| Base | Conjectured Sierpinski k | Covering set | k's that make a full covering set with all or partial algebraic factors | Trivial k's (factor) | Remaining k to find prime (n testing limit) |
Top 10 k's with largest first primes: k (n) | Comments / GFn's without a prime / accounting of all k's |
|---|---|---|---|---|---|---|---|
| 2 | 78557 | 3, 5, 7, 13, 19, 37, 73 | none | 21181 (38.7M) 22699 (38.9M) 24737 (38.7M) 55459 (38.7M) 67607 (38.9M) |
10223 (31172165) 19249 (13018586) 27653 (9167433) 28433 (7830457) 33661 (7031232) 5359 (5054502) 4847 (3321063) 54767 (1337287) 69109 (1157446) 65567 (1013803) |
All k's are being worked on by PrimeGrid's
Seventeen or Bust project. See k's and test limits at
Seventeen or Bust stats. k = 65536 is a GFn with no known prime. all-ks-sierp-base2.txt |
|
| 2 2nd conjecture |
271129 | 3, 5, 7, 13, 17, 241 | none | 79309 (28.8M) 79817 (28.5M) 90646 (10M) 91549 (23.3M) 101746 (10M) 131179 (23.3M) 152267 (28.6M) 156511 (28.6M) 163187 (23.4M) 200749 (23.3M) 209611 (23.3M) 222113 (28.5M) 225931 (28.4M) 227723 (23.3M) 229673 (23.3M) 237019 (28.3M) 238411 (23.3M) |
202705 (21320516) 168451 (19375200) 99739 (14019102) 193997 (11452891) 90527 (9162167) 161041 (7107964) 258317 (5450519) 265711 (4858008) 211195 (3224974) 94373 (3206717) |
Only k>78557 are considered. Prime k's are being worked on by PrimeGrid's Prime Sierpinski Problem project. See k's and test limits at Prime Sierpinski stats. Composite odd k's are being worked on by PrimeGrid's Extended Sierpinski Problem project. See k's and test limits at Extended Sierpinski stats. k = 131072 and 262144 are GFn's with no known prime. all-ks-sierp-base2-2nd-conj.zip |
|
| 2 even-n |
66741 | 5, 7, 13, 17, 241 | k = = 2 mod 3 (3) | none - proven | 23451 (3739388) 60849 (3067914) 42717 (905792) 33879 (378022) 33771 (178200) 23799 (105890) 51171 (93736) 14661 (91368) 41709 (80594) 58791 (79420) |
Only k's where k = = 3 mod 6 are considered. See additional details at The Liskovets-Gallot conjectures. all-ks-sierp-base2-evenn.txt |
|
| 2 odd-n |
95283 | 5, 7, 13, 19, 73, 109 | k = = 1 mod 3 (3) | 9267 (15M) 32247 (10M) 53133 (10M) |
84363 (2222321) 85287 (1890011) 60357 (1676907) 80463 (468141) 24693 (357417) 37953 (298913) 70467 (268503) 39297 (169495) 61137 (162967) 91437 (161615) |
Only k's where k = = 3 mod 6 are considered. See additional details at The Liskovets-Gallot conjectures. all-ks-sierp-base2-oddn.txt |
|
| 4 | 66741 | 5, 7, 13, 17, 241 | k = = 2 mod 3 (3) | 18534 (7.5M) 21181 (19.35M) 22699 (19.45M) 49474 (19.35M) 55459 (19.35M) 64494 (5M) |
20446 (15586082) 19249 (6509293) 55306 (4583716) 56866 (3915228) 33661 (3515616) 5359 (2527251) 23451 (1869694) 9694 (1660531) 60849 (1533957) 44131 (497986) |
k's where k = = 1 mod 3 are being worked on by PrimeGrid's
Seventeen or Bust project. k's, test limits, and primes are converted from base 2. k = 65536 is a GFn with no known prime. all-ks-sierp-base4.txt |
|
| 8 | 47 | 3, 5, 13 | All k = m^3 for all n; factors to: (m*2^n + 1) * (m^2*4^n - m*2^n + 1) |
