × (2×19^n/2+1) if n is even	14 = 23 (length 2, index 1)	always divisible by 3 (in fact, also combine of factor 5 and difference-of-two-squares factorization) divisible by 5 if n is odd, 19ⁿ−4 = (19^n/2−2) × (19^n/2+2) if n is even	always divisible by 2 (in fact, always divisible by 6)	always divisible by 2	60₁₃1 = 6×19¹⁴+1 (length 15, index 28464)	5I = 113 (length 2, index 22)	always divisible by 2	always divisible by 2 (in fact, always divisible by 6)	always divisible by 3 (in fact, always divisible by 9)	7I = 151 (length 2, index 28)	always divisible by 2	always divisible by 2 (in fact, also combine of factor 5 and difference-of-two-squares factorization) divisible by 5 if n is odd, 9×19ⁿ−1 = (3×19^n/2−1) × (3×19^n/2+1) if n is even	A1 = 191 (length 2, index 35)	always divisible by 3 (in fact, always divisible by 9)	always divisible by 2 (in fact, always divisible by 6)	always divisible by 2	C1 = 229 (length 2, index 42)	BI = 227 (length 2, index 41)	I0₂₈1 = 18×19²⁹+1 (length 30, index 30322)	HI₆ = 18×19⁶−1 (length 7, index 17286)	1I = 37 (length 2, index 4)	II1 = 6841 (length 3, index 496)
20	111 = 421 (length 3, index 73)	101 = 401 (length 3, index 71)	–	21 = 41 (length 2, index 5)	1J₁₀ = 2×20¹⁰−1 (length 11, index 3015)	always divisible by 2	always divisible by 2	31 = 61 (length 2, index 10)	2J = 59 (length 2, index 9)	13 = 23 (length 2, index 1)	JH = 397 (length 2, index 70)	401 = 1601 (length 3, index 120)	3J = 79 (length 2, index 14)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2 (in fact, always divisible by 4)	51 = 101 (length 2, index 18)	4JJ = 1999 (length 3, index 145)	60₁₄1 = 6×20¹⁵+1 (length 16, index 3165)	5JJ = 2399 (length 3, index 157)	701 = 2801 (length 3, index 162)	6J = 139 (length 2, index 26)	always divisible by some element of {3,7} divisible by 3 if n is even, divisible by 7 if n is odd	always divisible by some element of {3,7} divisible by 3 if n is odd, divisible by 7 if n is even	91 = 181 (length 2, index 34)	8J = 179 (length 2, index 33)	A01 = 4001 (length 3, index 200)	9J = 199 (length 2, index 38)	B001 = 88001 (length 4, index 572)	AJ₈ = 11×20⁸−1 (length 9, index 2844)	C1 = 241 (length 2, index 45)	BJ = 239 (length 2, index 44)	J0₁₃1 = 19×20¹⁴+1 (length 15, index 3160)	IJ = 379 (length 2, index 67)	10J = 419 (length 3, index 72)	J₁₆1 = 20¹⁷−19 (length 17, index 3185)
21	111 = 463 (length 3, index 78)	always divisible by 2	AAAB = 97241 (length 4, index 941)	21 = 43 (length 2, index 6)	1K = 41 (length 2, index 5)	12 = 23 (length 2, index 1)	KJ = 439 (length 2, index 77)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2	always divisible by 2 (in fact, always divisible by 12)	always divisible by 2 (in fact, always divisible by 6)	always divisible by 5	3K = 83 (length 2, index 15)	always divisible by 5	KKH = 9257 (length 3, index 501)	always divisible by 2	always divisible by 2 (in fact, always divisible by 4)	61 = 127 (length 2, index 23)	always divisible by 5	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2	801 = 3529 (length 3, index 239)	7K = 167 (length 2, index 31)	always divisible by 2 (in fact, always divisible by 10)	always divisible by 2 (in fact, always divisible by 4)	A1 = 211 (length 2, index 39)	9KK = 4409 (length 3, index 288)	always divisible by 2 (in fact, always divisible by 4)	always divisible by 2 (in fact, always divisible by 10)	C0₉1 = 12×21¹⁰+1 (length 11, index 11383)	BK = 251 (length 2, index 46)	K1 = 421 (length 2, index 74)	JK = 419 (length 2, index 73)	1K = 41 (length 2, index 5)	K1 = 421 (length 2, index 74)
22	11 = 23 (length 2, index 1)	11 = 23 (length 2, index 1)	–	always divisible by 3	1L = 43 (length 2, index 6)	always divisible by 2 (in fact, always divisible by 6)	always divisible by 2	31 = 67 (length 2, index 11)	2LL = 1451 (length 3, index 127)	103 = 487 (length 3, index 85)	L₅J = 22⁶−3 (length 6, index 4633)	41 = 89 (length 2, index 16)	always divisible by 3	always divisible by 2 (in fact, always divisible by 4 for n ≥ 2)	always divisible by 2 (in fact, always divisible by 12)	always divisible by 3	4L = 109 (length 2, index 21)	always divisible by 7	5L = 131 (length 2, index 24)	701 = 3389 (length 3, index 184)	always divisible by 3	always divisible by 3	always divisible by 7	91 = 199 (length 2, index 38)	8L = 197 (length 2, index 37)	A0₁₄1 = 10×22¹⁵+1 (length 16, index 7653)	always divisible by 3	always divisible by 3	AL = 241 (length 2, index 45)	C0001 = 2811073 (length 5, index 2186)	BL = 263 (length 2, index 48)	L1 = 463 (length 2, index 82)	KL = 461 (length 2, index 81)	1L = 43 (length 2, index 6)	L1 = 463 (length 2, index 82)

Links for top (probable) primes: (also pages for the largest known prime: https://en.wikipedia.org/wiki/Largest_known_prime_number, https://en.wikipedia.org/wiki/List_of_largest_known_primes_and_probable_primes, http://www.numericana.com/answer/primes.htm#history, and related pages: https://web.archive.org/web/20210416051711/https://en.wikipedia.org/wiki/Titanic_prime, https://web.archive.org/web/20210219091535/https://en.wikipedia.org/wiki/Gigantic_prime, https://en.wikipedia.org/wiki/Megaprime, https://t5k.org/glossary/xpage/TitanicPrime.html, https://t5k.org/glossary/xpage/GiganticPrime.html, https://t5k.org/glossary/xpage/Megaprime.html, https://www.rieselprime.de/ziki/Titanic_prime, https://www.rieselprime.de/ziki/Gigantic_prime, https://www.rieselprime.de/ziki/Megaprime, https://www.rieselprime.de/ziki/Gigaprime, https://mathworld.wolfram.com/TitanicPrime.html, https://mathworld.wolfram.com/GiganticPrime.html, titanic primes are the primes with ≥ 1000 decimal digits, gigantic primes are the primes with ≥ 10000 decimal digits, megaprimes are the primes with ≥ 1000000 decimal digits, bevaprimes (also called gigaprimes) are the primes with ≥ 1000000000 decimal digits)

https://t5k.org/primes/lists/all.txt (top definitely primes)
https://t5k.org/primes/lists/all.zip (top definitely primes, zipped file)
https://t5k.org/primes/lists/short.txt (definitely primes with ≥ 800000 decimal digits)
https://t5k.org/primes/search.php?OnList=all&Number=1000000&Style=HTML (all numbers in the list of top definitely primes, html version)
https://t5k.org/primes/search.php?OnList=all&Number=1000000 (all numbers in the list of top definitely primes, text version)
https://t5k.org/primes/ (index of top definitely primes)
https://t5k.org/primes/download.php (download page of top definitely primes)
https://t5k.org/primes/status.php (primes (if any) which are currently awaiting verificiation (of any age) as well as those modified (for any reason) in the last 72 hours for top definitely primes)
https://t5k.org/primes/status.php?hours=1000 (primes (if any) which are currently awaiting verificiation (of any age) as well as those modified (for any reason) in the last 1000 hours for top definitely primes)
https://t5k.org/primes/status.php?hours=0 (primes (if any) which are currently awaiting verificiation (of any age) for top definitely primes)
https://t5k.org/largest.html (the information page of top definitely primes)
https://t5k.org/notes/by_year.html (the information page of the largest known prime by year)
https://t5k.org/notes/faq/why.html (the information page of why do people find these large primes)
https://t5k.org/primes/search.php (the search page of top definitely primes)
https://t5k.org/primes/search.php?Advanced=1 (the advanced search page of top definitely primes)
https://t5k.org/primes/page.php (the search page of top definitely primes for a single prime, searching by database ID and/or prime rank and/or prime description)
https://t5k.org/primes/help/search_description.php (examples of advanced search page of top definitely primes)
https://t5k.org/primes/search_proth.php (the search page of top definitely primes of the form k×bⁿ±1)
https://t5k.org/top20/index.php (index of the top 20 definitely primes of certain selected forms)
https://t5k.org/top20/home.php (the home page of the top 20 definitely primes of certain selected forms)
https://t5k.org/top20/search.php (the search page of the top 20 definitely primes of certain selected forms)
https://t5k.org/top20/sizes.php (currently smallest allowed size (i.e. smallest allowed number of decimal digits) of the top 20 definitely primes of each certain selected form)
https://t5k.org/bios/submission.php (submit page of top definitely primes)
https://t5k.org/bios/newprover.php (submit page of top definitely primes, create a new prover account)
https://t5k.org/bios/newcode.php (submit page of top definitely primes, create a new prover code)
https://t5k.org/bios/index.php (index of the provers and programs and projects of top definitely primes)
https://t5k.org/bios/search.php (the search page of the provers and programs and projects of top definitely primes)
https://t5k.org/bios/help/program_does.php (the help page for some explanation of the programs of top definitely primes)
https://t5k.org/bios/top20.php?type=person&by=PrimesRank (top 20 persons of top definitely primes sorted by number of primes)
https://t5k.org/bios/top20.php?type=person&by=ScoreRank (top 20 persons of top definitely primes sorted by score)
https://t5k.org/bios/top20.php?type=person&by=ScoreNormal (top 20 persons of top definitely primes sorted by normalized score)
https://t5k.org/bios/top20.php?type=program&by=PrimesRank (top 20 programs of top definitely primes sorted by number of primes)
https://t5k.org/bios/top20.php?type=program&by=ScoreRank (top 20 programs of top definitely primes sorted by score)
https://t5k.org/bios/top20.php?type=program&by=ScoreNormal (top 20 programs of top definitely primes sorted by normalized score)
https://t5k.org/bios/top20.php?type=project&by=PrimesRank (top 20 projects of top definitely primes sorted by number of primes)
https://t5k.org/bios/top20.php?type=project&by=ScoreRank (top 20 projects of top definitely primes sorted by score)
https://t5k.org/bios/top20.php?type=project&by=ScoreNormal (top 20 projects of top definitely primes sorted by normalized score)
http://www.primenumbers.net/prptop/prptop.php (top probable primes)
http://www.primenumbers.net/prptop/latest.php (recently found top probable primes)
http://www.primenumbers.net/prptop/searchform.php?form=%3F&action=Search (all numbers in the list of top probable primes)
http://www.primenumbers.net/prptop/searchform.php (search page of top probable primes)
http://www.primenumbers.net/prptop/submit.php (submit page of top probable primes)
http://www.primenumbers.net/prptop/topdisc.php (index of the provers of top probable primes)

and the search result page for the top (probable) primes of special forms: (note: a large prime of the form (a×bⁿ+c)/d with small a, b, c, d and large n can be easily proven prime if and only if c = ±1 and d = 1)

(Note: The top definitely primes page converts the perfect power (https://oeis.org/A001597, https://en.wikipedia.org/wiki/Perfect_power, https://mathworld.wolfram.com/PerfectPower.html, https://www.numbersaplenty.com/set/perfect_power/) bases (i.e. b = m^r with r > 1) to their "ground bases" (https://oeis.org/A052410) (i.e. b = m), i.e. the bases are normalized, e.g. it converts the prime 2805222×25^2805222+1 to 2805222×5^5610444+1 (i.e. converts base 25 = 5² to base 5) (see https://t5k.org/primes/page.php?id=129893 for the entry of this prime in the top definitely primes page), and it converts the prime 2622×121⁸¹⁰⁹⁶⁰−1 to 2622×11^1621920−1 (i.e. converts base 121 = 11² to base 11) (see https://t5k.org/primes/page.php?id=119929 for the entry of this prime in the top definitely primes page), thus do not search the perfect power bases in the top definitely primes page (otherwise, you will find nothing!), see https://www.mersenneforum.org/showpost.php?p=121374&postcount=1 and https://www.mersenneforum.org/showpost.php?p=656659&postcount=1, however, unlike the top definitely primes page, the top probable primes page does not convert, e.g. it has the probable primes (16^1025393+1)/17 (see http://www.primenumbers.net/prptop/searchform.php?form=%2816%5E1025393%2B1%29%2F17&action=Search for the entry of this probable prime in the top probable primes page) and (9⁸⁶⁰⁰²⁹+1)/10 (see http://www.primenumbers.net/prptop/searchform.php?form=%289%5E860029%2B1%29%2F10&action=Search for the entry of this probable prime in the top probable primes page), and does not convert base 16 = 2⁴ to base 2 and and does not convert base 9 = 3² to base 3, thus of course you can search the perfect power bases in the top probable primes page (unlike the top definitely primes page))

