| Base | Conjectured Riesel 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 / accounting of all k's |
|---|---|---|---|---|---|---|---|
| 2 | 509203 | 3, 5, 7, 13, 17, 241 | none | 44 k's remaining at n>=9M. See k's and test limits at Riesel Base 2 remain. |
97139 (18397548) 93839 (15337656) 192971 (14773498) 206039 (13104952) 2293 (12918431) 9221 (11392194) 146561 (11280802) 273809 (8932416) 502573 (7181987) 402539 (7173024) |
All odd k's are being worked on by PrimeGrid's
Riesel Problem
project. See k's and test limits at
Riesel Problem stats. all-ks-riesel-base2.zip |
|
| 2 2nd conjecture |
762701 | 3, 5, 7, 13, 17, 241 | none | 26 k's remaining at n=6.5M. See k's at Riesel 2nd Base 2 remain. |
554051 (6517658) 521921 (6101122) 519397 (4908893) 612749 (4254500) 543131 (3529754) 700057 (3113753) 582971 (3053414) 543539 (2536028) 721751 (2123838) 609179 (2111132) |
Only k>509203 are considered. all-ks-riesel-base2-2nd-conj.zip |
|
| 2 even-n |
39939 | 5, 7, 13, 19, 73, 109 | All k where k = m^2: let k = m^2 and let n = 2*q; factors to: (m*2^q - 1) * (m*2^q + 1) |
k = = 1 mod 3 (3) | 9519 (16.777M) 14361 (9M) |
19401 (3086450) 20049 (1687252) 26511 (167154) 30171 (76286) 15639 (66328) 26601 (46246) 2181 (37890) 11379 (32252) 8961 (30950) 31959 (19704) |
Only k's where k = = 3 mod 6 are considered. k=3^2, 9^2, 15^2, (etc. repeating every 6m) proven composite by full algebraic factors. See additional details at The Liskovets-Gallot conjectures. all-ks-riesel-base2-evenn.txt |
| 2 odd-n |
172677 | 5, 7, 13, 17, 241 | All k where k = 2*m^2: let k = 2*m^2 and let n = 2*q-1; factors to: (m*2^q - 1) * (m*2^q + 1) |
k = = 2 mod 3 (3) | 39687 (9M) 103947 (9M) 154317 (9M) 163503 (9M) |
155877 (2273465) 148323 (1973319) 147687 (843689) 133977 (811485) 6927 (743481) 30003 (613463) 106377 (475569) 145257 (443077) 86613 (356967) 8367 (313705) |
Only k's where k = = 3 mod 6 are considered. No k's proven composite by algebraic factors. See additional details at The Liskovets-Gallot conjectures. all-ks-riesel-base2-oddn.txt |
| 4 | 39939 | 5, 7, 13, 19, 73, 109 | All k = m^2 for all n; factors to: (m*2^n - 1) * (m*2^n + 1) |
k = = 1 mod 3 (3) | 9519 (8.388M) 14361 (4.5M) 19464 (4.5M) 23669 (7.25M) 31859 (7.25M) |
4586 (6459215) 9221 (5696097) 19401 (1543225) 20049 (843626) 659 (400258) 13854 (371740) 16734 (156852) 39269 (143524) 25229 (119326) 14459 (85572) |
k = 3^2, 6^2, 9^2, (etc. repeating every 3m) proven composite by full
algebraic factors. k's where k = = 2 mod 3 are being worked on by PrimeGrid's Riesel Problem project. k's, test limits, and primes are converted from base 2. all-ks-riesel-base4.txt |
