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2020-10-31, 03:36
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#2 |
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3·1,193 Posts |
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Link 1:
* Smallest prime of the form k*b^n+-1 with n>=1 for bases 2<=b<=1030 and k<CK Link 2: * Primes of the form n*b^n-1 with n>=b-1 for bases 3<=b<=10000 * Primes of the form n*b^n+1 with n>=1 for bases 101<=b<=10000 * Primes of the form x^y*y^x+1 * Primes of the form x^y*y^x-1 * Primes of the form (n+-1)*b^n+-1 with n>=1 for bases 2<=b<=128 * Primes of the form (x^y+-1)*y^+-1 with x=2 or y=2 * Primes of the form b*(b+1)^n-1 with n>=1 and bases 2<=b<=2048 * Primes of the form (b^n+-1)^2-2 with n>=1 and bases b = 2, 6, 10, 14, 22, 204 * Numbers n such that k*2^n+1 and k*2^(n+1)+1 are both primes Link 3: * Primes of the form n*b^n+1 with n>=1 for bases 3<=b<=100 Link 4: * Primes of the form (b^p-1)/(b-1) with prime p for 2<=b<=160 * Primes of the form (b^p+1)/(b+1) with odd prime p for 2<=b<=160 * Primes of the form (b+1)^p-b^p with prime p for 1<=b<=160 * Primes p such that n^p-1 == 1 mod p^2 for 2<=n<=10125 Link 5: * Numbers n such that k*2^n+-1 are both primes * Numbers n such that k*2^n-1 and k*2^(n+1)-1 are both primes Link 6: * Smallest prime of the form k*2^n+-1 with even/odd n>=1 for k<CK |
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2020-10-31, 03:45
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#3 |
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3·1,193 Posts |
GitHub Pages for the smallest n>=1 such that (k*b^n+-1)/gcd(k+-1,b-1) created by me:
k<CK, b<=128 or 256, 512, 1024 k<=1024, b<=32 or b = 64, 128, 256 k<4th CK, b<=64 (except 2, 3, 6, 15, 22, 24, 28, 30, 36, 40, 42, 46, 48, 52, 58, 60, 63) or b = 100, 128, 256, 512, 1024 k<=12, b<=1024 |
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2020-10-31, 23:14
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#4 |
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3·1,193 Posts |
Links for the dual Sierpinski problem:
* https://oeis.org/A076336/a076336c.html * https://mersenneforum.org/showthread.php?t=10761 * http://sierpinski.insider.com/dual (broken link and excluded from wayback machine: from archive today cached copy) * http://www.mit.edu/~kenta/three/prim...rp-excerpt.txt * https://www.rechenkraft.net/wiki/Five_or_Bust * https://oeis.org/A067760 * https://oeis.org/A033919 Links for the dual Riesel problem: * https://mersenneforum.org/showthread.php?t=6545 * https://oeis.org/A252168 * https://oeis.org/A096502 * https://oeis.org/A276417 The "mixed Sierpinski conjecture base 2" is proven. The k remaining for the original Sierpinski conjecture base 2 are: {21181, 22699, 24737, 55459, 67607} (references: http://www.prothsearch.com/sierp.html, http://www.primegrid.com/forum_thread.php?id=1647, http://www.noprimeleftbehind.net/cru...es-powers2.htm, http://www.primegrid.com/stats_sob_llr.php) and for the dual primes (2^n+k): Code:
k n 21181 28 22699 26 24737 17 55459 14 67607 16389 The k remaining for the original Sierpinski conjecture base 5 are: {6436, 7528, 10918, 26798, 29914, 31712, 36412, 41738, 44348, 44738, 45748, 51208, 58642, 60394, 62698, 64258, 67612, 67748, 71492, 74632, 76724, 83936, 84284, 90056, 92906, 93484, 105464, 126134, 139196, 152588} (references: http://www.primegrid.com/forum_thread.php?id=5087, http://www.noprimeleftbehind.net/cru...e5-reserve.htm, http://primegrid.com/stats_sr5_llr.php) and for the dual primes (5^n+k): Code:
k n 6436 24 7528 36 10918 144 26798 1505 29914 4 31712 50669 36412 458 41738 3 44348 9 44738 485 45748 12 51208 12 58642 46 60394 12 62698 2 64258 2 67612 10 67748 41 71492 13 74632 74 76724 7 83936 3 84284 21 90056 181 92906 23 93484 4 105464 11 126134 11 139196 1 152588 15 Some pdf files: 1. http://www.kurims.kyoto-u.ac.jp/EMIS...rs/i61/i61.pdf 2. https://scholar.rose-hulman.edu/cgi/...&context=rhumj 3. https://www.utm.edu/staff/caldwell/preprints/2to100.pdf 4. https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf 5. https://www.ams.org/journals/mcom/19...-0427213-2.pdf 6. http://chesswanks.com/num/LTPs/ 7. https://oeis.org/A028491/a028491.pdf 8. http://emis.impa.br/EMIS/journals/JI...NER/dubner.pdf Sierpinski conjectures in bases 2<=b<=128 and b = 256, 512, 1024 Riesel conjectures in bases 2<=b<=128 and b = 256, 512, 1024 Sierpinski conjectures in bases 2<=b<=200 and b = 256, 512, 1024 Riesel conjectures in bases 2<=b<=200 and b = 256, 512, 1024 First 4 Riesel conjectures in selected bases 2<=b<=64 and b = 100, 128, 256, 512, 1024 (the zip file is for the archive today's archive for website which are excluded from wayback machine) Last fiddled with by sweety439 on 2021-09-13 at 07:18 |
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2020-11-06, 12:07
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#6 |
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
67738 Posts |
A link of generalized repunit primes (achieved):
Index (broken link: from wayback machine cached copy) List of generalized repunit proven primes >= 1000 decimal digits (broken link: from wayback machine cached copy) List of generalized repunit (probable) primes bases 2 to 999 (broken link: from wayback machine cached copy) List of generalized repunit proven primes >= 1000 decimal digits (broken link: from wayback machine cached copy) List of generalized repunit probable primes >= 1000 decimal digits (broken link: from wayback machine cached copy) Last fiddled with by sweety439 on 2021-08-10 at 13:41 |
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2020-11-08, 11:18
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#7 |
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
1101111110112 Posts |
Base-dependent types of primes (in various bases)
Links for left truncatable primes:
http://primerecords.dk/left-truncatable.txt http://rosettacode.org/wiki/Truncatable_primes http://chesswanks.com/num/LTPs/ http://www.primerecords.dk/left-truncatable.htm http://www.worldofnumbers.com/truncat.htm http://www.lifl.fr/~jdelahay/dnalor/ChasseursNbPr.pdf https://rosettacode.org/wiki/Find_la...n_a_given_base https://www.ams.org/journals/mcom/19...-0427213-2.pdf http://www.wschnei.de/digit-related-...ar-primes.html (broken link: from wayback machine cached copy) https://www.primepuzzles.net/puzzles/puzz_002.htm Links for right truncatable primes: http://primerecords.dk/right-truncatable.txt http://fatphil.org/maths/rtp/rtp.html http://www.worldofnumbers.com/truncat.htm http://www.lifl.fr/~jdelahay/dnalor/ChasseursNbPr.pdf https://codegolf.meta.stackexchange....es/17229#17229 https://hlma.math.cuhk.edu.hk/wp-con...ea1b2408fa.pdf https://www.ams.org/journals/mcom/19...-0427213-2.pdf http://www.wschnei.de/digit-related-...ar-primes.html (broken link: from wayback machine cached copy) https://www.primepuzzles.net/puzzles/puzz_002.htm Links for deletable primes: http://www.wschnei.de/digit-related-...ar-primes.html (broken link: from wayback machine cached copy) https://www.primepuzzles.net/puzzles/puzz_002.htm Links for minimal primes: http://www.wiskundemeisjes.nl/wp-con...02/minimal.pdf https://www.pourlascience.fr/sd/math...idaux-4744.php https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf https://scholar.colorado.edu/downloads/hh63sw661 https://cs.uwaterloo.ca/~cbright/tal...mal-slides.pdf https://doi.org/10.1080/10586458.2015.1064048 (need