Definitely primes (i.e. c = ±1 and d = 1):

bⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
bⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×bⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*[[:digit:]]%7B1,%7D%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×bⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*[[:digit:]]%7B1,%7D%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×2ⁿ+1 (which includes a×4ⁿ+1, a×8ⁿ+1, a×16ⁿ+1, a×32ⁿ+1) (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*2%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×2ⁿ−1 (which includes a×4ⁿ−1, a×8ⁿ−1, a×16ⁿ−1, a×32ⁿ−1) (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*2%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×3ⁿ+1 (which includes a×9ⁿ+1, a×27ⁿ+1) (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*3%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×3ⁿ−1 (which includes a×9ⁿ−1, a×27ⁿ−1) (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*3%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×5ⁿ+1 (which includes a×25ⁿ+1) (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*5%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×5ⁿ−1 (which includes a×25ⁿ−1) (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*5%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×6ⁿ+1 (which includes a×36ⁿ+1) (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*6%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×6ⁿ−1 (which includes a×36ⁿ−1) (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*6%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×7ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*7%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×7ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*7%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×10ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*10%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×10ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*10%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×11ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*11%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×11ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*11%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×12ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*12%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×12ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*12%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×13ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*13%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×13ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*13%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×14ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*14%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×14ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*14%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×15ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*15%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×15ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*15%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×17ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*17%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×17ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*17%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×18ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*18%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×18ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*18%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×19ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*19%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×19ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*19%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×20ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*20%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×20ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*20%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×21ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*21%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×21ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*21%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×22ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*22%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×22ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*22%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×23ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*23%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×23ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*23%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×24ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*24%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×24ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*24%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×26ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*26%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×26ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*26%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×28ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*28%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×28ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*28%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×29ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*29%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×29ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*29%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×30ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*30%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×30ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*30%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×31ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*31%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×31ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*31%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×33ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*33%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×33ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*33%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×34ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*34%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×34ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*34%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
a×35ⁿ+1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*35%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000&Style=HTML
a×35ⁿ−1 (html version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*35%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000&Style=HTML
bⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
bⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×bⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*[[:digit:]]%7B1,%7D%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×bⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*[[:digit:]]%7B1,%7D%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×2ⁿ+1 (which includes a×4ⁿ+1, a×8ⁿ+1, a×16ⁿ+1, a×32ⁿ+1) (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*2%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×2ⁿ−1 (which includes a×4ⁿ−1, a×8ⁿ−1, a×16ⁿ−1, a×32ⁿ−1) (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*2%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×3ⁿ+1 (which includes a×9ⁿ+1, a×27ⁿ+1) (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*3%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×3ⁿ−1 (which includes a×9ⁿ−1, a×27ⁿ−1) (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*3%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×5ⁿ+1 (which includes a×25ⁿ+1) (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*5%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×5ⁿ−1 (which includes a×25ⁿ−1) (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*5%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×6ⁿ+1 (which includes a×36ⁿ+1) (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*6%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×6ⁿ−1 (which includes a×36ⁿ−1) (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*6%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×7ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*7%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×7ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*7%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×10ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*10%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×10ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*10%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×11ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*11%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×11ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*11%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×12ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*12%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×12ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*12%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×13ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*13%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×13ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*13%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×14ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*14%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×14ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*14%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×15ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*15%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×15ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*15%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×17ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*17%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×17ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*17%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×18ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*18%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×18ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*18%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×19ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*19%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×19ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*19%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×20ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*20%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×20ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*20%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×21ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*21%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×21ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*21%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×22ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*22%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×22ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*22%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×23ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*23%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×23ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*23%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×24ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*24%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×24ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*24%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×26ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*26%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×26ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*26%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×28ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*28%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×28ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*28%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×29ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*29%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×29ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*29%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×30ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*30%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×30ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*30%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×31ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*31%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×31ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*31%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×33ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*33%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×33ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*33%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×34ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*34%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×34ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*34%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×35ⁿ+1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*35%5E[[:digit:]]%7B1,%7D%2B1$&OnList=all&Number=1000000
a×35ⁿ−1 (text version): https://t5k.org/primes/search.php?Description=^[[:digit:]]%7B1,%7D*35%5E[[:digit:]]%7B1,%7D-1$&OnList=all&Number=1000000
a×2ⁿ±1 (which includes a×4ⁿ±1, a×8ⁿ±1, a×16ⁿ±1, a×32ⁿ±1) (text version): https://t5k.org/primes/search_proth.php?base=2&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×3ⁿ±1 (which includes a×9ⁿ±1, a×27ⁿ±1) (text version): https://t5k.org/primes/search_proth.php?base=3&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×5ⁿ±1 (which includes a×25ⁿ±1) (text version): https://t5k.org/primes/search_proth.php?base=5&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×6ⁿ±1 (which includes a×36ⁿ±1) (text version): https://t5k.org/primes/search_proth.php?base=6&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×7ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=7&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×10ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=10&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×11ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=11&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×12ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=12&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×13ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=13&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×14ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=14&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×15ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=15&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×17ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=17&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×18ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=18&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×19ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=19&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×20ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=20&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×21ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=21&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×22ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=22&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×23ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=23&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×24ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=24&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×26ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=26&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×28ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=28&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×29ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=29&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×30ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=30&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×31ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=31&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×33ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=33&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×34ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=34&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search
a×35ⁿ±1 (text version): https://t5k.org/primes/search_proth.php?base=35&min_k=&max_k=&min_n=&max_n=&plus=on&minus=on&number=1000000&search=Start+Search

Probable primes (i.e. c ≠ ±1 or/and d ≠ 1):

Index pages of searching the primes of the form (a×bⁿ+c)/gcd(a+c,b−1):

Index pages of factoring the numbers of the form (a×bⁿ+c)/gcd(a+c,b−1):

https://homes.cerias.purdue.edu/~ssw/cun/index.html
https://maths-people.anu.edu.au/~brent/factors.html
http://myfactors.mooo.com/
https://web.archive.org/web/20190315214330/http://cage.ugent.be/~jdemeyer/cunningham/
https://www.mersenne.org/
https://www.mersenne.ca/
https://mers.sourceforge.io/mersenne.html
http://www.fermatsearch.org/
http://www.prothsearch.com/ (section "Fermat numbers")
https://web.archive.org/web/20211011120227/http://mprime.s3-website.us-west-1.amazonaws.com/
http://www.doublemersennes.org/
https://web.archive.org/web/20231126215849/http://bearnol.is-a-geek.com/Mersenneplustwo/Mersenneplustwo.html (warning: currently it is still unknown whether the number 2^2¹²⁷−1−1 is prime, in fact, many subpages in https://web.archive.org/web/20151025022357/http://www.bearnol.pwp.blueyonder.co.uk/Math/ (including https://web.archive.org/web/20151025022406/http://www.bearnol.pwp.blueyonder.co.uk/Math/mmprime.html) are only hoaxes (although some subpages are not), e.g. Riemann hypothesis (https://en.wikipedia.org/wiki/Riemann_hypothesis, https://t5k.org/glossary/xpage/RiemannHypothesis.html, https://mathworld.wolfram.com/RiemannHypothesis.html, http://www.numericana.com/answer/open.htm#rh) and abc conjecture (https://en.wikipedia.org/wiki/Abc_conjecture, https://mathworld.wolfram.com/abcConjecture.html, http://www.numericana.com/answer/open.htm#abc) and Collatz conjecture (https://en.wikipedia.org/wiki/Collatz_conjecture, https://mathworld.wolfram.com/CollatzProblem.html, http://www.numericana.com/answer/open.htm#collatz, https://oeis.org/A006370, https://oeis.org/A070165, https://oeis.org/A006577, https://oeis.org/A006877, https://oeis.org/A006878, https://oeis.org/A025586, https://oeis.org/A006884, https://oeis.org/A006885) and Beal's conjecture (https://en.wikipedia.org/wiki/Beal_conjecture, https://t5k.org/glossary/xpage/BealsConjecture.html, https://mathworld.wolfram.com/BealsConjecture.html) and Goldbach's conjecture (https://en.wikipedia.org/wiki/Goldbach%27s_conjecture, https://t5k.org/glossary/xpage/GoldbachConjecture.html, https://mathworld.wolfram.com/GoldbachConjecture.html, http://www.numericana.com/answer/open.htm#goldbach, https://oeis.org/A045917, https://oeis.org/A035026, https://oeis.org/A002375, https://oeis.org/A002372) and twin prime conjecture (https://en.wikipedia.org/wiki/Twin_prime_conjecture, https://t5k.org/glossary/xpage/TwinPrimeConjecture.html, https://mathworld.wolfram.com/TwinPrimeConjecture.html, http://www.numericana.com/answer/open.htm#twin, https://oeis.org/A001097, https://oeis.org/A077800, https://oeis.org/A001359, https://oeis.org/A006512) are currently still unsolved problems, but this page has false proofs of Riemann hypothesis and Collatz conjecture and Beal's conjecture and twin prime conjecture, and has false disproofs of abc conjecture and Goldbach's conjecture, also, the Catalan-Mersenne number conjecture (https://en.wikipedia.org/wiki/Catalan%E2%80%93Mersenne_number_conjecture, https://mathworld.wolfram.com/Catalan-MersenneNumber.html, https://t5k.org/mersenne/index.html#c, https://oeis.org/A007013) is currently still an unsolved problem, it is still unknown whether the number 2^2¹²⁷−1−1 is prime, and the New Mersenne conjecture (https://en.wikipedia.org/wiki/New_Mersenne_conjecture, https://t5k.org/glossary/xpage/NewMersenneConjecture.html, https://mathworld.wolfram.com/NewMersennePrimeConjecture.html, https://t5k.org/mersenne/NewMersenneConjecture.html, http://www.hoegge.dk/mersenne/NMC.html, http://www.primenumbers.net/rl/nmc/, https://web.archive.org/web/20010809112857/http://orca.st.usm.edu/~cwcurry/NMC.html, https://web.archive.org/web/20211128180850/http://mprime.s3-website.us-west-1.amazonaws.com/new_mersenne_conjecture.html, https://oeis.org/A107360, https://oeis.org/A122834, https://oeis.org/A120334) is currently also still an unsolved problem, however, it is known that the Catalan-Mersenne number conjecture and the New Mersenne conjecture is not both true, i.e. at least one of them is false, since the prime 886407410000361345663448535540258622490179142922169401 divides the number (2^2¹²⁷−1+1)/3 (this prime factor is found by trial division, all prime factors of (2^2¹²⁷−1+1)/3 and all prime factors of 2^2¹²⁷−1−1 are == 1 mod 2×(2¹²⁷−1)), see https://www.mersenneforum.org/showpost.php?p=549829&postcount=1 and https://t5k.org/curios/cpage/40578.html)
https://web.archive.org/web/20130530210800/http://www.euronet.nl/users/bota/medium-p.htm
https://stdkmd.net/
https://kurtbeschorner.de/
https://repunit-koide.jimdofree.com/
https://gmplib.org/~tege/repunit.html
https://web.archive.org/web/20070708171301/http://www.ludwigsgymnasium.de/unterr/mathe/prim/zehnp.htm
http://chesswanks.com/pxp/repfactors.html
https://alfredreichlg.de/
https://web.archive.org/web/20021001222643/http://www.users.globalnet.co.uk/~aads/index.html
http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/index.htm
http://mklasson.com/factors/index.php
https://cs.stanford.edu/people/rpropper/math/factors/3n-2.txt
https://web.archive.org/web/20020320010222/http://proth.cjb.net/
https://brnikat.com/nums/index.html
https://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/index.htm
https://www.lirmm.fr/~ochem/opn/
https://web.archive.org/web/20120426061657/http://oddperfect.org/
https://web.archive.org/web/20190211112446/http://home.earthlink.net/~elevensmooth/
https://2721.hddkillers.com/
https://web.archive.org/web/20081006071311/http://www-staff.maths.uts.edu.au/~rons/fact/fact.htm
https://homes.cerias.purdue.edu/~ssw/bell/index.html
http://www.loria.fr/~zimmerma/ecmnet/ (finding the factors of the numbers)
https://www.rechenkraft.net/yoyo/ (finding the factors of the numbers)
http://escatter11.fullerton.edu/nfs/ (finding the factors of the numbers)

OEIS sequences for the exponents n for the primes in given families in given base b (only list those for families {x}, x{y}, {x}y, x{0}y (where x and y are any digits in base b), since the smallest prime in these families must be minimal primes in the same base b (except the cases that the repeating digit (i.e. y in x{y}, or x in {x}y) is 1), also only count the primes > b):

base b = 2:

1{0}1: https://oeis.org/A019434 (corresponding primes), https://oeis.org/A092506 (corresponding primes, with an additional prime 2)
{1}: https://oeis.org/A000043, https://oeis.org/A090748 (n replaced by n−1), https://oeis.org/A000668 (corresponding primes)

base b = 3:

1{0}2: https://oeis.org/A051783, https://oeis.org/A057735 (corresponding primes, with an additional prime 3)
{1}: https://oeis.org/A028491, https://oeis.org/A090747 (n replaced by n−1), https://oeis.org/A076481 (corresponding primes)
{1}2: https://oeis.org/A171381, https://oeis.org/A093625 (corresponding primes, with an additional prime 2)
1{2}: https://oeis.org/A003307, https://oeis.org/A079363 (corresponding primes)
2{0}1: https://oeis.org/A003306, https://oeis.org/A216888 (n replaced by n−1), https://oeis.org/A111974 (corresponding primes, with an additional prime 3)
{2}1: https://oeis.org/A014224, https://oeis.org/A014232 (corresponding primes)

base b = 4:

1{0}1: https://oeis.org/A222008 (corresponding primes), https://oeis.org/A019434 (corresponding primes, with an additional prime 3), https://oeis.org/A092506 (corresponding primes, with two additional primes 2 and 3)
1{0}3: https://oeis.org/A089437, https://oeis.org/A228026 (corresponding primes)
{1}3: https://oeis.org/A261539
1{3}: https://oeis.org/A146768, https://oeis.org/A090748 (n replaced by 2×n, with an additional term 1), https://oeis.org/A000043 (n replaced by 2×n+1, with an additional term 2), https://oeis.org/A000668 (corresponding primes, with an additional prime 3)
{2}3: https://oeis.org/A127936, https://oeis.org/A000978 (n replaced by 2×n+1), https://oeis.org/A000979 (corresponding primes, with an additional prime 3)
2{3}: https://oeis.org/A272057
3{0}1: https://oeis.org/A326655
{3}1: https://oeis.org/A059266, https://oeis.org/A135535 (corresponding primes)

base b = 5:

1{0}2: https://oeis.org/A087885, https://oeis.org/A182330 (corresponding primes, with an additional prime 3)
1{0}4: https://oeis.org/A124621, https://oeis.org/A228028 (corresponding primes, with an additional prime 5)
{1}: https://oeis.org/A004061, https://oeis.org/A086123 (n replaced by n−1), https://oeis.org/A086122 (corresponding primes)
1{4}: https://oeis.org/A120375, https://oeis.org/A120376 (corresponding primes)
2{0}1: https://oeis.org/A058934, https://oeis.org/A205771 (corresponding primes, with an additional prime 3)
3{4}: https://oeis.org/A046865
4{0}1: https://oeis.org/A204322
{4}1: https://oeis.org/A059613, https://oeis.org/A181285 (corresponding primes)
{4}3: https://oeis.org/A109080, https://oeis.org/A204578 (corresponding primes, with an additional prime 3)

base b = 6:

1{0}1: https://oeis.org/A182331 (corresponding primes, with an additional prime 2)
1{0}5: https://oeis.org/A145106, https://oeis.org/A104118 (corresponding primes)
{1}: https://oeis.org/A004062, https://oeis.org/A165210 (corresponding primes)
1{5}: https://oeis.org/A057472, https://oeis.org/A319535 (corresponding primes)
2{0}1: https://oeis.org/A120023, https://oeis.org/A205776 (corresponding primes, with an additional prime 3)
2{5}: https://oeis.org/A186106, https://oeis.org/A186104 (corresponding primes, with an additional prime 2)
3{0}1: https://oeis.org/A186112, https://oeis.org/A186105 (corresponding primes)
{4}5: https://oeis.org/A248613
4{5}: https://oeis.org/A079906
5{0}1: https://oeis.org/A247260
{5}1: https://oeis.org/A059614, https://oeis.org/A290008 (corresponding primes)

base b = 7:

1{0}4: https://oeis.org/A096305, https://oeis.org/A104065 (corresponding primes, with an additional prime 5)
1{0}6: https://oeis.org/A217130, https://oeis.org/A228030 (corresponding primes, with an additional prime 7)
{1}: https://oeis.org/A004063, https://oeis.org/A102170 (corresponding primes)
1{6}: https://oeis.org/A002959, https://oeis.org/A158795 (corresponding primes)
4{0}1: https://oeis.org/A204323
5{6}: https://oeis.org/A046866
6{0}1: https://oeis.org/A245241
{6}1: https://oeis.org/A191469, https://oeis.org/A291861 (corresponding primes)
{6}5: https://oeis.org/A090669, https://oeis.org/A093612 (corresponding primes, with an additional prime 5)

base b = 8:

1{0}3: https://oeis.org/A217354, https://oeis.org/A228032 (corresponding primes)
1{0}5: https://oeis.org/A217355, https://oeis.org/A228033 (corresponding primes)
1{0}7: https://oeis.org/A217381, https://oeis.org/A144360 (corresponding primes)
1{7}: https://oeis.org/A216518 (n replaced by 3×n+1, with an additional term 3)
3{7}: https://oeis.org/A216519 (n replaced by 3×n+2)
6{7}: https://oeis.org/A268061
7{0}1: https://oeis.org/A269544
{7}1: https://oeis.org/A217380
{7}3: https://oeis.org/A217356
{7}5: https://oeis.org/A217353

base b = 9:

1{0}2: https://oeis.org/A090649, https://oeis.org/A228034 (corresponding primes, with an additional prime 3)
1{0}4: https://oeis.org/A217384
1{0}8: https://oeis.org/A217385
1{4}: https://oeis.org/A090747 (n replaced by 2×n), https://oeis.org/A028491 (n replaced by 2×n+1), https://oeis.org/A076481 (corresponding primes)
2{0}1: https://oeis.org/A056802
4{0}1: https://oeis.org/A056801
{4}5: https://oeis.org/A093625 (corresponding primes, with two additional primes 2 and 5)
6{0}1: https://oeis.org/A056800
{6}7: https://oeis.org/A007658 (n replaced by 2×n+1), https://oeis.org/A111010 (corresponding primes, with two additional primes 2 and 7)
7{8}: https://oeis.org/A268356
8{0}1: https://oeis.org/A056799
{8}1: https://oeis.org/A177093, https://oeis.org/A177094 (corresponding primes)
{8}7: https://oeis.org/A128455

base b = 10:

1{0}3: https://oeis.org/A049054, https://oeis.org/A159352 (corresponding primes)
1{0}7: https://oeis.org/A088274, https://oeis.org/A159031 (corresponding primes)
1{0}9: https://oeis.org/A088275
{1}: https://oeis.org/A004023, https://oeis.org/A004022 (corresponding primes)
{1}3: https://oeis.org/A097683, https://oeis.org/A056654 (n replaced by n−1), https://oeis.org/A093011 (corresponding primes, with an additional prime 3)
{1}7: https://oeis.org/A097684, https://oeis.org/A056655 (n replaced by n−1), https://oeis.org/A093139 (corresponding primes, with an additional prime 7)
{1}9: https://oeis.org/A097685, https://oeis.org/A056659 (n replaced by n−1), https://oeis.org/A093400 (corresponding primes)
1{3}: https://oeis.org/A056698, https://oeis.org/A093671 (corresponding primes)
1{7}: https://oeis.org/A089147, https://oeis.org/A088465 (corresponding primes)
1{9}: https://oeis.org/A002957, https://oeis.org/A055558 (corresponding primes)
2{0}3: https://oeis.org/A081677, https://oeis.org/A177134 (corresponding primes, with an additional prime 5)
2{0}9: https://oeis.org/A101392
2{1}: https://oeis.org/A056700, https://oeis.org/A068814 (corresponding primes, with an additional prime 2)
{2}1: https://oeis.org/A084832, https://oeis.org/A056660 (n replaced by n−1), https://oeis.org/A091189 (corresponding primes)
{2}3: https://oeis.org/A096506, https://oeis.org/A056656 (n replaced by n−1), https://oeis.org/A093162 (corresponding primes, with an additional prime 3)
{2}7: https://oeis.org/A099409, https://oeis.org/A056677 (n replaced by n−1), https://oeis.org/A093167 (corresponding primes, with an additional prime 7)
{2}9: https://oeis.org/A099410, https://oeis.org/A056678 (n replaced by n−1), https://oeis.org/A093401 (corresponding primes)
2{3}: https://oeis.org/A056701, https://oeis.org/A093672 (corresponding primes, with an additional prime 2)
2{7}: https://oeis.org/A056702, https://oeis.org/A093938 (corresponding primes, with an additional prime 2)
2{9}: https://oeis.org/A056703, https://oeis.org/A055559 (corresponding primes, with an additional prime 2)
3{0}1: https://oeis.org/A056807, https://oeis.org/A259866 (corresponding primes)
3{0}7: https://oeis.org/A100501
3{1}: https://oeis.org/A056704, https://oeis.org/A068813 (corresponding primes)
{3}1: https://oeis.org/A055557, https://oeis.org/A055520 (n replaced by n−1), https://oeis.org/A123568 (corresponding primes)
{3}7: https://oeis.org/A099411, https://oeis.org/A056680 (n replaced by n−1), https://oeis.org/A093168 (corresponding primes, with an additional prime 7)
3{7}: https://oeis.org/A056705, https://oeis.org/A093939 (corresponding primes, with an additional prime 3)
4{0}1: https://oeis.org/A056806, https://oeis.org/A177506 (corresponding primes, with an additional prime 5)
4{0}3: https://oeis.org/A101397, https://oeis.org/A177507 (corresponding primes, with an additional prime 7)
4{0}7: https://oeis.org/A101395
4{0}9: https://oeis.org/A101394
4{1}: https://oeis.org/A056706, https://oeis.org/A068815 (corresponding primes)
4{3}: https://oeis.org/A056707, https://oeis.org/A093673 (corresponding primes)
{4}1: https://oeis.org/A099412, https://oeis.org/A056681 (n replaced by n−1), https://oeis.org/A093174 (corresponding primes)
{4}3: https://oeis.org/A096845, https://oeis.org/A056661 (n replaced by n−1), https://oeis.org/A093163 (corresponding primes, with an additional prime 3)
{4}7: https://oeis.org/A099413, https://oeis.org/A056682 (n replaced by n−1), https://oeis.org/A092480 (corresponding primes, with an additional prime 7)
{4}9: https://oeis.org/A099414, https://oeis.org/A056683 (n replaced by n−1), https://oeis.org/A093402 (corresponding primes)
4{7}: https://oeis.org/A056708, https://oeis.org/A093940 (corresponding primes)
4{9}: https://oeis.org/A056712, https://oeis.org/A093945 (corresponding primes)
5{0}3: https://oeis.org/A096254, https://oeis.org/A177120 (corresponding primes)
5{0}9: https://oeis.org/A103004
5{1}: https://oeis.org/A056713, https://oeis.org/A068816 (corresponding primes)
5{3}: https://oeis.org/A056714, https://oeis.org/A093674 (corresponding primes, with an additional prime 5)
{5}1: https://oeis.org/A099415, https://oeis.org/A056684 (n replaced by n−1)
{5}3: https://oeis.org/A099416, https://oeis.org/A056685 (n replaced by n−1), https://oeis.org/A093164 (corresponding primes, with an additional prime 3)
{5}7: https://oeis.org/A099417, https://oeis.org/A056686 (n replaced by n−1), https://oeis.org/A093169 (corresponding primes, with an additional prime 7)
{5}9: https://oeis.org/A099418, https://oeis.org/A056687 (n replaced by n−1), https://oeis.org/A093403 (corresponding primes)
5{7}: https://oeis.org/A056715, https://oeis.org/A093941 (corresponding primes, with an additional prime 5)
5{9}: https://oeis.org/A056716, https://oeis.org/A093946 (corresponding primes, with an additional prime 5)
6{0}1: https://oeis.org/A056805, https://oeis.org/A177132 (corresponding primes, with an additional prime 7)
6{0}7: https://oeis.org/A103026
6{1}: https://oeis.org/A056717, https://oeis.org/A093631 (corresponding primes)
{6}1: https://oeis.org/A098088, https://oeis.org/A056658 (n replaced by n−1), https://oeis.org/A092571 (corresponding primes)
{6}7: https://oeis.org/A096507, https://oeis.org/A056657 (n replaced by n−1), https://oeis.org/A093170 (corresponding primes, with an additional prime 7)
6{7}: https://oeis.org/A056718, https://oeis.org/A093942 (corresponding primes)
7{0}1: https://oeis.org/A056804
7{0}3: https://oeis.org/A097970
7{0}9: https://oeis.org/A097954
7{1}: https://oeis.org/A056719, https://oeis.org/A093632 (corresponding primes, with an additional prime 7)
7{3}: https://oeis.org/A056720, https://oeis.org/A093675 (corresponding primes, with an additional prime 7)
{7}1: https://oeis.org/A099419, https://oeis.org/A056688 (n replaced by n−1), https://oeis.org/A093176 (corresponding primes)
{7}3: https://oeis.org/A099420, https://oeis.org/A056689 (n replaced by n−1), https://oeis.org/A093165 (corresponding primes, with an additional prime 3)
{7}9: https://oeis.org/A098089, https://oeis.org/A056693 (n replaced by n−1), https://oeis.org/A093404 (corresponding primes)
7{9}: https://oeis.org/A056721, https://oeis.org/A093947 (corresponding primes, with an additional prime 7)
8{0}3: https://oeis.org/A103069
8{0}9: https://oeis.org/A103070
8{1}: https://oeis.org/A056722, https://oeis.org/A093633 (corresponding primes)
8{3}: https://oeis.org/A056723, https://oeis.org/A093676 (corresponding primes)
8{7}: https://oeis.org/A056724, https://oeis.org/A093943 (corresponding primes)
{8}1: https://oeis.org/A099421, https://oeis.org/A056664 (n replaced by n−1), https://oeis.org/A092675 (corresponding primes)
{8}3: https://oeis.org/A099422, https://oeis.org/A056694 (n replaced by n−1), https://oeis.org/A093166 (corresponding primes, with an additional prime 3)
{8}7: https://oeis.org/A096846, https://oeis.org/A056695 (n replaced by n−1), https://oeis.org/A093171 (corresponding primes, with an additional prime 7)
{8}9: https://oeis.org/A096508, https://oeis.org/A056663 (n replaced by n−1), https://oeis.org/A093405 (corresponding primes)
8{9}: https://oeis.org/A056725, https://oeis.org/A093948 (corresponding primes)
9{0}1: https://oeis.org/A056797
9{0}7: https://oeis.org/A096774
9{1}: https://oeis.org/A056726, https://oeis.org/A093634 (corresponding primes)
9{7}: https://oeis.org/A056727, https://oeis.org/A093944 (corresponding primes)
{9}1: https://oeis.org/A095714, https://oeis.org/A056696 (n replaced by n−1), https://oeis.org/A093177 (corresponding primes)
{9}7: https://oeis.org/A089675, https://oeis.org/A056662 (n replaced by n−1), https://oeis.org/A093172 (corresponding primes, with an additional prime 7)

base b = 11:

1{0}2: https://oeis.org/A109076
{1}: https://oeis.org/A005808
1{A}: https://oeis.org/A120378, https://oeis.org/A120377 (corresponding primes)
2{0}1: https://oeis.org/A141774
9{A}: https://oeis.org/A046867
A{0}1: https://oeis.org/A057462
{A}9: https://oeis.org/A133982, https://oeis.org/A133858 (corresponding primes)

base b = 12:

base b = 13:

base b = 14:

base b = 15:

base b = 16:

1{0}1: https://oeis.org/A222008 (corresponding primes, with an additional prime 5), https://oeis.org/A019434 (corresponding primes, with two additional primes 3 and 5), https://oeis.org/A092506 (corresponding primes, with three additional primes 2 and 3 and 5)
1{F}: https://oeis.org/A145040 (n replaced by 4×n+1), https://oeis.org/A112634 (n replaced by 4×n+1, with an additional term 2)
7{F}: https://oeis.org/A112633 (n replaced by 4×n+3)
{A}B: https://oeis.org/A361563 (n replaced by 4×n+1)

base b = 17:

base b = 18:

{1}: https://oeis.org/A133857

base b = 19:

{1}: https://oeis.org/A006035
{I}H: https://oeis.org/A128460

base b = 20:

base b = 21:

base b = 22:

{1}: https://oeis.org/A127997

base b = 23:

base b = 24:

{1}: https://oeis.org/A127998

base b = 25:

1{0}4: https://oeis.org/A124621 (n replaced by 2×n), https://oeis.org/A228028 (corresponding primes, with an additional prime 5)
1{6}: https://oeis.org/A086123 (n replaced by 2×n), https://oeis.org/A004061 (n replaced by 2×n+1), https://oeis.org/A086122 (corresponding primes)
1{O}: https://oeis.org/A002958, https://oeis.org/A120375 (n replaced by 2×n), https://oeis.org/A120376 (corresponding primes)
4{0}1: https://oeis.org/A204322 (n replaced by 2×n)
5{0}2: https://oeis.org/A087885 (n replaced by 2×n+1, with an additional term 0), https://oeis.org/A182330 (corresponding primes, with two additional primes 3 and 7)
5{0}8: https://oeis.org/A217133 (n replaced by 2×n+1), https://oeis.org/A102910 (corresponding primes, with an additional prime 13)
A{0}1: https://oeis.org/A058934 (n replaced by 2×n+1, with an additional term 0), https://oeis.org/A205771 (corresponding primes, with two additional primes 3 and 11)
J{O}: https://oeis.org/A046865 (n replaced by 2×n+1, with an additional term 0)
{K}L: https://oeis.org/A057171 (n replaced by 2×n+1), https://oeis.org/A138647 (corresponding primes)
{O}H: https://oeis.org/A217134 (n replaced by 2×n)
{O}N: https://oeis.org/A109080 (n replaced by 2×n, with an additional term 1), https://oeis.org/A204578 (corresponding primes, with two additional primes 3 and 23)

base b = 26:

{1}: https://oeis.org/A127999

base b = 27:

1{0}2: https://oeis.org/A138051, https://oeis.org/A176495 (corresponding primes, with an additional prime 3)

base b = 28:

{1}: https://oeis.org/A128000

base b = 29:

base b = 30:

{1}: https://oeis.org/A098438

base b = 31:

{1}: https://oeis.org/A128002

base b = 32:

(none of these sequences is currently in OEIS)

base b = 33:

1{0}2: https://oeis.org/A247957
{1}: https://oeis.org/A209120

base b = 34:

{1}: https://oeis.org/A185073

base b = 35:

1{0}2: https://oeis.org/A247958
{1}: https://oeis.org/A348170

base b = 36:

1{0}1: https://oeis.org/A182331 (corresponding primes, with two additional primes 2 and 7)
1{7}: https://oeis.org/A004062 (n replaced by 2×n+1, with an additional term 2), https://oeis.org/A165210 (corresponding primes, with an additional prime 7)
{U}V: https://oeis.org/A057172 (n replaced by 2×n+1)

References of minimal primes (https://en.wikipedia.org/wiki/Minimal_prime_(recreational_mathematics), https://t5k.org/glossary/xpage/MinimalPrime.html) (the original definition, i.e. prime > base (b) is not required):

http://www.cs.uwaterloo.ca/~shallit/Papers/minimal5.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_11.pdf) (base b = 10)
https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_17.pdf) (bases 2 ≤ b ≤ 30)
https://cs.uwaterloo.ca/~shallit/Papers/br10.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_18.pdf) (bases 2 ≤ b ≤ 30)
https://cs.uwaterloo.ca/~cbright/talks/minimal-slides.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_19.pdf) (bases 2 ≤ b ≤ 30)
https://doi.org/10.1080/10586458.2015.1064048 (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_20.pdf) (bases 2 ≤ b ≤ 30)
https://scholar.colorado.edu/downloads/hh63sw661 (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_16.pdf) (bases 2 ≤ b ≤ 10) (warning: the datas for bases b = 8 and b = 10 have errors, the data for base b = 8 misses the prime 6101 and the data for base b = 10 misses the primes 9001 and 9049 and instead wrongly includes the primes 90001, 90469, and 9000049, and the correct values of S_m for bases b = 8 and b = 10 are 15 and 26 (instead of 14 and 27), respectively, also, the "number of minimal primes base b" and the "length of the largest minimal prime base b" are not the same sizes of b but the same sizes of e^{γ×(b−1)×eulerphi(b)}, this article has this error is because it only search bases 2 ≤ b ≤ 10, and for the data of 2 ≤ b ≤ 10 for the original minimal problem, you may think that they are the same sizes of b (however, if you extend the data to 2 ≤ b ≤ 16, then you will know that they are not the same sizes of b), since bases b = 7 and b = 9 have very large differences of the "number of minimal primes base b" between the original minimal problem and this new minimal prime problem (b = 7: 9 v.s. 71, b = 9: 12 v.s. 151), and bases b = 5 and b = 8 and b = 9 have very large differences of the "length of the largest minimal prime base b" between the original minimal problem and this new minimal prime problem (b = 5: 5 v.s. 96, b = 8: 9 v.s. 221, b = 9: 4 v.s. 1161))
https://github.com/curtisbright/mepn-data (bases 2 ≤ b ≤ 30)
https://github.com/curtisbright/mepn (bases 2 ≤ b ≤ 30)
https://github.com/RaymondDevillers/primes (bases 28 ≤ b ≤ 50)
http://recursed.blogspot.com/2006/12/prime-game.html (base b = 10)
https://inzitan.blogspot.com/2007/07/prime-game.html (in Spain) (base b = 10)
http://www.pourlascience.fr/ewb_pages/a/article-nombres-premiers-inevitables-et-pyramidaux-24978.php (in French) (base b = 10)
http://villemin.gerard.free.fr/aNombre/TYPMULTI/PremInev.htm (base b = 10)
https://schoolbag.info/mathematics/numbers/66.html (base b = 10)
https://www.microsiervos.com/archivo/ciencia/2-3-5-7-11.html (in Spain) (base b = 10)
https://math.stackexchange.com/questions/58292/how-to-check-if-an-integer-has-a-prime-number-in-it (base b = 10)
https://www.metafilter.com/62794/3-is-an-odd-prime-5-is-an-odd-prime-7-is-an-odd-prime-9-is-a-very-odd-prime (base b = 10)
https://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1165031124 (base b = 10)
https://www.cristal.univ-lille.fr/profil/jdelahay/pls:2002:094.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_100.pdf) (bases 2 ≤ b ≤ 10) (warning: the data for base b = 8 has error, the data misses the primes 444641 and 444444441)
https://logs.esolangs.org/freenode-esoteric/2011-02-04.html (bases 2 ≤ b ≤ 10) (warning: the data for base b = 8 has error, the data misses the prime 111 and instead wrongly includes the primes 1101, 101111, 600111, 1000011, 1000111, 4411111, 64111111, 601111111, 41111111111111111, and possibly 6111111111111111111111 if the author of this article continues to search, in fact, the data for base b = 8 misses not only 111 but also 1011)
http://www.bitman.name/math/article/730 (in Italian) (bases 2 ≤ b ≤ 20)
http://www.bitman.name/math/table/497 (in Italian) (bases 2 ≤ b ≤ 16)
http://www.bitman.name/math/table/498 (in Italian) (base b = 17)
http://www.bitman.name/math/table/499 (in Italian) (base b = 18)
http://www.bitman.name/math/table/500 (in Italian) (base b = 19)
http://www.bitman.name/math/table/501 (in Italian) (base b = 20)
https://www.primepuzzles.net/puzzles/puzz_178.htm (base b = 10)
https://oeis.org/A326609 (largest minimal prime in base b)
https://oeis.org/A330049 (length of the largest minimal prime in base b)
https://oeis.org/A330048 (number of minimal primes in base b)
https://oeis.org/A071062 (base b = 10)
https://oeis.org/A110600 (base b = 12)

Other researches for the digits of the primes:

Left-truncatable primes (https://en.wikipedia.org/wiki/Truncatable_prime, https://t5k.org/glossary/xpage/LeftTruncatablePrime.html, https://mathworld.wolfram.com/TruncatablePrime.html, https://www.numbersaplenty.com/set/truncatable_prime/), i.e. every nonempty suffix is prime:

http://primerecords.dk/left-truncatable.txt (base b = 10)
http://chesswanks.com/num/LTPs/ (bases 3 ≤ b ≤ 120)
https://rosettacode.org/wiki/Find_largest_left_truncatable_prime_in_a_given_base (bases 3 ≤ b ≤ 17)
https://www.ams.org/journals/mcom/1977-31-137/S0025-5718-1977-0427213-2/S0025-5718-1977-0427213-2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_28.pdf) (bases 3 ≤ b ≤ 11)
http://www.primerecords.dk/left-truncatable.htm (base b = 10)
http://rosettacode.org/wiki/Truncatable_primes (base b = 10)
https://www.primepuzzles.net/puzzles/puzz_002.htm (base b = 10)
https://web.archive.org/web/20041204160717/http://www.wschnei.de/digit-related-numbers/circular-primes.html (base b = 10)
http://www.bitman.name/math/article/1155 (in Italian) (bases 2 ≤ b ≤ 20)
http://www.bitman.name/math/table/524 (in Italian) (bases 2 ≤ b ≤ 20)
https://oeis.org/A103443 (largest left-truncatable prime in base b)
https://oeis.org/A103463 (length of the largest left-truncatable prime in base b)
https://oeis.org/A076623 (number of left-truncatable primes in base b)
https://oeis.org/A024785 (base b = 10)
https://oeis.org/A129940 (base b = 4)
https://oeis.org/A024779 (base b = 4, written in base b)
https://oeis.org/A129941 (base b = 5)
https://oeis.org/A024780 (base b = 5, written in base b)
https://oeis.org/A129942 (base b = 6)
https://oeis.org/A024781 (base b = 6, written in base b)
https://oeis.org/A129943 (base b = 7)
https://oeis.org/A024782 (base b = 7, written in base b)
https://oeis.org/A129944 (base b = 8)
https://oeis.org/A024783 (base b = 8, written in base b)
https://oeis.org/A129945 (base b = 9)
https://oeis.org/A024784 (base b = 9, written in base b)

Right-truncatable primes (https://en.wikipedia.org/wiki/Truncatable_prime, https://t5k.org/glossary/xpage/RightTruncatablePrime.html, https://mathworld.wolfram.com/TruncatablePrime.html, https://www.numbersaplenty.com/set/truncatable_prime/), i.e. every nonempty prefix is prime:

http://primerecords.dk/right-truncatable.txt (base b = 10)
http://fatphil.org/maths/rtp/rtp.html (bases 3 ≤ b ≤ 90)
https://www.ams.org/journals/mcom/1977-31-137/S0025-5718-1977-0427213-2/S0025-5718-1977-0427213-2.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_28.pdf) (bases 3 ≤ b ≤ 15)
http://rosettacode.org/wiki/Truncatable_primes (base b = 10)
https://www.primepuzzles.net/puzzles/puzz_002.htm (base b = 10)
https://web.archive.org/web/20041204160717/http://www.wschnei.de/digit-related-numbers/circular-primes.html (base b = 10)
http://www.bitman.name/math/article/1155 (in Italian) (bases 2 ≤ b ≤ 20)
http://www.bitman.name/math/table/525 (in Italian) (bases 2 ≤ b ≤ 20)
https://oeis.org/A023107 (largest right-truncatable prime in base b)
https://oeis.org/A103483 (length of the largest right-truncatable prime in base b)
https://oeis.org/A076586 (number of right-truncatable primes in base b)
https://oeis.org/A024770 (base b = 10)
https://oeis.org/A129669 (base b = 3)
https://oeis.org/A024763 (base b = 3, written in base b)
https://oeis.org/A129670 (base b = 4)
https://oeis.org/A024764 (base b = 4, written in base b)
https://oeis.org/A129671 (base b = 5)
https://oeis.org/A024765 (base b = 5, written in base b)
https://oeis.org/A129672 (base b = 6)
https://oeis.org/A024766 (base b = 6, written in base b)
https://oeis.org/A129673 (base b = 7)
https://oeis.org/A024767 (base b = 7, written in base b)
https://oeis.org/A129692 (base b = 8)
https://oeis.org/A024768 (base b = 8, written in base b)
https://oeis.org/A129693 (base b = 9)
https://oeis.org/A024769 (base b = 9, written in base b)
https://oeis.org/A237600 (base b = 16)

Other researches for the minimal elements of other subsets of positive integers written in the positional numeral system with radix b, as digit strings with subsequence ordering:

Primes == 1 mod 4:

https://www.primepuzzles.net/puzzles/puzz_178.htm (base b = 10)
https://github.com/curtisbright/mepn-data/blob/master/data/primes1mod4/minimal.10.txt (base b = 10)
https://www.primepuzzles.net/puzzles/Minimal%20Primes%204k+1,%204k-1,%20pu%20178.doc (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/doc_1.doc) (base b = 10) (warning: the data has many errors, the data wrongly including many primes which are not minimal primes, including the largest "minimal 4×k+1 prime" in the list: 9₆₃₀493, this prime is not a minimal 4×k+1 prime since 9949 is also a prime == 1 mod 4, and 9949 is a subsequence of 9₆₃₀493, there are 146 (instead of 173) minimal 4×k+1 primes and 113 (instead of 138) minimal 4×k−1 primes, and the largest minimal 4×k+1 prime is 8₇₇33 = (8×10⁷⁹−503)/9 instead of 9₆₃₀493 = 10⁶³³−507)
https://oeis.org/A111055 (base b = 10)
https://oeis.org/A111057 (base b = 12)

Primes == 3 mod 4:

https://www.primepuzzles.net/puzzles/puzz_178.htm (base b = 10)
https://github.com/curtisbright/mepn-data/blob/master/data/primes3mod4/minimal.10.txt (base b = 10)
https://www.primepuzzles.net/puzzles/Minimal%20Primes%204k+1,%204k-1,%20pu%20178.doc (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/doc_1.doc) (base b = 10) (warning: the data has many errors, the data wrongly including many primes which are not minimal primes, including the largest "minimal 4×k+1 prime" in the list: 9₆₃₀493, this prime is not a minimal 4×k+1 prime since 9949 is also a prime == 1 mod 4, and 9949 is a subsequence of 9₆₃₀493, there are 146 (instead of 173) minimal 4×k+1 primes and 113 (instead of 138) minimal 4×k−1 primes, and the largest minimal 4×k+1 prime is 8₇₇33 = (8×10⁷⁹−503)/9 instead of 9₆₃₀493 = 10⁶³³−507)
https://oeis.org/A111056 (base b = 10) (warning: the b-file does not include the prime 2₁₉₁₅₁99 since the limit of the numbers in the b-files in OEIS is 10¹⁰⁰⁰−1)

Palindromic primes:

https://www.primepuzzles.net/puzzles/puzz_178.htm (base b = 10)
https://oeis.org/A114835 (base b = 10) (warning: the b-file does not include the probable prime 994₃₄₀₁₉99 since the limit of the numbers in the b-files in OEIS is 10¹⁰⁰⁰−1)

Composites:

https://github.com/curtisbright/mepn-data/tree/master/data/composites (bases 2 ≤ b ≤ 30)
http://www.bitman.name/math/table/504 (bases 2 ≤ b ≤ 20)
https://oeis.org/A071070 (base b = 10)

Squares:

http://recursed.blogspot.com/2006/12/prime-game.html (base b = 10)
https://oeis.org/A130448 (base b = 10)

Powers of 2:

https://oeis.org/A071071/a071071.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_13.pdf) (base b = 10)
https://oeis.org/A071071 (base b = 10)

Multiples of 3:

https://oeis.org/A071073 (base b = 10)

Multiples of 4:

https://oeis.org/A071072 (base b = 10)

Other sets:

https://arxiv.org/pdf/1607.01548.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_14.pdf) (sums of three squares, quadratic residues mod 6, quadratic residues mod 7, range of Euler's totient function, range of "Euler's totient function + 3", range of Dedekind psi function, perfect numbers) (base b = 10)
https://nntdm.net/papers/nntdm-25/NNTDM-25-1-036-047.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_15.pdf) (range of "Euler's totient function + n", for 0 ≤ n ≤ 5) (base b = 10)

The prime curios for them:

https://t5k.org/curios/cpage/40841.html (primes > b, b = 10)
https://t5k.org/curios/cpage/40899.html (primes > b, b = 10, number of minimal primes)
https://t5k.org/curios/cpage/43236.html (primes > b, b = 5)
https://t5k.org/curios/cpage/42961.html (primes > b, b = 7)
https://t5k.org/curios/cpage/42048.html (primes > b, b = 16) (warning: this curio is not true, this prime (DB₃₂₂₃₄) is just the third-largest minimal prime in base b = 16, at the time of this curio was submitted the first-largest and second-largest minimal primes in base b = 16 (3₁₁₆₁₃₇AF and 4₇₂₇₈₅DD, respectively) were still not found, even the families corresponding to the first-largest and second-largest minimal primes in base b = 16 ({3}AF and {4}DD, respectively) were not found)
https://t5k.org/curios/cpage/5154.html (all primes (includes the primes ≤ b), b = 10)
https://t5k.org/curios/cpage/5060.html (all primes (includes the primes ≤ b), b = 10, number of minimal primes)
https://t5k.org/curios/cpage/5425.html (all primes (includes the primes ≤ b), b = 6)
https://t5k.org/curios/cpage/5426.html (all primes (includes the primes ≤ b), b = 7)
https://t5k.org/curios/cpage/5481.html (all primes (includes the primes ≤ b), b = 8)
https://t5k.org/curios/cpage/5480.html (all primes (includes the primes ≤ b), b = 9)
https://t5k.org/curios/cpage/13013.html (primes == 3 mod 4)
https://t5k.org/curios/cpage/40914.html (palindromic primes)