| 8 | 14 | 3, 5, 13 | k = = 1 mod 7 (7) | none - proven | 11 (18) 5 (4) 12 (3) 7 (3) 2 (2) 13 (1) 10 (1) 9 (1) 6 (1) 4 (1) |
all-ks-riesel-base8.txt | |
| 16 | 33965 | 7, 13, 17, 241 | All k = m^2 for all n; factors to: (m*4^n - 1) * (m*4^n + 1) |
k = = 1 mod 3 (3) k = = 1 mod 5 (5) |
443 (1.5M) 2297 (1.5M) 9519 (4.194M) 13380 (1M) 13703 (1M) 19464 (2.25M) 19772 (1M) 21555 (1M) 23669 (3.625M) 24987 (1M) 26378 (1M) 28967 (1M) 29885 (1M) 31859 (3.625M) 33023 (1M) |
18344 (3229607) 12587 (615631) 3620 (435506) 20049 (421813) 7673 (366247) 33863 (236436) 6852 (216571) 2993 (211161) 15068 (204680) 659 (200129) |
k = 3^2, 12^2, 15^2, 18^2, 27^2, 30^2, (etc. pattern repeating every 30m)
proven composite by full algebraic factors. k's where k = = 14 mod 15 are being worked on by PrimeGrid's Riesel Problem project. k's, test limits, and primes are converted from base 2. all-ks-riesel-base16.txt |
| 32 | 10 | 3, 11 | k = = 1 mod 31 (31) | none - proven | 3 (11) 2 (6) 9 (3) 8 (2) 5 (2) 7 (1) 6 (1) 4 (1) |
all-ks-riesel-base32.txt | |
| 64 | 14 | 5, 13 | All k = m^2 for all n; factors to: (m*8^n - 1) * (m*8^n + 1) -or- All k = m^3 for all n; factors to: (m*4^n - 1) * (m^2*16^n + m*4^n + 1) |
k = = 1 mod 3 (3) k = = 1 mod 7 (7) |
none - proven | 11 (9) 12 (6) 5 (2) 6 (1) 3 (1) 2 (1) |
k = 9 proven composite by full algebraic factors. all-ks-riesel-base64.txt |
| 128 | 44 | 3, 43 | k = = 1 mod 127 (127) | none - proven | 29 (211192) 23 (2118) 26 (1442) 37 (699) 16 (459) 42 (246) 35 (98) 30 (66) 36 (59) 12 (46) |
all-ks-riesel-base128.txt | |
| 256 | 10364 | 7, 13, 241 | All k = m^2 for all n; factors to: (m*16^n - 1) * (m*16^n + 1) |
k = = 1 mod 3 (3) k = = 1 mod 5 (5) k = = 1 mod 17 (17) |
659 (750K) 807 (750K) 1695 (750K) 1808 (750K) 2237 (750K) 2297 (750K) 2759 (750K) 4377 (750K) 4559 (750K) 5768 (750K) 7088 (750K) 7130 (750K) 7673 (750K) 7968 (750K) 8087 (750K) 8334 (750K) 8765 (750K) 9519 (2.097M) 10154 (750K) |
6332 (748660) 5502 (400821) 5903 (367343) 7335 (336135) 7913 (284458) 10110 (280347) 7890 (236791) 3480 (231670) 3620 (217753) 6213 (206892) |
k = 9, 144, 225, 729, 900, 1764, 2025, 2304, 3249, 3600, 3969, 5184, 5625,
6084, 7569, 8100, and 8649 proven composite by full algebraic factors. all-ks-riesel-base256.txt |
| 512 | 14 | 3, 5, 13 | k = = 1 mod 7 (7) k = = 1 mod 73 (73) |
none - proven | 4 (2215) 13 (2119) 9 (7) 11 (6) 6 (6) 5 (2) 3 (2) 2 (2) 12 (1) 10 (1) |
all-ks-riesel-base512.txt | |
| 1024 | 81 | 5, 41 | All k = m^2 for all n; factors to: (m*32^n - 1) * (m*32^n + 1) |
k = = 1 mod 3 (3) k = = 1 mod 11 (11) k = = 1 mod 31 (31) |
29 (1M) | 74 (666084) 39 (4070) 65 (93) 69 (54) 3 (47) 71 (41) 44 (36) 26 (29) 68 (25) 59 (16) |
k = 9 and 36 proven composite by full algebraic factors. all-ks-riesel-base1024.txt |