access) http://recursed.blogspot.com/2006/12/prime-game.html https://github.com/curtisbright/mepn-data https://github.com/RaymondDevillers/primes https://www.primepuzzles.net/puzzles/puzz_178.htm Links for weakly primes: https://arxiv.org/pdf/1510.03401 https://arxiv.org/pdf/2101.08898 https://arxiv.org/pdf/0802.3361 https://people.math.sc.edu/filaseta/...Primes2021.pdf https://doi.org/10.1017%2FS1446788712000043 https://www.quantamagazine.org/mathe...rimes-20210330 http://people.missouristate.edu/lesreid/Soln12.html https://www.primepuzzles.net/puzzles/puzz_017.htm https://www.primepuzzles.net/puzzles/puzz_612.htm Links for permutable primes: https://arxiv.org/pdf/1811.08613.pdf https://www.jstor.org/stable/2689862 https://www.jstor.org/stable/2689222 https://www.tandfonline.com/doi/abs/....1974.11976408 https://oeis.org/A003459/a003459.pdf http://www.lifl.fr/~jdelahay/dnalor/ChasseursNbPr.pdf https://zbmath.org/?format=complete&q=an:0054.02305 http://www.lacim.uqam.ca/~plouffe/OE...ute_Primes.pdf (broken link: from wayback machine, pdf file attached below) http://www.wschnei.de/digit-related-...ar-primes.html (broken link: from wayback machine cached copy) Links for circular primes: http://www.worldofnumbers.com/circular.htm https://tangente-mag.com/maths_etonnantes.php?id=3139 http://www.lifl.fr/~jdelahay/dnalor/ChasseursNbPr.pdf https://www.mathpages.com/home/kmath362.htm http://www.wschnei.de/digit-related-...ar-primes.html (broken link: from wayback machine cached copy) Links for repunit primes: https://stdkmd.net/nrr/repunit/ http://www.kurtbeschorner.de/ http://www.elektrosoft.it/matematica...it/repunit.htm https://gmplib.org/~tege/repunit.html http://repunit:1031@repunits.skoberne.net/list/ (broken link: from wayback machine cached copy) http://www.fermatquotient.com/PrimSerien/GenRepu.txt http://www.primenumbers.net/Henri/us/MersFermus.htm https://listserv.nodak.edu/cgi-bin/w...;417ab0d6.0906 (archive today cannot automatically return the archive page, if you use archive today, click https://archive.is/WCvbi) http://www.users.globalnet.co.uk/~aads/primes.html (broken link: from wayback machine cached copy) Links for palindromic primes: http://www.worldofnumbers.com/palpri.htm https://www.mathpages.com/home/kmath359.htm (excluded from wayback machine: cached copy) https://arxiv.org/pdf/math/0405056 http://www.maa.org/mathland/mathtrek_5_10_99.html (broken link: from wayback machine cached copy) https://primes.utm.edu/top20/page.php?id=53 Links for reversible primes: https://www.primepuzzles.net/puzzles/puzz_020.htm https://www.primepuzzles.net/puzzles/puzz_973.htm Links for Smarandache primes: http://sprott.physics.wisc.edu/picko...ianglegod.html http://www.worldofnumbers.com/factorlist.htm https://vixra.org/pdf/1005.0104v2.pdf http://fs.unm.edu/micha.txt http://www.asahi-net.or.jp/~KC2H-MSM...tha1/micha.txt http://chesswanks.com/pxp/smfactors.html http://99.121.249.54:1200/ (broken link and both wayback machine and archive today did not achieve) https://www.primepuzzles.net/puzzles/puzz_008.htm https://mersenneforum.org/showthread.php?t=20527 https://mersenneforum.org/showthread.php?t=20535 Links for Smarandache-Wellin primes: https://www.primepuzzles.net/puzzles/puzz_008.htm http://www.asahi-net.or.jp/~KC2H-MSM...1/sm_prime.htm http://fs.unm.edu/SmConPri.txt My GitHub page for left truncatable primes, right truncatable primes, minimal primes, two-sided primes (both left truncatable and right truncatable) (all in bases 2 to 160): https://github.com/xayahrainie4793/m...catable-primes My GitHub pages for all these types of primes: https://raw.githubusercontent.com/xa...%20to%2012.txt https://raw.githubusercontent.com/xa...