The sets of the minimal elements of these sets under the subsequence ordering are:

set (in decimal, i.e. base b = 10)	the set of the minimal elements under the subsequence ordering	number of such elements	length of the longest such element
primes == 1 mod 4	5, 13, 17, 29, 37, 41, 61, 73, 89, 97, 101, 109, 149, 181, 233, 277, 281, 349, 409, 433, 449, 677, 701, 709, 769, 821, 877, 881, 1669, 2221, 3001, 3121, 3169, 3221, 3301, 3833, 4969, 4993, 6469, 6833, 6949, 7121, 7477, 7949, 9001, 9049, 9221, 9649, 9833, 9901, 9949, 11969, 19121, 20021, 20201, 21121, 23021, 23201, 43669, 44777, 47777, 60493, 60649, 66749, 80833, 90121, 91121, 91921, 91969, 94693, 111121, 112121, 119921, 199921, 220301, 466369, 470077, 666493, 666649, 772721, 777221, 777781, 779981, 799921, 800333, 803333, 806033, 833033, 833633, 860333, 863633, 901169, 946369, 946669, 999169, 1111169, 1999969, 4007077, 4044077, 4400477, 4666693, 8000033, 8000633, 8006633, 8600633, 8660033, 8830033, 8863333, 8866633, 22000001, 40400077, 44040077, 60000049, 66000049, 66600049, 79999981, 80666633, 83333333, 86606633, 86666633, 88600033, 88883033, 88886033, 400000477, 400444477, 444000077, 444044477, 836666333, 866663333, 888803633, 888806333, 888880633, 888886333, 8888800033, 8888888033, 88888883333, 440444444477, 7777777777921, 8888888888333, 40000000000777, 44444444400077, 40444444444444477, 44444444444444477, 88888888888888633, 999999999999999121, 8₇₇33	146	79
primes == 3 mod 4	3, 7, 11, 19, 59, 251, 491, 499, 691, 991, 2099, 2699, 2999, 4051, 4451, 4651, 5051, 5651, 5851, 6299, 6451, 6551, 6899, 8291, 8699, 8951, 8999, 9551, 9851, 22091, 22291, 66851, 80051, 80651, 84551, 85451, 86851, 88651, 92899, 98299, 98899, 200891, 208891, 228299, 282299, 545551, 608851, 686051, 822299, 828899, 848851, 866051, 880091, 885551, 888091, 888451, 902299, 909299, 909899, 2000291, 2888299, 2888891, 8000099, 8000891, 8000899, 8028299, 8808299, 8808551, 8880551, 8888851, 9000451, 9000899, 9908099, 9980099, 9990899, 9998099, 9999299, 60000851, 60008651, 60086651, 60866651, 68666651, 80088299, 80555551, 80888299, 88808099, 88808899, 88880899, 90000299, 90080099, 222222899, 800888899, 808802899, 808880099, 808888099, 888800299, 888822899, 992222299, 2222288899, 8808888899, 8888800099, 8888888299, 8888888891, 48555555551, 555555555551, 999999999899, 88888888888099, 2228888888888899, 9222222222222299, 2288888888888888888888899, 8₄₃99, 86₄₇51, 2₁₉₁₅₁99	113	19153
palindromic primes	2, 3, 5, 7, 11, 919, 94049, 94649, 94849, 94949, 96469, 98689, 9809089, 9888889, 9889889, 9908099, 9980899, 9989899, 900808009, 906686609, 906989609, 908000809, 908444809, 908808809, 909848909, 960898069, 968999869, 988000889, 989040989, 996686699, 996989699, 999686999, 90689098609, 90899999809, 90999899909, 96099899069, 96600800669, 96609890669, 98000000089, 98844444889, 9009004009009, 9099094909909, 9600098900069, 9668000008669, 9699998999969, 9844444444489, 9899900099989, 9900004000099, 9900994990099, 900006898600009, 900904444409009, 966666989666669, 966668909866669, 966699989996669, 999090040090999, 999904444409999, 90000006860000009, 90000008480000009, 90000089998000009, 90999444444499909, 96000060806000069, 99900944444900999, 99990009490009999, 99999884448899999, 9000090994990900009, 9000094444444900009, 9666666080806666669, 9666666668666666669, 9909999994999999099, 9999444444444449999, 9999909994999099999, 9999990994990999999, 900000000080000000009, 900999994444499999009, 90000000009490000000009, 90909444444444444490909, 98999999444444499999989, 9904444444444444444444099, 999999999844444448999999999, 90944444444444444444444444909, 99999999999944444999999999999, 99999999999999499999999999999, 9999999999990004000999999999999, 900000000999999949999999000000009, 989999999999998444899999999999989, 9000000999999999994999999999990000009, ..., 994₃₄₀₁₉99, ... (this set is not known to be complete)	≥ 87	≥ 34023
composites	4, 6, 8, 9, 10, 12, 15, 20, 21, 22, 25, 27, 30, 32, 33, 35, 50, 51, 52, 55, 57, 70, 72, 75, 77, 111, 117, 171, 371, 711, 713, 731	32	3
squares	1, 4, 9, 25, 36, 576, 676, 7056, 80656, 665856, 2027776, 2802276, 22282727076, 77770707876, 78807087076, 7888885568656, 8782782707776, 72822772707876, 555006880085056, 782280288087076, 827702888070276, 888288787822276, 2282820800707876, 7880082008070276, 80077778877070276, 88778000807227876, 782828878078078276, 872727072820287876, 2707700770820007076, 7078287780880770276, 7808287827720727876, 8008002202002207876, 27282772777702807876, 70880800720008787876, 72887222220777087876, 80028077888770207876, 80880700827207270276, 87078270070088278276, 88002002000028027076, 2882278278888228807876, 8770777780888228887076, 77700027222828822007876, 702087807788807888287876, 788708087882007280808827876, 880070008077808877000002276, 888000227087070707880827076, 888077027227228277087787076, 888588886555505085888555556, 7770000800780088788282227776, 7782727788888878708800870276, 5000060065066660656065066555556, 8070008800822880080708800087876, 80787870808888808272077777227076, 800008088070820870870077778827876, 822822722220080888878078820887876, ... (this set is currently not known, and might be extremely difficult to found)	≥ 55	≥ 33
powers of 2	1, 2, 4, 8, 65536 (this set is conjectured to be complete by Jeffrey Shallit, but not proven, this conjecture is true if all powers of 2 except 65536 contain at least one of 1, 2, 4, 8, only powers of 16 can be exceptions)	≥ 5	≥ 5
multiples of 3	0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 42, 45, 48, 51, 54, 57, 72, 75, 78, 81, 84, 87, 111, 114, 117, 141, 144, 147, 171, 174, 177, 222, 225, 228, 252, 255, 258, 282, 285, 288, 411, 414, 417, 441, 444, 447, 471, 474, 477, 522, 525, 528, 552, 555, 558, 582, 585, 588, 711, 714, 717, 741, 744, 747, 771, 774, 777, 822, 825, 828, 852, 855, 858, 882, 885, 888	76	3
multiples of 4	0, 4, 8, 12, 16, 32, 36, 52, 56, 72, 76, 92, 96	13	2
range of Euler's totient function	1, 2, 4, 6, 8, 30, 70, 500, 900, 990, 5590, 9550, 555555555550	13	12
range of Dedekind psi function	1, 3, 4, 6, 8, 20, 72, 90, 222, 252, 500, 522, 552, 570, 592, 750, 770, 992, 7000, 5₆₉0	20	70
range of "Euler's totient function + 1"	2, 3, 5, 7, 9, 11, 41, 61, 81	9	2
range of "Euler's totient function + 2"	3, 4, 6, 8, 10, 12, 20, 22, 50, 72, 90, 770, 992, 5592, 9552, 555555555552 (this set is conjectured to be complete, but not proven, this conjecture is true if and only if there are no totients of the form 6{9}8, and such totients are conjectured not exist, since such totients are == 2 mod 12, thus must be of the form (p−1)×pⁿ with p prime and n odd)	16~17	12 or > 5000
range of "Euler's totient function + 3"	4, 5, 7, 9, 11, 13, 21, 23, 31, 33, 61, 63, 81, 83	14	2
range of "Euler's totient function + 4"	5, 6, 8, 10, 12, 14, 20, 22, 24, 32, 34, 40, 44, 70, 74, 92, 300, 472, 772, 900, 904, 994 (this set is conjectured to be complete, but not proven, this conjecture is true if and only if there are no totients of the form {3,9}26 or {3,9}86, and such totients are conjectured not exist, since such totients are == 2 mod 12, thus must be of the form (p−1)×pⁿ with p prime and n odd)	≥ 22	3 or > 5000
range of "Euler's totient function + 5"	6, 7, 9, 11, 13, 15, 21, 23, 25, 33, 35, 41, 45, 51, 53, 83, 85, 301, 443, 505, 801, 881, 555555555555 (this set is conjectured to be complete, but not proven, this conjecture is true if and only if there are no totients of the form 3{9}8, and such totients are conjectured not exist, since such totients are == 2 mod 12, thus must be of the form (p−1)×pⁿ with p prime and n odd)	23~24	12 or > 5000
perfect numbers	6, 28 (this set is conjectured to be complete, but not proven, this conjecture is true if there are no odd perfect numbers, since all even perfect numbers end with either 6 or 28, and odd perfect numbers are conjectured not exist, this is a famous open problem)	≥ 2	2 or > 1500

(for the primality certificate for the largest element in the minimal set of "primes == 3 mod 4" (2₁₉₁₅₁99), see http://factordb.com/cert.php?id=1100000000301493137 and https://stdkmd.net/nrr/cert/2/2w99_19153.zip and http://www.lix.polytechnique.fr/Labo/Francois.Morain/Primes/Certif/shallit.certif.gz, note that this prime is also an element of the minimal set of the primes > 100 in base b = 100, since this prime is written 2:22₉₅₇₅:99 in base b = 100 (use the character ":" to saparate the digits for bases b > 36 (and just use decimal to write the digits), just like https://baseconvert.com/ and https://baseconvert.com/high-precision), and both families 2:{22} in base b = 100 and {22}:99 in base b = 100 contain no primes, however, the element 994₃₄₀₁₉99 in the minimal set of "palindromic primes" is only a probable prime, i.e. not a definitely prime)

Besides, the sets of the minimal elements of other classical sets under the subsequence ordering are:

set (in decimal, i.e. base b = 10)	the set of the minimal elements under the subsequence ordering	number of such elements	length of the longest such element
cubes	1, 8, 27, 64, 343, 729, 3375, 4096, 35937, 39304, 46656, 50653, 79507, 97336, 300763, 405224, 456533, 474552, 493039, 636056, 704969, 3307949, 4330747, 5545233, 5639752, 5735339, 6539203, 9663597, 23393656, 23639903, 29503629, 37933056, 40353607, 45499293, 50243409, 54439939, 57066625, 57960603, 70444997, 70957944, 73560059, 76765625, 95443993, 202262003, 236029032, 350402625, 377933067, 379503424, 445943744, 454756609, 537367797, 549353259, 563559976, 567663552, 773620632, 907039232, ... (this set is currently not known, and might be extremely difficult to found)	≥ 56	≥ 9
4th powers	1, 256, 625, 4096, 20736, 65536, 456976, 4477456, 8503056, 9834496, 59969536, 78074896, 84934656, 303595776, 362673936, 688747536, ... (this set is currently not known, and might be extremely difficult to found)	≥ 16	≥ 9
perfect powers	1, 4, 8, 9, 25, 27, 32, 36, 576, 676, 3375, 7056, 7776, 50653, 20226200, ... (this set is currently not known, and might be extremely difficult to found)	≥ 15	≥ 8
powerful numbers	1, 4, 8, 9, 25, 27, 32, 36, 72, 200, 500, 576, 675, 676, 3375, 7056, 7776, 50653, 60552, 357075, 570375, 665523, 735075, 766656, 7555707, ... (this set is currently not known, and might be extremely difficult to found)	≥ 25	≥ 7
prime powers	2, 3, 4, 5, 7, 8, 9, 11, 16, 61	10	2
powers of 3	1, 3, 9, 27 (this set is conjectured to be complete, but not proven, this conjecture is true if all powers of 3 except 27 contain at least one of 1, 3, 9, only (4×m+3)th powers of 3 can be exceptions)	≥ 4	≥ 2
squarefree numbers	1, 2, 3, 5, 6, 7, 89, 94, 409, 449, 498, 499, 998	13	3
triangular numbers	1, 3, 6, 28, 45, 55, 78, 820, 990, 2775, 7750, 9870, 24090, 25200, 40470, 49770, 57970, 70500, 97020, 292995, 299925, 422740, 442270, 588070, 702705, 749700, 870540, 2474200, 4744740, 5727420, 7279020, 7799275, 8588440, 20740020, 27524490, 27792240, 40002040, 52270200, 54920440, ... (this set is currently not known, and might be extremely difficult to found)	≥ 39	≥ 8
Pronic numbers	2, 6, 30, 90, 110, 870, 5550, 5700, 7140, 8010, 15500, 15750, 48180, 50400, 50850, 57840, 144780, 147840, 475410, 504810, 757770, 845480, 884540, 1477440, 4517750, 4754580, 7185080, 7450170, 10077450, 10500840, 14588580, 17770440, 17854850, 40710780, 41480040, 41544470, 45501770, 47755010, 54471780, ... (this set is currently not known, and might be extremely difficult to found)	≥ 39	≥ 8
semiprimes	4, 6, 9, 10, 15, 21, 22, 25, 33, 35, 38, 51, 55, 57, 58, 77, 82, 85, 87, 111, 118, 123, 178, 183, 203, 237, 278, 301, 302, 327, 371, 502, 703, 713, 718, 723, 731, 753, 781, 803, 813, 818, 831, 1137, 1317, 3007, 3117, 8801, 8881, 28883, 50003, 80081, 888883, 7000001, 8000011	55	7
Mersenne primes	3, 7, 8191 (this set is conjectured to be complete, but not proven, this conjecture is true if all Mersenne primes other than 8191 contain either 3 or 7, only Mersenne primes with exponents == 1 mod 4 can be exceptions)	≥ 3	≥ 4
Fermat primes	3, 5, 17 (this set is conjectured to be complete, but not proven, this conjecture is true if all Fermat primes other than 17 contain either 3 or 5, of course this conjecture is true if 65537 is the largest Fermat prime)	≥ 3	≥ 2
factorial numbers	1, 2, 6, 5040 (this set is conjectured to be complete, but not proven, this conjecture is true if all factorial numbers other than 5040 contain at least one of 1, 2, 6)	≥ 4	≥ 4
primorial numbers	1, 2, 6, 30 (this set is conjectured to be complete, but not proven, this conjecture is true if all primorial numbers other than 30 contain at least one of 1, 2, 6)	≥ 4	≥ 2
Fibonacci numbers	1, 2, 3, 5, 8 (this set is conjectured to be complete, but not proven, this conjecture is true if all Fibonacci numbers contain at least one of 1, 2, 3, 5, 8)	≥ 5	≥ 1
Lucas numbers	1, 3, 4, 7, 29 (this set is conjectured to be complete, but not proven, this conjecture is true if all Lucas numbers other than 29 contain at least one of 1, 3, 4, 7)	≥ 5	≥ 2