k = = 6 mod 7 (7) | none - proven | 31 (20) 46 (4) 40 (4) 37 (4) 28 (4) 45 (3) 38 (3) 36 (3) 26 (3) 23 (3) |
k = 1 and 8 proven composite by full algebraic factors. all-ks-sierp-base8.txt |
| 16 | 66741 | 7, 13, 17, 241 | All
k=4*q^4 for all n: let k=4*q^4 and let m=q*2^n; factors to: (2*m^2 + 2m + 1) * (2*m^2 - 2m + 1) |
k = = 2 mod 3 (3) k = = 4 mod 5 (5) |
2908 (1M) 6663 (1M) 10183 (1M) 17118 (1M) 21181 (9.675M) 24582 (1M) 30397 (1M) 35818 (1M) 40410 (1M) 42745 (1M) 44035 (1M) 57867 (1M) 60070 (1M) 64620 (1M) |
20446 (7793041) 55306 (2291858) 56866 (1957614) 33661 (1757808) 21436 (1263625) 23451 (934847) 65077 (901486) 38776 (830265) 53653 (577962) 18598 (484327) |
k's where k = = 1 mod 15 are being worked on by PrimeGrid's
Seventeen or Bust project. k's, test limits, and primes are converted from base 2. k = 2500 and 40000 proven composite by full algebraic factors. k=65536 is a GFn with no known prime. all-ks-sierp-base16.txt |
| 32 | 10 | 3, 11 | All k = m^5 for all n; factors to: (m*2^n + 1) * (m^4*16^n - m^3*8^n + m^2*4^n - m*2^n + 1) |
k = = 30 mod 31 (31) | none - proven | 9 (13) 7 (4) 5 (3) 6 (1) 3 (1) |
k = 1 proven composite by full algebraic factors. k = 4 is a GFn with no known prime. all-ks-sierp-base32.txt |
| 64 | 51 | 5, 13 | All k = m^3 for all n; factors to: (m*4^n + 1) * (m^2*16^n - m*4^n + 1) |
k = = 2 mod 3 (3) k = = 6 mod 7 (7) |
none - proven | 24 (31) 31 (10) 30 (6) 39 (3) 46 (2) 45 (2) 40 (2) 37 (2) 36 (2) 28 (2) |
k = 1 proven composite by full algebraic factors. all-ks-sierp-base64.txt |
| 128 | 44 | 3, 43 | All k = m^7 for all n; factors to: (m*2^n + 1) * (m^6*64^n - m^5*32^n + m^4*16^n - m^3*8^n + m^2*4^n - m*2^n + 1) |
k = = 126 mod 127 (127) | 40 (1.2857M) | 41 (39271) 42 (13001) 20 (473) 28 (322) 38 (291) 19 (178) 25 (64) 3 (27) 17 (21) 31 (20) |
k = 1 proven composite by full algebraic factors. k = 16 is a GFn with no known prime. k = 8 and 32 are GFn's with no possible prime. all-ks-sierp-base128.txt |
| 256 | 1221 | 7, 13, 241 | k = = 2 mod 3 (3) k = = 4 mod 5 (5) k = = 16 mod 17 (17) |
831 (1M) | 535 (109243) 691 (25890) 712 (19406) 946 (6821) 346 (2914) 1165 (2368) 751 (1914) 1132 (1763) 523 (1428) 888 (1360) |
all-ks-sierp-base256.txt | |
| 512 | 18 | 5, 13, 19 | All k = m^3 for all n; factors to: (m*8^n + 1) * (m^2*64^n - m*8^n + 1) |
k = = 6 mod 7 (7) k = = 72 mod 73 (73) |
5 (1M) | 12 (23) 14 (21) 7 (20) 11 (9) 9 (7) 10 (6) 17 (3) 3 (2) 15 (1) |
k = 1 and 8 proven composite by full algebraic factors. k = 2, 4, and 16 are GFn's with no known prime. all-ks-sierp-base512.txt |
| 1024 | 81 | 5, 41 | All k = m^5 for all n; factors to: (m*4^n + 1) * (m^4*256^n - m^3*64^n + m^2*16^n - m*4^n + 1) |
k = = 2 mod 3 (3) k = = 10 mod 11 (11) k = = 30 mod 31 (31) |
none - proven | 9 (323) 51 (266) 33 (142) 48 (53) 24 (35) 55 (22) 52 (8) 45 (6) 31 (6) 34 (5) |
k = 1 proven composite by full algebraic factors. k = 4 and 16 are GFn's with no known prime. all-ks-sierp-base1024.txt |