%20to%2036.txt My sites for all these types of primes: https://sites.google.com/view/base-d...pes-of-primes/ https://sites.google.com/view/larges...endent-primes/ Prime Glossary pages: (no article for "Smarandache prime") left truncatable prime right truncatable prime deletable prime minimal prime weakly prime permutable prime circular prime repunit palindromic prime reversible prime Smarandache-Wellin prime Wikipedia pages: truncatable prime deletable prime (broken link: from wayback machinie) minimal prime weakly prime permutable prime circular prime repunit palindromic prime reversible prime Smarandache prime (broken link: from wayback machine) Smarandache-Wellin prime Mathworld pages: (no article for "minimal prime") truncatable prime deletable prime weakly prime permutable prime circular prime repunit palindromic prime reversible prime Smarandache prime Smarandache-Wellin prime Numbers Aplenty pages: truncatable prime weakly prime palindromic prime reversible prime Prime Curios! pages for the largest/smallest such primes: left truncatable prime (b=10) right truncatable prime (b=10) two-sided prime (b=10) minimal prime (b=5) minimal prime (b=6) minimal prime (b=7) minimal prime (b=8) minimal prime (b=9) minimal prime (b=10) weakly prime (b=10) permutable prime (b=10) circular prime (b=10) repunit prime (b=10) Bitman pages: (b is the base) (no "data" for "two-sided prime" and "permutable prime" and "Smarandache prime" and "Smarandache-Wellin prime", for the data see corresponding "article", also there is an article about the conjecture about "Smarandache prime") truncatable prime (article) left truncatable prime (data for 2<=b<=20) right truncatable prime (data for 2<=b<=20) deletable prime (article) deletable prime (data for 2<=b<=20) minimal prime (article) minimal prime (data for 2<=b<=16) minimal prime (data for b=17) minimal prime (data for b=18) minimal prime (data for b=19) minimal prime (data for b=20) weakly prime (article) weakly prime (data for 2<=b<=20) permutable prime (article) circular prime (article) circular prime (data for 2<=b<=20) repunit prime (article) repunit prime (data for 2<=b<=100) palindromic prime (article) palindromic prime (data for 2<=b<=10) palindromic prime (data for 11<=b<=20) reversible prime (article) reversible prime (data for 2<=b<=20) Smarandache prime, Smarandache-Wellin prime (article) OEIS sequences: #1 = left truncatable primes #2 = right truncatable primes #3 = two-sided primes (both left truncatable and right truncatable) #4 = deletable primes #5 = minimal primes #6 = weakly primes #7 = permutable primes (for sequences B, C, D and "sequences of such primes in various bases b", repunit primes are excluded) #8 = circular primes (for sequences B, C, D and "sequences of such primes in various bases b", repunit primes are excluded) #9 = repunit primes #10 = palindromic primes #11 = reversible primes #12 = Smarandache primes #13 = Smarandache-Wellin primes (for sequence B and C, the prime 2 is excluded, since 2 is Smarandache-Wellin prime in every base, make it trivial and uninteresting) A = Such primes in base 10 B = Largest (or smallest, in case of weakly prime and repunit prime and Smarandache prime and Smarandache-Wellin prime) such prime in base n (written in base 10) C = Length of largest (or smallest, in case of weakly prime and repunit prime and Smarandache prime and Smarandache-Wellin prime) such prime in base n D = Number of such primes in base n Code:
A B C D #1 A024785 A103443 A103463 A076623 #2 A024770 A023107 A103483 A076586 #3 A020994 A323137 A?????? A323390 #4 A305352 (no sequences B, C, D since such primes are conjectured to exist infinitely many in every base) #5 A071062 A326609 A330049 A330048 #6 A050249 A186995 A?????? (no sequences D since such primes are conjectured to exist infinitely many in every base) #7 A003459 A317689 A?????? A?????? #8 A068652 A293142 A?????? A?????? #9 A004022 A084738 A084740 (no sequences D since such primes are conjectured to exist infinitely many in every base which is not perfect power, but there is OEIS sequence A085104 for the primes which is nontrivial such primes in some base) #10 A002385 (no sequences B, C, D since such primes are conjectured to exist infinitely many in every base, but there is OEIS sequence A016038 for the numbers which is not nontrivial such primes in any base, all such numbers >6 are primes) #11 A006567 (no sequences B, C, D since such primes are conjectured to exist infinitely many in every base) #12 A?????? A?????? A?????? (no sequences D since such primes are conjectured to exist infinitely many in every base) #13 A069151 A?????? A?????? (no sequences D since such primes are conjectured to exist infinitely many in every base) Code:
b 2 3 4 5 6 7 8 9 10 11 12 #1 A000000 A?????? A129940 A129941 A129942 A129943 A129944 A129945 A024785 A?????? A?????? #2 A000000 A129669 A129670 A129671 A129672 A129673 A129692 A129693 A024770 A?????? A?????? #3 A000000 A?????? A?????? A?????? A?????? A?????? A?????? A?????? A020994 A?????? A?????? #4 A000000 A319596 A321657 A321700 A322173 A321910 A322443 A322471 A305352 A322475 A322477 #5 A?????? A?????? A?????? A?????? A?????? A?????? A?????? A?????? A071062 A?????? A110600 #6 A137985 A?????? A?????? A?????? A?????? A?????? A?????? A?????? A050249 A?????? A?????? #7 A000000 A?????? A?????? A?????? A?????? A?????? A?????? A?????? A317688 A?????? A?????? #8 A000000 A?????? A293657 A293658 A293659 A293660 A293661 A293662 A293663 A?????? A?????? #9 A000668 A076481 A?????? A086122 A165210 A102170 A?????? A000000 A004022 A?????? A?????? #10 A016041 A029971 A029972 A029973 A029974 A029975 A029976 A029977 A002385 A029978 A029979 #11 A080790 A?????? A?????? A?????? A?????? A?????? A?????? A?????? A006567 A?????? A?????? #12 A?????? A?????? A?????? A?????? A?????? A?????? A?????? A?????? A?????? A?????? A?????? #13 A?????? A?????? A?????? A?????? A?????? A?????? A?????? A?????? A069151 A?????? A?????? Code:
#1,b=3 2, 5, 23 #3,b=3 2, 23 #3,b=4 2, 3, 11 #5,b=2 2, 3 #5,b=3 2, 3, 13 #5,b=4 2, 3, 5 #7,b=3 2, 5, 7 #8,b=3 2, 5, 7 #9,b=4 5 #9,b=8 73 Conjectured cardinality of the set of these 13 types of primes in given base: #1 "left truncatable primes": Conjectured finite in every base (reference: https://www.ams.org/journals/mcom/19...-0427213-2.pdf https://rosettacode.org/wiki/Find_la...n_a_given_base http://chesswanks.com/num/LTPs/) #2 "right truncatable primes": Conjectured finite in every base (reference: https://www.ams.org/journals/mcom/19...-0427213-2.pdf http://fatphil.org/maths/rtp/rtp.html) #3 "two-sided primes": Conjectured finite in every base (since all two-sided primes are also left truncatable primes and right truncatable primes) #4 "deletable primes": Conjectured infinite in every base (reference: https://primes.utm.edu/glossary/xpag...ablePrime.html) #5 "minimal primes": Proven finite in every base (reference: http://www.wiskundemeisjes.nl/wp-con...02/minimal.pdf https://cs.uwaterloo.ca/~cbright/tal...mal-slides.pdf http://recursed.blogspot.com/2006/12/prime-game.html #6 "weakly primes": Proven infinite in every base (reference: https://arxiv.org/pdf/0802.3361.pdf https://www.cambridge.org/core/journ...5432734E9A87FD) #7 "permutable primes": Conjectured finite in every base if repunit primes are not counted (reference: https://www.jstor.org/stable/2689222 https://www.tandfonline.com/doi/abs/....1974.11976408 https://oeis.org/A317689) #8 "circular primes" Conjectured finite in every base if repunit primes