Tools about this research: (in fact, you can also use Wolfram Alpha (https://www.wolframalpha.com/) or online Magma calculator (http://magma.maths.usyd.edu.au/calc/) or Pari/GP (https://pari.math.u-bordeaux.fr/) or Wolfram Mathematica (https://www.wolfram.com/mathematica/) or Maple (https://www.maplesoft.com/)) (many of these tools have a limit of 2⁵³, this is because the limit of the significant figures (https://en.wikipedia.org/wiki/Significant_figures, https://mathworld.wolfram.com/SignificantDigits.html) of the double-precision floating-point format (https://en.wikipedia.org/wiki/Double-precision_floating-point_format, https://mathworld.wolfram.com/Floating-PointNumber.html) is 53 bits (https://en.wikipedia.org/wiki/Bit, https://mathworld.wolfram.com/Bit.html))

Prime checkers:

https://t5k.org/curios/includes/primetest.php (limit: 2⁵³−1)
https://www.numberempire.com/primenumbers.php (choose "Check") (also give the index for the primes ≤ 10⁹−1) (limit: 10¹⁰⁰⁰−1)
http://www.numbertheory.org/php/lucas.html (no limit)
https://www.alpertron.com.ar/ECM.HTM (click "Prime") (no limit)
http://www.javascripter.net/faq/numberisprime.htm (just type "isPrime(n)") (no limit)
http://www.javascripter.net/math/primes/millerrabinprimalitytest.htm (just type "isPrimeMR18(n)") (no limit)
http://www.javascripter.net/math/calculators/100digitbigintcalculator.htm (just type x and click "prime?") (no limit)
http://www.prime-numbers.org/ (use the box "Key in a number to check it's a prime number or not" and click "Check") (limit: 10¹¹−1)
https://www.walter-fendt.de/html5/men/primenumbers_en.htm (limit: 10¹²)
http://www.math.com/students/calculators/source/prime-number.htm (limit: 2⁵³)
https://www.calculatorsoup.com/calculators/math/prime-number-calculator.php (limit: 10¹³−1)
https://onlinemathtools.com/test-prime-number (choose "Test All Numbers") (no limit)
https://www.bigprimes.net/primalitytest (use the first box) (limit: 2⁵³−4)
https://www.archimedes-lab.org/primOmatic.html (limit: 10¹²−1)
http://www.sonic.net/~undoc/java/PrimeCalc.html (click "y=IsPrime(x)") (no limit)
https://web.archive.org/web/20021011204430/http://www.miroe.de/proth/pr_prim.htm (limit: 10¹⁰−34)
https://www.bigprimes.net/cruncher/ (limit: 10⁶−1)
https://math.tools/numbers/is-prime/ (limit: 2³¹−1)
http://www.primzahlen.de/primzahltests/testverfahren.htm (in German) (use the box "Miller-Rabin-Test" and click "Test") (limit: 49106×10¹⁰)
http://www.proftnj.com/calcprem.htm (in French) (use the box "Rechercher si un nombre est premier" and click "Rechercher") (limit: 2⁵³)
http://www.positiveintegers.org/ (just enter the number) (limit: 1000000)
https://numdic.com/ (just enter the number) (limit: 700000)
https://numbermatics.com/ (just enter the number) (limit: 10²⁶+2)
https://metanumbers.com/ (just enter the number) (limit: 2⁶³−1)
https://int.darkbyte.ru/ (just enter the number) (limit: 2³¹−2)
https://www.numbersaplenty.com/ (just enter the number) (limit: 10¹⁵−1)
http://factordb.com/ (online factor database, "P" means definitely prime, "PRP" means unproven probable prime, "FF" means composite and fully factored, "CF" means composite and has known proper factor but not fully factored, "C" means composite and has no known proper factor, "U" means number with unknown status, "Unit" means the number "1", "Zero" means the number "0", see http://factordb.com/status.html, also, this online factor database uses colors to show the status of the numbers, black means definitely prime ("P"), blue means composite ("C" or "CF" or "FF"), brown means unproven probable prime ("PRP"), red means number with unknown status ("U"), also, this online factor database automatically stores all numbers < 10¹⁸ and automatically checks the probable-primality of the numbers with unknown status < 10²⁰⁰⁰ (see http://factordb.com/show_config.php) and automatically reserves to the probable-primality tests of the numbers with unknown status < 10⁴⁹⁹⁹⁹ and automatically trial factors all numbers with the primes p < 5000000 (see http://factordb.com/show_config.php) and automatically algebraic factors all numbers (see https://www.mersenneforum.org/showpost.php?p=640196&postcount=1) and automatically proves the primality of the probable primes < 10²⁹⁹ (see https://web.archive.org/web/20150812084455/http://factordb.com/status.php) and automatically factors the composites < 10⁶⁹ (see https://web.archive.org/web/20150812084455/http://factordb.com/status.php)) (limit: 10^10000000−1 (see http://factordb.com/index.php?query=999999999%5E999999999%2B1) or 10^4000000−1 for Fibonacci and Lucas numbers (see http://factordb.com/index.php?query=I999999999 and http://factordb.com/index.php?query=L999999999) or 10^2000000−1 for factorial and primorial (see http://factordb.com/index.php?query=999999999%21%2B1 and http://factordb.com/index.php?query=999999999%23%2B1))
https://578d0722p8.goho.co/index.html (more types of numbers in the online factor database) (limit: 10^10000000−1 (see http://factordb.com/index.php?query=999999999%5E999999999%2B1) or 10^4000000−1 for Fibonacci and Lucas numbers (see http://factordb.com/index.php?query=I999999999 and http://factordb.com/index.php?query=L999999999) or 10^2000000−1 for factorial and primorial (see http://factordb.com/index.php?query=999999999%21%2B1 and http://factordb.com/index.php?query=999999999%23%2B1))
https://t5k.org/nthprime/ (calculate the nth prime (use the box "Nth prime"), calculate the index of a prime (use the box "Pi function")) (limit: 3×10¹³)
http://www.numbertheory.org/php/nprime.html (calculate the next (probable) prime above N, in fact, links 2, 7, 11, 12, 13 can also calculate the next prime above N, besides, links 2, 7 can also calculate the previous prime below N, for link 2 choose "Find next" to calculate the next prime above N, or choose "Find previous" to calculate the previous prime below N, for link 7 just type x and click "next p" to calculate the next prime above N, or just type x and click "prev p" to calculate the previous prime below N, for link 11 use the second box to calculate the next prime above N, for link 13 click "y=NextPrime(x)" to calculate the next prime above N) (no limit)
http://factordb.com/nextprime.php (calculate the next (probable) prime above N, in fact, links 2, 7, 11, 12, 13 can also calculate the next prime above N, besides, links 2, 7 can also calculate the previous prime below N, for link 2 choose "Find next" to calculate the next prime above N, or choose "Find previous" to calculate the previous prime below N, for link 7 just type x and click "next p" to calculate the next prime above N, or just type x and click "prev p" to calculate the previous prime below N, for link 11 use the second box to calculate the next prime above N, for link 13 click "y=NextPrime(x)" to calculate the next prime above N) (limit: 10²⁰⁰⁰−1)

Integer factorizers:

https://www.numberempire.com/numberfactorizer.php (limit: 10⁷⁰−1)
https://www.alpertron.com.ar/ECM.HTM (click "Factor") (no limit)
http://www.numbertheory.org/php/factor.html (limit: 10²⁵−1)
http://www.numbertheory.org/php/lprimefactor.html (only find the least prime factor) (limit: 10²⁵−1)
https://www.mersenne.ca/factor.php (use the box "Get prime factorization for small (<=50 decimal digits) numbers") (limit: 10⁵⁰−1)
http://www.javascripter.net/math/calculators/primefactorscalculator.htm (limit: 10²⁰−1)
http://www.javascripter.net/faq/numberisprime.htm (only find the least prime factor, just type "leastFactor(n)") (no limit)
http://www.javascripter.net/math/primes/millerrabinprimalitytest.htm (only find the least prime factor, just type "leastFactor(n)") (no limit)
https://www.walter-fendt.de/html5/men/primenumbers_en.htm (limit: 10¹²)
https://web.archive.org/web/20230122202627/https://betaprojects.com/calculators/prime_factors.html (limit: 2⁵³−1)
https://www.emathhelp.net/calculators/pre-algebra/prime-factorization-calculator/ (limit: 10⁹)
https://primefan.tripod.com/Factorer.html (limit: 2⁵³)
https://www.calculatorsoup.com/calculators/math/prime-factors.php (also all (prime or composite or unit) factors of N) (limit: 10¹³−1)
https://www.calculator.net/prime-factorization-calculator.html (limit: 10¹⁴−1)
http://www.se16.info/js/factor.htm (limit: 2⁵³)
https://web.archive.org/web/20230918044810/http://math.fau.edu/Richman/mla/factor-f.htm (limit: 2⁵³)
http://www.rsok.com/~jrm/factor.html (no limit)
http://www.brennen.net/primes/FactorApplet.html (need run with Java)
https://web.archive.org/web/20161004191531/http://britton.disted.camosun.bc.ca/jbprimefactor.htm (limit: 10⁶)
http://wims.unice.fr/~wims/en_tool~algebra~factor.en.html (no limit)
http://www.analyzemath.com/Calculators_3/prime_factors.html (limit: 2⁵³)
https://www.archimedes-lab.org/primOmatic.html (limit: 10¹²−1)
https://math.tools/calculator/prime-factors/ (limit: 2³¹−1)
https://www.bigprimes.net/cruncher/ (all (prime or composite or unit) factors of N) (limit: 10¹⁷−1)
http://www.proftnj.com/calcprem.htm (in French) (use the box "Factoriser un nombre" and click "Factoriser") (limit: 2⁵³)
http://www.positiveintegers.org/ (just enter the number) (also all (prime or composite or unit) factors of N) (limit: 1000000)
https://numdic.com/ (just enter the number) (also all (prime or composite or unit) factors of N) (limit: 700000)
https://numbermatics.com/ (just enter the number) (also all (prime or composite or unit) factors of N) (limit: 10²⁶+2)
https://metanumbers.com/ (just enter the number) (also all (prime or composite or unit) factors of N) (limit: 2⁶³−1)
https://int.darkbyte.ru/ (just enter the number) (also all (prime or composite or unit) factors of N) (limit: 2³¹−2)
https://www.numbersaplenty.com/ (just enter the number) (also all (prime or composite or unit) factors of N) (limit: 10¹⁵−1)
http://factordb.com/ (online factor database, "P" means definitely prime, "PRP" means unproven probable prime, "FF" means composite and fully factored, "CF" means composite and has known proper factor but not fully factored, "C" means composite and has no known proper factor, "U" means number with unknown status, "Unit" means the number "1", "Zero" means the number "0", see http://factordb.com/status.html, also, this online factor database uses colors to show the status of the numbers, black means definitely prime ("P"), blue means composite ("C" or "CF" or "FF"), brown means unproven probable prime ("PRP"), red means number with unknown status ("U"), also, this online factor database automatically stores all numbers < 10¹⁸ and automatically checks the probable-primality of the numbers with unknown status < 10²⁰⁰⁰ (see http://factordb.com/show_config.php) and automatically reserves to the probable-primality tests of the numbers with unknown status < 10⁴⁹⁹⁹⁹ and automatically trial factors all numbers with the primes p < 5000000 (see http://factordb.com/show_config.php) and automatically algebraic factors all numbers (see https://www.mersenneforum.org/showpost.php?p=640196&postcount=1) and automatically proves the primality of the probable primes < 10²⁹⁹ (see https://web.archive.org/web/20150812084455/http://factordb.com/status.php) and automatically factors the composites < 10⁶⁹ (see https://web.archive.org/web/20150812084455/http://factordb.com/status.php)) (limit: 10^10000000−1 (see http://factordb.com/index.php?query=999999999%5E999999999%2B1) or 10^4000000−1 for Fibonacci and Lucas numbers (see http://factordb.com/index.php?query=I999999999 and http://factordb.com/index.php?query=L999999999) or 10^2000000−1 for factorial and primorial (see http://factordb.com/index.php?query=999999999%21%2B1 and http://factordb.com/index.php?query=999999999%23%2B1))
https://578d0722p8.goho.co/index.html (more types of numbers in the online factor database) (limit: 10^10000000−1 (see http://factordb.com/index.php?query=999999999%5E999999999%2B1) or 10^4000000−1 for Fibonacci and Lucas numbers (see http://factordb.com/index.php?query=I999999999 and http://factordb.com/index.php?query=L999999999) or 10^2000000−1 for factorial and primorial (see http://factordb.com/index.php?query=999999999%21%2B1 and http://factordb.com/index.php?query=999999999%23%2B1))
http://myfactorcollection.mooo.com:8090/dbio.html (online factor database for numbers of the form bⁿ±1)
http://myfactorcollection.mooo.com:8090/interactive.html (online factor database for numbers of the form bⁿ±1) (only list the greatest prime factor (for fully factored numbers) or the composite factor with no known proper factor (for non-fully factored numbers), and only list the number of decimal digits of this factor if this factor is > 10⁶, but you can click the lattices to see other prime factors) (the lattices saparated to two lattices means the number has Aurifeuillean factorization, and for such lattices, the left lattice is for the Aurifeuillean L part, and the right lattice is for the Aurifeuillean M part)
https://web.archive.org/web/20120722020628/http://homes.cerias.purdue.edu/~ssw/cun/prime.php (online factor database for numbers of the form bⁿ±1 for 2 ≤ b ≤ 12)
https://web.archive.org/web/20120330032919/http://homes.cerias.purdue.edu/~ssw/cun/clientold.html (online factor database for numbers of the form bⁿ±1 for 2 ≤ b ≤ 12)

