Tuesday, June 12, 2012

[tjunbzke] Mersenne-like numbers

The primitive part of 2^n-1 is prime for the following odd exponents n: 3 5 7 9 13 15 17 19 27 31 33 49 61 65 69 77 85 89 93 107 127 129 133 145 165 195 261 345 425 447 471 507 521 567 579 607 745 795 897 909.   These are Mersenne-prime-like numbers.  Actual Mersenne primes are in bold.

The primitive part of 2^n+1 is prime for the following exponents n: 1 2 3 4 5 6 7 8 11 12 13 15 16 17 19 20 21 23 28 31 39 40 43 45 49 60 61 63 75 79 85 87 92 96 101 104 117 127 140 148 156 161 167 183 187 191 199 205 207 275 295 300 313 345 347 356 408 477 495 553 596 612 615 692 693 701 732 756 777 781 800 835 917 952 995 996 1004 1149.  These are Fermat-prime-like numbers.  Actual Fermat primes are in bold.

Aurifeuillian factorization exponents with prime primitive part: 10L 10M 14L 14M 18L 18M 22L 22M 26L 30L 30M 34M 38M 42L 42M 54L 54M 58L 58M 66L 66M 70L 70M 86L 90M 94L 98L 102M 106L 110L 110M 114M 126L 126M 130L 138L 138M 146L 158L 170M 174L 178M 186L 210L 222L 226L 242M 258L 294M 302L 314M 326M 334L 350M 378M 434L 462L 462M 478L 482L 522L 566L 566M 602L 638L 646M 706L 726M 734L 750L 758M 770L 782L 914L 1062L 1086L 1114L 1126L 1150M 1226L 1242M 1266L 1302M 1358L 1382L 1434L 1482M 1558M 1638M 1710M 1742L 1770M 1926L 1970M 1994M

These are from analyzing the Cunningham project tables.  These lists could easily be extended, since all we care about is primality.

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