are not counted (reference: https://oeis.org/A293142 https://oeis.org/A327835) #9 "repunit primes": Proven finite (only 0 or 1 such primes) in every perfect-power base and conjecture infinite in every non-perfect-power base (reference: https://listserv.nodak.edu/cgi-bin/w...;417ab0d6.0906 https://web.archive.org/web/20021111...ds/primes.html http://www.fermatquotient.com/PrimSerien/GenRepu.txt) #10 "palindromic primes": Conjectured infinite in every base (reference: http://www.worldofnumbers.com/nobase10.htm http://web.archive.org/web/201212291...k_5_10_99.html https://arxiv.org/pdf/math/0405056.pdf) #11 "reversible primes": Conjectured infinite in every base (reference: https://en.wikipedia.org/wiki/Emirp) #12 "Smarandache primes": Conjectured infinite in every base (reference: https://mersenneforum.org/showthread.php?t=20527 https://mersenneforum.org/showthread.php?t=20535) #13 "Smarandache-Wellin primes": Conjectured infinite in every base (reference: https://en.wikipedia.org/wiki/Talk:S...Wellin_primes?) All single-digit primes (i.e. primes < base) are trivial these 13 types of primes (except "weakly prime", "repunit prime", "reversible prime", "Smarandache primes", "Smarandache-Wellin primes") in the same base. All repunit primes are trivial permutable primes, circular primes, and palindromic primes in the same base, besides, the smallest repunit prime (if exists) is always minimal prime in the same base, and this prime is the only repunit prime which is also minimal prime in the same base, also, a repunit prime cannot be left truncatable prime, right truncatable prime, or deletable prime in the same base, since 1 is not prime. All left truncatable primes and all right truncatable primes are deletable primes in the same base. A minimal prime cannot be left truncatable prime, right truncatable prime, or deletable prime in the same base, unless it is single-digit prime. The attached text file does not include "deletable prime", "palindromic prime", and "reversible prime", since it is conjectured there are infinitely many such primes in every base, and unlikely weakly prime and repunit prime (it is also conjectured that there are infinitely many weakly primes in every base, and it is also conjectured that there are infinitely many repunit primes in every base which is not perfect power; for perfect power bases, all repunit numbers are not primes; the only possible exception is when the base b is m^(p^r) with p prime and m>=2, r>=1, only the repunit with length p may be prime; if the base b is m^r with m>=2 and r is not prime or prime power, then all repunit numbers are not primes), the smallest such primes are only 2 Edit: There seems to be a proof that there are infinitely many weakly primes in every base, but I do not know that there is also a proof for deletable primes, palindromic primes, and reversible primes (I only know that there is no proof for repunit primes). All base b given type in these 13 types of primes (except "weakly prime", "repunit prime", "palindromic prime", "reversible prime", "Smarandache primes", "Smarandache-Wellin primes") are also the same type of primes in base b^n for every n>=1 By the theorem that there are no infinite antichains for the subsequence ordering, there are only finitely minimal primes in every base, but no proof is known for left truncatable primes, right truncatable primes, and two-sided primes, however, it is likely that there are only finitely many left truncatable primes and finitely many right truncatable primes (thus only finitely many two-sided primes, since all two-sided primes are also left truncatable primes and right truncatable primes) in every base, even no proof is known for non-repunit permutable primes