Prime generators:

http://www.numbertheory.org/php/prime_generator.html
http://www.se16.info/js/prime.htm
http://www.rsok.com/~jrm/printprimes.html
http://www.sonic.net/~undoc/java/PrimeCalc.html (click "ShowPrimes(x..y)")
http://www.primzahlen.de/primzahltests/testverfahren.htm (in German) (use the box "Primzahlgenerator" and click "erzeugen")

Base converters:

https://baseconvert.com/ (any base b) (no limit)
https://baseconvert.com/high-precision (any base b) (no limit)
https://baseconvert.com/ieee-754-floating-point (for IEEE 754 (https://en.wikipedia.org/wiki/IEEE_754), only bases b = 2, 10, 16) (no limit)
https://www.calculand.com/unit-converter/zahlen.php?og=Base+2-36&ug=1 (bases 2 ≤ b ≤ 36) (use lower case letters instead of upper case letters) (limit: 12 digits in the input base b)
https://www.calculand.com/unit-converter/zahlen.php?og=Base62&ug=1 (covert base b = 62 to any base 2 ≤ b ≤ 200) (no limit)
https://www.calculand.com/unit-converter/zahlen.php?og=Base64&ug=1 (covert base b = 64 to any base 2 ≤ b ≤ 200) (no limit)
https://www.calculand.com/unit-converter/zahlen.php?og=Base85&ug=1 (covert base b = 85 to any base 2 ≤ b ≤ 200) (no limit)
https://www.calculand.com/unit-converter/zahlen.php?og=System+calculand&ug=1 (bases 2 ≤ b ≤ 200) (limit: 2⁵³)
http://www.unitconversion.org/unit_converter/numbers.html (bases 2 ≤ b ≤ 36) (limit: 2⁵³)
http://www.unitconversion.org/unit_converter/numbers-ex.html (bases 2 ≤ b ≤ 36) (limit: 2⁵³)
https://web.archive.org/web/20161126114837/http://bmanolov.free.fr/numbaseconv.php (bases 2 ≤ b ≤ 36) (limit: 2⁵³)
https://math.tools/calculator/base/ (bases 2 ≤ b ≤ 64) (no limit)
http://extraconversion.com/base-number (bases 2 ≤ b ≤ 36) (use lower case letters instead of upper case letters) (limit: 2⁶³−1)
http://www.math.com/students/converters/source/base.htm (any base b) (limit: 2⁵²)
https://www.dcode.fr/base-n-convert (bases 2 ≤ b ≤ 62) (no limit)
https://www.convertworld.com/en/numerals/ (bases b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20) (limit: 2⁵³)
https://www.cut-the-knot.org/binary.shtml (bases b = 2, 3, 5, 8, 10, 12, 16, 36) (limit: 2⁵³)
https://www.cut-the-knot.org/Curriculum/Algorithms/BaseConversion.shtml (bases b = 2, 8, 10, 16) (limit: 2⁵³)
http://www.tonymarston.net/php-mysql/converter.php (bases b = 2, 8, 10, 16, 36) (no limit)
https://web.archive.org/web/20230918043634/http://math.fau.edu/Richman/mla/convert.htm (any base b) (limit: 2⁵³)
https://web.archive.org/web/20190629223750/http://thedevtoolkit.com/tools/base_conversion (bases 2 ≤ b ≤ 36) (use lower case letters instead of upper case letters) (no limit)
https://web.archive.org/web/20170204004954/http://ultrastudio.org/en/MechengburakalkanApplet-1.7.zip (bases 2 ≤ b ≤ 36) (use lower case letters instead of upper case letters) (limit: 2⁵³)
https://www.bigprimes.net/cruncher/ (bases b = 2, 3, 4, 5, 8, 10, 16) (no limit)
http://www.mathsisfun.com/numbers/convert-base.php (bases b = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 20, 26) (use 0−9, A−H, J−K instead of 0−9, A−J for b = 20, and use Z, A−Y instead of 0−9, A−P for b = 26) (no limit)
http://www.kwuntung.net/hkunit/base/base.php (in Chinese) (bases 2 ≤ b ≤ 36) (use lower case letters instead of upper case letters) (limit: 2⁵³)
https://linesegment.web.fc2.com/application/math/numbers/RadixConversion.html (in Japanese) (bases 2 ≤ b ≤ 36 and b = 62) (limit: 2⁵³)
http://www.positiveintegers.org/ (just enter the number) (bases 2 ≤ b ≤ 36) (limit: 1000000)
https://numdic.com/ (just enter the number) (bases b = 2, 3, 4, 5, 6, 7, 8, 10, 16, 24, 36) (use lower case letters instead of upper case letters) (limit: 700000)
https://numbermatics.com/ (just enter the number) (bases b = 2, 16, 36) (limit: 10²⁶+2)
https://metanumbers.com/ (just enter the number) (bases b = 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 36) (use lower case letters instead of upper case letters) (limit: 2⁶³−1)
https://int.darkbyte.ru/ (just enter the number) (bases 2 ≤ b ≤ 36) (use lower case letters instead of upper case letters) (limit: 2³¹−2)
https://www.numbersaplenty.com/ (just enter the number) (bases 2 ≤ b ≤ 16) (use lower case letters instead of upper case letters) (limit: 10¹⁵−1)
http://factordb.com/index.php?showid=1000000000000000127 (you can change the "showid" to the ID for your number) (bases 2 ≤ b ≤ 36) (use lower case letters instead of upper case letters) (limit: 10^10000000−1 (see http://factordb.com/index.php?query=999999999%5E999999999%2B1) or 10^4000000−1 for Fibonacci and Lucas numbers (see http://factordb.com/index.php?query=I999999999 and http://factordb.com/index.php?query=L999999999) or 10^2000000−1 for factorial and primorial (see http://factordb.com/index.php?query=999999999%21%2B1 and http://factordb.com/index.php?query=999999999%23%2B1))

Expression generators:

https://stdkmd.net/nrr/exprgen.htm (only support base 10 forms)
https://www.numberempire.com/simplifyexpression.php (e.g. for the form 5{7} in base 11, type "5*11^n+7*(11^n-1)/10")

Maple (https://www.maplesoft.com/, https://en.wikipedia.org/wiki/Maple_(software))
Wolfram Mathematica (https://www.wolfram.com/mathematica/, https://en.wikipedia.org/wiki/Wolfram_Mathematica)
Pari/GP (https://pari.math.u-bordeaux.fr/, https://en.wikipedia.org/wiki/PARI/GP)
Python (https://www.python.org/, https://en.wikipedia.org/wiki/Python_(programming_language))
GMP (https://gmplib.org/, https://en.wikipedia.org/wiki/GNU_Multiple_Precision_Arithmetic_Library)
Magma (http://magma.maths.usyd.edu.au/, https://en.wikipedia.org/wiki/Magma_(computer_algebra_system))
SageMath (https://www.sagemath.org/, https://en.wikipedia.org/wiki/SageMath)

Lists of small primes: (see https://t5k.org/notes/faq/LongestList.html, long lists just waste storage, and if placed on the Internet, they just waste bandwidth, since small primes are too easy to find, they can be found far faster than they can be read from a hard disk, so no one bothers to keep long lists (say past 10¹²), also see https://t5k.org/notes/faq/x_digit_primes.html, although we can quickly determine whether a number < 10³⁰⁰ is prime or not, but there is no list of all primes < 10³⁰⁰, since the space which we need is larger than the number of elementary particles (https://en.wikipedia.org/wiki/Elementary_particle) (i.e. quarks (https://en.wikipedia.org/wiki/Quark) and electrons (https://en.wikipedia.org/wiki/Electron)) in the universe (https://en.wikipedia.org/wiki/Universe), also see https://www.mersenneforum.org/showthread.php?t=24417)

https://t5k.org/lists/small/1000.txt (limit: first 1000 primes, up to 7919)
https://t5k.org/lists/small/10000.txt (limit: first 10000 primes, up to 104729)
https://t5k.org/lists/small/100000.txt (limit: first 100008 primes, up to 1299827)
https://t5k.org/lists/small/millions/ (limit: first 50000000 primes, up to 982451653)
https://oeis.org/A000040/b000040.txt (limit: first 10000 primes, up to 104729)
https://oeis.org/A000040/a000040.txt (limit: first 100000 primes, up to 1299709)
https://oeis.org/A000040/b000040_1.txt (limit: first 500000 primes, up to 7368787)
https://oeis.org/A000040/a000040_1B.7z (limit: first 1000000000 primes, up to 22801763489)
http://www.prime-numbers.org/ (limit: first 4118044813 primes, up to 99999999977)
https://web.archive.org/web/20091027064420/http://geocities.com/primes_r_us/small/index.html (limit: first 5800000 primes, up to 100711433)
http://prime-numbers.org/sample.zip (limit: first 1000 primes, up to 7919)
https://metanumbers.com/prime-numbers (limit: first 1229 primes, up to 9973)
https://www.numberempire.com/primenumberstable.php (page limit: first 25 primes, up to 97, total limit: first 1229 primes, up to 9973)
https://www.calculatorsoup.com/calculators/math/prime-numbers.php (limit: first 1009 primes, up to 8011)
https://www2.cs.arizona.edu/icon/oddsends/primes.htm (limit: first 50000 primes, up to 611953)
https://www.numbersaplenty.com/set/prime_number/more.php (limit: first 600 primes, up to 4409)
https://web.archive.org/web/20050412073754/http://www.mindspring.com/~benbradley/basep.hpp (limit: first 6542 primes, up to 65521)
https://cdn1.byjus.com/wp-content/uploads/2021/10/Prime-Numbers-from-1-to-1000.png (limit: first 168 primes, up to 997)
http://noe-education.org/D11102.php (in French) (limit: first 5133 primes, up to 49999)
https://math.tools/numbers/prime/ (limit: first 150 primes, up to 863)
https://math.tools/list/prime-numbers (limit: first 3000 primes, up to 27449) (warning: this site uses index n−1 for the nth prime)
https://web.archive.org/web/20060513054350/http://www.walter-fendt.de/m14i/primes_i.htm (in Italian) (limit: first 37607912018 primes, up to 999999999989)
https://primefan.tripod.com/500Primes1.html (limit: first 501 primes, up to 3581) (warning: this site incorrectly includes 1 as a prime and misses the primes 3229 and 3329, thus this site actually lists the first 500−1+2 = 501 primes)
https://www.gutenberg.org/files/65/65.txt (limit: first 101341 primes, up to 1318699)
https://web.archive.org/web/20231024091219/http://www.primos.mat.br/indexen.html (page limit: first 168 primes, up to 997, total limit: first 37607912018 primes, up to 999999999989)
https://www.walter-fendt.de/html5/men/primenumbers_en.htm (limit: first 37607912018 primes, up to 999999999989)
https://www.rsok.com/~jrm/first100primes.html (limit: first 100 primes, up to 541)
http://www.rsok.com/~jrm/printprimes.html (limit: first 98222287 primes, up to 1999999973)
http://mrteverett.com/numbers/primes/factest.txt (limit: first 14172 primes, up to 153757) (warning: this site does not list the primes 2 and 3 and start with the prime 5, thus this site actually only has 14172−2 = 14170 primes)
http://www.primzahlen.de/primzahltests/2-100003.htm (in German) (limit: first 9593 primes, up to 100003)
https://jocelyn.quizz.chat/np/cache/index.html (in French) (limit: first 1000000 primes, up to 15485863)
http://www.sosmath.com/tables/prime/prime.html (limit: first 1000 primes, up to 7919)
https://www.bigprimes.net/archive/prime (page limit: first 100 primes, up to 541, total limit: first 1000099 primes, up to 15487457)
https://web.archive.org/web/20201130071856/http://www.mathematical.com/primelist1to100kk.html (limit: first 664579 primes, up to 9999991)
https://web.archive.org/web/20191118082053/http://www.tsm-resources.com/alists/prim.html (limit: first 2000 primes, up to 17389)
https://web.archive.org/web/20090917191047/http://planetmath.org/encyclopedia/FirstThousandPositivePrimeNumbers.html (limit: first 1000 primes, up to 7919)
https://openlibrary.org/books/OL16553580M (limit: first 664999 primes, up to 10006721)
https://sites.google.com/view/the-first-25000-primes (limit: first 25000 primes, up to 287117)
https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html (the longest list ever calculated, with all primes < 2⁶⁴ (but unlikely other lists here, the primes are not all stored))
https://en.wikipedia.org/wiki/List_of_prime_numbers#The_first_1000_prime_numbers (limit: first 1000 primes, up to 7919)

Lists of factorizations of small integers:

http://primefan.tripod.com/500factored.html (page limit: 500, total limit: 2500)
http://www.sosmath.com/tables/factor/factor.html (page limit: 200, total limit: 1000)
https://sites.google.com/view/prime-factorization-of-integer (limit: 25000)
https://web.archive.org/web/20060210182347/http://bearnol.is-a-geek.com/Panfur%20Project/ (limit: 20000000, however, currently the data is only available up to 1500000 in the archive pages, the data for numbers > 1500000 has no available archive pages) (warning: this site does not factor the composite numbers 15, 51, 85, 91, 255, 435, 451, 561, 595, 679, 703, 771, 1105, 1261, 1285, 1351, 1387, ...)
http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/ (limit: 10000)
http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/?infinity (no limit)
https://oeis.org/A027746/b027746.txt (flattened rows, the Nth row ends with the term with index "the term N of https://oeis.org/A022559") (limit: 2048)
https://oeis.org/A112798/b112798.txt (replace the nth prime by n, flattened rows, the Nth row ends with the term with index "the term N of https://oeis.org/A022559") (limit: 3275)
https://oeis.org/A027750/a027750.txt (all (prime or composite or unit) factors of N) (limit: 10000)
https://oeis.org/A027750/b027750.txt (all (prime or composite or unit) factors of N, flattened rows, the Nth row ends with the term with index "the term N of https://oeis.org/A006218") (limit: 1000)
https://oeis.org/A054841/b054841.txt (the nth rightmost decimal digit represents the exponent of the nth prime, but only for the exponents ≤ 9, thus the number will be incorrect if N is divisible by a 10th power (> 1), thus, the number is incorrect only for 9 values of N, namely N = 1024, 2048, 3072, 4096, 5120, 6144, 7168, 8192, 9216, since the limit of N is 10000) (limit: 10000)
http://factorzone.tripod.com/factors.htm (all (prime or composite or unit) factors of N) (limit: 1100)
http://functions.wolfram.com/NumberTheoryFunctions/Divisors/03/02 (all (prime or composite or unit) factors of N) (limit: 50)
https://www.asahi-net.or.jp/~KC2H-MSM/cn/old/p01n002.txt (limit: 1001)
https://en.wikipedia.org/wiki/Table_of_prime_factors (limit: 1000)
https://en.wikipedia.org/wiki/Table_of_divisors (all (prime or composite or unit) factors of N) (limit: 1000)
http://factordb.com/index.php?query=n&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show (from factordb) (the limit in the list is 199, but you can change the number to get the list of the factorizations of larger integers (at most 1000000000000000000000000000198, since the start value of n in factordb must be ≤ 999999999999999999999999999999))
http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=2&TBase=20001&FExp=1&TExp=1&c0=-&EN=&LM= (from an online factor database for numbers of the form bⁿ±1) (the limit in the list is 20000, but you can change the number to get the list of the factorizations of larger integers (at most 1099999, since the base b in http://myfactors.mooo.com/ must be ≤ 1100000))
http://myfactorcollection.mooo.com:8090/cgi-bin/showFullRep?FBase=2&TBase=20001&FExp=1&TExp=1&c0=%2B&EN=&LM= (from an online factor database for numbers of the form bⁿ±1) (the limit in the list is 20002, but you can change the number to get the list of the factorizations of larger integers (at most 1100001, since the base b in http://myfactors.mooo.com/ must be ≤ 1100000))

Lists of small integers in various bases:

https://sites.google.com/view/integer-in-various-base (bases 2 ≤ b ≤ 36) (limit: 12500)
https://math.tools/table/bases-table/ (bases 2 ≤ b ≤ 35) (use lower case letters instead of upper case letters) (limit: 256)
https://math.tools/table/base/ (bases 2 ≤ b ≤ 64) (limit: 64, together with 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000)
https://linesegment.web.fc2.com/application/math/numbers/RadixConversion.html (in Japanese) (bases 2 ≤ b ≤ 36 and b = 62) (limit: 1024 for b = 2 and b = 4, 2187 for b = 3, 3125 for b = 5, b⁴ for 6 ≤ b ≤ 8, 729 for b = 9, 3993 for b = 11, 3456 for b = 12, 4394 for b = 13, b³ for 14 ≤ b ≤ 17, b² for 18 ≤ b ≤ 36, 3843 for b = 62)
https://en.wikipedia.org/wiki/Table_of_bases (bases 2 ≤ b ≤ 36) (limit: 1296)

Also, programs related to this research: (some of these programs can also be downloaded in http://www.fermatsearch.org/download.php or https://www.mersenne.org/download/freeware.php or https://download.mersenne.ca/) (some of these programs need to use GMP (https://gmplib.org/))

Primality (or probable primality) testing (https://en.wikipedia.org/wiki/Primality_test, https://www.rieselprime.de/ziki/Primality_test, https://mathworld.wolfram.com/PrimalityTest.html, https://t5k.org/prove/index.html) programs (https://www.rieselprime.de/ziki/Primality_testing_program):

Sieving (https://www.rieselprime.de/ziki/Sieving, https://www.rieselprime.de/ziki/Sieving_a_range_of_sequences, https://mathworld.wolfram.com/Sieve.html, http://www.rechenkraft.net/yoyo/y_status_sieve.php, https://www.primegrid.com/stats_psp_sieve.php, https://www.primegrid.com/stats_pps_sieve.php, https://www.primegrid.com/stats_sr5_sieve.php, https://www.primegrid.com/stats_cw_sieve.php, https://www.primegrid.com/sieving/rsp/) programs (https://www.rieselprime.de/ziki/Sieving_program):

Integer factoring (https://en.wikipedia.org/wiki/Integer_factorization, https://www.rieselprime.de/ziki/Factorization, https://mathworld.wolfram.com/PrimeFactorization.html, https://mathworld.wolfram.com/PrimeFactorizationAlgorithms.html, http://www.numericana.com/answer/factoring.htm) programs (https://www.rieselprime.de/ziki/Factoring_program): (for more integer factoring programs see https://www.mersenneforum.org/showthread.php?t=3255)

For the files in this page:

File "kernel b": Data for all known minimal primes in base b, expressed as base b strings
File "sqkern b": Data for all known minimal primes in base b, expressed as base b strings, but with x(y^n)z format (which in the README files it is denoted as "xy_nz") (y^n means n copies of y, e.g. 34(5^6)78 is 3455555578, this n is written in decimal) for the minimal primes in base b with (base b) length > 1000
File "left b": x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b) families in base b such that we were unable to determine if they contain a prime > b or not (i.e. x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b) families in base b such that no prime member > b could be found, nor could the family be ruled out as only containing composites (only count the numbers > b)), we reduce these families by removing all trailing digits y from x, and removing all leading digits y from z, to make the families be easier, e.g. family 12333{3}33345 in base b is reduced to family 12{3}45 in base b, since they are in fact the same family, these families are sorted by "the length n number in these families, from the smallest number to the largest number, this n is large enough such that n replaced to any larger number does not affect the sorting" (e.g. for base 17, we sort with B{0}B3 -> B{0}DB -> {B}2BE -> {B}2E -> {B}E9 -> {B}EE, since in this case 7 digits is enough, B0000B3 < B0000DB < BBBB2BE < BBBBB2E < BBBBBE9 < BBBBBEE, if the 7 replaced to any larger number, this result of the sorting will not change (edit: the base 17 family {B}2E was already solved (the probable prime found is B₆₇₁₀₃2E), and the base 17 family {B}2BE is now unneeded since this family is covered by the family {B}2E, but I just use some examples to show how I sort the families in the "left b" files)) (just like https://stdkmd.net/nrr/1/ and https://stdkmd.net/nrr/2/ and https://stdkmd.net/nrr/3/ and https://stdkmd.net/nrr/4/ and https://stdkmd.net/nrr/5/ and https://stdkmd.net/nrr/6/ and https://stdkmd.net/nrr/7/ and https://stdkmd.net/nrr/8/ and https://stdkmd.net/nrr/9/ and https://stdkmd.net/nrr/cont/#form, but not completely like https://stdkmd.net/nrr/cert/1/ and https://stdkmd.net/nrr/cert/2/ and https://stdkmd.net/nrr/cert/3/ and https://stdkmd.net/nrr/cert/4/ and https://stdkmd.net/nrr/cert/5/ and https://stdkmd.net/nrr/cert/6/ and https://stdkmd.net/nrr/cert/7/ and https://stdkmd.net/nrr/cert/8/ and https://stdkmd.net/nrr/cert/9/, e.g. "1w77" ({1}77 in the notation for this project) should be between "11173" ({1}73 in the notation for this project) and "11179" ({1}79 in the notation for this project), "337w" (33{7} in the notation for this project) should be between "337w3" (33{7}3 in the notation for this project) and "337w9" (33{7}9 in the notation for this project), etc.) (note that some of the left families may cover another left family, e.g. the base 19 left family 5{H}5 covers another base 19 left family 5{H}05, and if the smallest prime in family 5{H}5 in base 19 has length n, and the family 5{H}05 in base 19 has no prime with length ≤ n, then family 5{H}05 in base 19 can be removed from the unsolved families for base 19, however, if the smallest prime in family 5{H}5 in base 19 has length n, but the family 5{H}05 in base 19 is not tested to length n or more, then family 5{H}05 in base 19 should not be removed from the unsolved families for base 19, since a number in family 5{H}05 covers the prime in family 5{H}5 with length n if and only if the length of this number is ≥ n+1; besides, the base 19 left family FH0{H} covers another base 19 left family FHHH0{H}, and if the smallest prime in family FH0{H} in base 19 has length n, and the family FHHH0{H} in base 19 has no prime with length ≤ n+1, then family FHHH0{H} in base 19 can be removed from the unsolved families for base 19, however, if the smallest prime in family FH0{H} in base 19 has length n, but the family FHHH0{H} in base 19 is not tested to length n+1 or more, then family FHHH0{H} in base 19 should not be removed from the unsolved families for base 19, since a number in family FHHH0{H} covers the prime in family FH0{H} with length n if and only if the length of this number is ≥ n+2; besides, the base 21 left family {9}D covers another base 21 left family F{9}D, and if the smallest prime in family {9}D in base 21 has length n, and the family F{9}D in base 21 has no prime with length ≤ n, then family F{9}D in base 21 can be removed from the unsolved families for base 21, however, if the smallest prime in family {9}D in base 21 has length n, but the family F{9}D in base 21 is not tested to length n or more, then family F{9}D in base 21 should not be removed from the unsolved families for base 21, since a number in family F{9}D covers the prime in family {9}D with length n if and only if the length of this number is ≥ n+1 (if a family has no primes, then we say "the smallest prime in this family has length ∞ (https://en.wikipedia.org/wiki/Infinity, https://t5k.org/glossary/xpage/Infinite.html, https://mathworld.wolfram.com/Infinity.html) (instead of 0 or −1)", see http://gladhoboexpress.blogspot.com/2019/05/prime-sandwiches-made-with-one-derbread.html and http://chesswanks.com/seq/a306861.txt (for the OEIS sequence https://oeis.org/A306861) and http://chesswanks.com/seq/a269254.txt (for the OEIS sequence https://oeis.org/A269254) (since this is more convenient, e.g. the n of the smallest prime in the base 21 family 9_nD, this family has been searched to n = 100000 with no prime or probable prime found, we can use ">100000" for the n of the smallest prime in the base 21 family 9_nD (while for the n of the smallest prime in the base 13 family A3_nA, it is 592199), ">100000" includes infinity (since infinity is > 100000) but does not includes 0 or −1, it is still possible that there is no prime in the base 21 family 9_nD, although by the heuristic argument (https://en.wikipedia.org/wiki/Heuristic_argument, https://t5k.org/glossary/xpage/Heuristic.html, https://mathworld.wolfram.com/Heuristic.html, https://web.archive.org/web/20230911032453/https://www.utm.edu/staff/caldwell/preprints/Heuristics.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_112.pdf), https://arxiv.org/pdf/2103.04483.pdf (cached copy at https://github.com/xayahrainie4793/pdf-files-cached-copy/blob/main/pdf_113.pdf)) above, this is very impossible, also "the smallest n ≥ 1 such that (a×bⁿ+c)/gcd(a+c,b−1) is prime" should be the infimum (https://en.wikipedia.org/wiki/Infimum, https://mathworld.wolfram.com/Infimum.html) of the set S of the numbers n ≥ 1 such that (a×bⁿ+c)/gcd(a+c,b−1) is prime, and if there is no n ≥ 1 such that (a×bⁿ+c)/gcd(a+c,b−1) is prime, then this set S is the empty set (https://en.wikipedia.org/wiki/Empty_set, https://mathworld.wolfram.com/EmptySet.html), and by the definition of "inf", the infimum of the empty set is ∞), ∞ is > any finite number, e.g. "the smallest n ≥ 1 such that k×2ⁿ+1 is prime" is ∞ for k = 78557, 157114, 271129, 271577, 314228, 322523, 327739, 482719, ..., while it is 31172165 for k = 10223 and 13018586 for k = 19249, another example is "the smallest n such that (bⁿ−1)/(b−1) is prime" is ∞ for b = 9, 25, 32, 49, 64, 81, 121, 125, 144, 169, 216, 225, 243, 289, 324, 343, 361, 441, 484, 529, 625, 729, 784, 841, 900, 961, 1000, ..., while it is 62903 for b = 691 and 41189 for b = 693))
File "special b": Non-linear families which cannot be ruled out by the "GMP.cc" program (https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/code/kGMP.cc), but you can either handle them by hand or analyse them with the "famk.cc" program (https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/code/famk.cc)

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README.md

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b	number of possible first digits of a prime > b in base b (equal b−1, since all digits except 0 can be the first digit)	number of possible last digits of a prime > b in base b (equal eulerphi(b), since only digits coprime to b (i.e. the digits in the reduced residue system mod b) can be the last digit)	number of possible (first digit,last digit) combos of a prime > b in base b (equal (b−1)×eulerphi(b), by the rule of product), also the relative hardness for the "minimal prime problem" in base b
2	1	1	1
3	2	2	4
4	3	2	6
5	4	4	16
6	5	2	10
7	6	6	36
8	7	4	28
9	8	6	48
10	9	4	36
11	10	10	100
12	11	4	44
13	12	12	144
14	13	6	78
15	14	8	112
16	15	8	120
17	16	16	256
18	17	6	102
19	18	18	324
20	19	8	152
21	20	12	240
22	21	10	210
23	22	22	484
24	23	8	184
25	24	20	480
26	25	12	300
27	26	18	468
28	27	12	324
29	28	28	784
30	29	8	232
31	30	30	900
32	31	16	496
33	32	20	640
34	33	16	528
35	34	24	816
36	35	12	420

b	number of possible first digits of a prime > b in base b (equal b−1, since all digits except 0 can be the first digit)	number of possible last digits of a prime > b in base b (equal eulerphi(b), since only digits coprime to b (i.e. the digits in the reduced residue system mod b) can be the last digit)	number of possible (first digit,last digit) combos of a prime > b in base b (equal (b−1)×eulerphi(b), by the rule of product), also the relative hardness for the "minimal prime problem" in base b
2	1	1	1
3	2	2	4
4	3	2	6
5	4	4	16
6	5	2	10
7	6	6	36
8	7	4	28
9	8	6	48
10	9	4	36
11	10	10	100
12	11	4	44
13	12	12	144
14	13	6	78
15	14	8	112
16	15	8	120
17	16	16	256
18	17	6	102
19	18	18	324
20	19	8	152
21	20	12	240
22	21	10	210
23	22	22	484
24	23	8	184
25	24	20	480
26	25	12	300
27	26	18	468
28	27	12	324
29	28	28	784
30	29	8	232
31	30	30	900
32	31	16	496
33	32	20	640
34	33	16	528
35	34	24	816
36	35	12	420

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b	number of possible first digits of a prime > b in base b (equal b−1, since all digits except 0 can be the first digit)	number of possible last digits of a prime > b in base b (equal eulerphi(b), since only digits coprime to b (i.e. the digits in the reduced residue system mod b) can be the last digit)	number of possible (first digit,last digit) combos of a prime > b in base b (equal (b−1)×eulerphi(b), by the rule of product), also the relative hardness for the "minimal prime problem" in base b
2	1	1	1
3	2	2	4
4	3	2	6
5	4	4	16
6	5	2	10
7	6	6	36
8	7	4	28
9	8	6	48
10	9	4	36
11	10	10	100
12	11	4	44
13	12	12	144
14	13	6	78
15	14	8	112
16	15	8	120
17	16	16	256
18	17	6	102
19	18	18	324
20	19	8	152
21	20	12	240
22	21	10	210
23	22	22	484
24	23	8	184
25	24	20	480
26	25	12	300
27	26	18	468
28	27	12	324
29	28	28	784
30	29	8	232
31	30	30	900
32	31	16	496
33	32	20	640
34	33	16	528
35	34	24	816
36	35	12	420