and non-repunit circular primes, but it is very likely that there are only finitely many non-repunit circular primes (thus only finitely many non-repunit permutable primes, since all permutable primes are also circular primes) in every base, e.g. in base 10, there are no non-repunit permutable primes >991 and <10^(6*10^175), reference: https://zbmath.org/?format=complete&q=an:0054.02305 The expected largest base b left truncatable prime is (see http://chesswanks.com/num/LTPs/), and the expected largest base b right truncatable prime is b^(e^sqrt(b)), and for the expected largest base b minimal prime, we should use the sense of https://mersenneforum.org/showpost.p...65&postcount=7 and https://mersenneforum.org/showpost.p...86&postcount=3 and https://mersenneforum.org/showpost.p...3&postcount=18 (finding the Nash weight (or difficulty)) to every unsolved families (example: base 25 and base 34), and the expected smallest base b weakly prime is b^(e^sqrt(eulerphi(b))), and the expected number of base b repunit primes <=n digits is (see http://www.fermatquotient.com/PrimSerien/GenRepu.txt and https://listserv.nodak.edu/cgi-bin/w...;417ab0d6.0906), and the expected number of base b palindromic primes <=n digits is 1/log(b^n)*Sum {k=1..n} (b-1)*b^floor[(k-1)/2], and the expected number of base b Smarandache primes <=n digits is (see https://mersenneforum.org/showpost.p...73&postcount=1) For the conjectured cardinality of the set of given types of primes in given base, and the excepted (number of such primes, the largest/smallest such primes) of given types of primes in given base, see https://oeis.org/wiki/User:Charles_R...special_primes for more information. Last fiddled with by sweety439 on 2022-04-02 at 20:46 |
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2020-11-08, 13:45
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#8 |
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3·1,193 Posts |
Links of factorization of many types of numbers:
b^n+-1 (b<=12) b^n+-1 (13<=b<=99, b^n<10^255) p^p+-1 (p is prime) Repunits and near-repdigits and quasi-repdigits Homogeneous Cunninghams numbers (a^n+-b^n) Fibonacci numbers and Lucas numbers Fermat numbers Generalized Fermat numbers Generalized Cullen/Woodall numbers (n*b^n+-1) k*2^n+-1 for k = 3, 5, 7, 9, 11, 13, 15 n!+-1 Bernoulli numbers and Euler numbers Last fiddled with by sweety439 on 2022-04-07 at 10:44 |
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2020-11-08, 13:50
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#9 |
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
1101111110112 Posts |
Link for pseudoprimes:
http://www.numericana.com/answer/pseudo.htm http://ntheory.org/pseudoprimes.html http://www.cecm.sfu.ca/Pseudoprimes/index-2-to-64.html http://gilchrist.ca/jeff/factoring/pseudoprimes.html Last fiddled with by sweety439 on 2021-06-11 at 18:27 |
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2020-11-08, 14:02
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#10 |
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3·1,193 Posts |
GIMPS main page (factorization of Mersenne numbers): https://www.mersenne.org/
For all known Mersenne primes (total 51), see https://www.mersenne.org/primes/ Last fiddled with by sweety439 on 2021-06-11 at 18:12 |
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2020-11-09, 16:35
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#11 |
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
357910 Posts |
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![Reply](data:image/svg+xml,<svg xmlns="http://www.w3.org/2000/svg" width="110" height="26"><rect fill-opacity="0"/></svg> "Reply") |
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