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Mersenne prime - Wikipedia
a b numbers n such that an − bn/a − b is prime
(some large terms are only probable primes, these n are checked up to 100000 for |b| ≤ 5 or |b| = a − 1, 20000 for 5 < |b| < a − 1) OEIS sequence 2 1 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, ..., 136279841, ... A000043 2 −1 3, 4*, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347, 701, 1709, 2617, 3539, 5807, 10501, 10691, 11279, 12391, 14479, 42737, 83339, 95369, 117239, 127031, 138937, 141079, 267017, 269987, 374321, 986191, 4031399, ..., 13347311, 13372531, ... A000978 3 2 2, 3, 5, 17, 29, 31, 53, 59, 101, 277, 647, 1061, 2381, 2833, 3613, 3853, 3929, 5297, 7417, 90217, 122219, 173191, 256199, 336353, 485977, 591827, 1059503, ... A057468 3 1 3, 7, 13, 71, 103, 541, 1091, 1367, 1627, 4177, 9011, 9551, 36913, 43063, 49681, 57917, 483611, 877843, ... A028491 3 −1 2*, 3, 5, 7, 13, 23, 43, 281, 359, 487, 577, 1579, 1663, 1741, 3191, 9209, 11257, 12743, 13093, 17027, 26633, 104243, 134227, 152287, 700897, 1205459, ... A007658 3 −2 3, 4*, 7, 11, 83, 149, 223, 599, 647, 1373, 8423, 149497, 388897, ... A057469 4 3 2, 3, 7, 17, 59, 283, 311, 383, 499, 521, 541, 599, 1193, 1993, 2671, 7547, 24019, 46301, 48121, 68597, 91283, 131497, 148663, 184463, 341233, ... A059801 4 1 2 (no others) 4 −1 2*, 3 (no others) 4 −3 3, 5, 19, 37, 173, 211, 227, 619, 977, 1237, 2437, 5741, 13463, 23929, 81223, 121271, ... A128066 5 4 3, 43, 59, 191, 223, 349, 563, 709, 743, 1663, 5471, 17707, 19609, 35449, 36697, 45259, 91493, 246497, 265007, 289937, ... A059802 5 3 13, 19, 23, 31, 47, 127, 223, 281, 2083, 5281, 7411, 7433, 19051, 27239, 35863, 70327, ... A121877 5 2 2, 5, 7, 13, 19, 37, 59, 67, 79, 307, 331, 599, 1301, 12263, 12589, 18443, 20149, 27983, ... A082182 5 1 3, 7, 11, 13, 47, 127, 149, 181, 619, 929, 3407, 10949, 13241, 13873, 16519, 201359, 396413, 1888279, ... A004061 5 −1 5, 67, 101, 103, 229, 347, 4013, 23297, 30133, 177337, 193939, 266863, 277183, 335429, ... A057171 5 −2 2*, 3, 17, 19, 47, 101, 1709, 2539, 5591, 6037, 8011, 19373, 26489, 27427, ... A082387 5 −3 2*, 3, 5, 7, 17, 19, 109, 509, 661, 709, 1231, 12889, 13043, 26723, 43963, 44789, ... A122853 5 −4 4*, 5, 7, 19, 29, 61, 137, 883, 1381, 1823, 5227, 25561, 29537, 300893, ... A128335 6 5 2, 5, 11, 13, 23, 61, 83, 421, 1039, 1511, 31237, 60413, 113177, 135647, 258413, ... A062572 6 1 2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099, ... A004062 6 −1 2*, 3, 11, 31, 43, 47, 59, 107, 811, 2819, 4817, 9601, 33581, 38447, 41341, 131891, 196337, ... A057172 6 −5 3, 4*, 5, 17, 397, 409, 643, 1783, 2617, 4583, 8783, ... A128336 7 6 2, 3, 7, 29, 41, 67, 1327, 1399, 2027, 69371, 86689, 355039, ... A062573 7 5 3, 5, 7, 113, 397, 577, 7573, 14561, 58543, ... A128344 7 4 2, 5, 11, 61, 619, 2879, 2957, 24371, 69247, ... A213073 7 3 3, 7, 19, 109, 131, 607, 863, 2917, 5923, 12421, ... A128024 7 2 3, 7, 19, 79, 431, 1373, 1801, 2897, 46997, ... A215487 7 1 5, 13, 131, 149, 1699, 14221, 35201, 126037, 371669, 1264699, ... A004063 7 −1 3, 17, 23, 29, 47, 61, 1619, 18251, 106187, 201653, ... A057173 7 −2 2*, 5, 23, 73, 101, 401, 419, 457, 811, 1163, 1511, 8011, ... A125955 7 −3 3, 13, 31, 313, 3709, 7933, 14797, 30689, 38333, ... A128067 7 −4 2*, 3, 5, 19, 41, 47, 8231, 33931, 43781, 50833, 53719, 67211, ... A218373 7 −5 2*, 11, 31, 173, 271, 547, 1823, 2111, 5519, 7793, 22963, 41077, 49739, ... A128337 7 −6 3, 53, 83, 487, 743, ... A187805 8 7 7, 11, 17, 29, 31, 79, 113, 131, 139, 4357, 44029, 76213, 83663, 173687, 336419, 615997, ... A062574 8 5 2, 19, 1021, 5077, 34031, 46099, 65707, ... A128345 8 3 2, 3, 7, 19, 31, 67, 89, 9227, 43891, ... A128025 8 1 3 (no others) 8 −1 2* (no others) 8 −3 2*, 5, 163, 191, 229, 271, 733, 21059, 25237, ... A128068 8 −5 2*, 7, 19, 167, 173, 223, 281, 21647, ... A128338 8 −7 4*, 7, 13, 31, 43, 269, 353, 383, 619, 829, 877, 4957, 5711, 8317, 21739, 24029, 38299, ... A181141 9 8 2, 7, 29, 31, 67, 149, 401, 2531, 19913, 30773, 53857, 170099, ... A059803 9 7 3, 5, 7, 4703, 30113, ... A273010 9 5 3, 11, 17, 173, 839, 971, 40867, 45821, ... A128346 9 4 2 (no others) 9 2 2, 3, 5, 13, 29, 37, 1021, 1399, 2137, 4493, 5521, ... A173718 9 1 (none) 9 −1 3, 59, 223, 547, 773, 1009, 1823, 3803, 49223, 193247, 703393, ... A057175 9 −2 2*, 3, 7, 127, 283, 883, 1523, 4001, ... A125956 9 −4 2*, 3, 5, 7, 11, 17, 19, 41, 53, 109, 167, 2207, 3623, 5059, 5471, 7949, 21211, 32993, 60251, ... A211409 9 −5 3, 5, 13, 17, 43, 127, 229, 277, 6043, 11131, 11821, ... A128339 9 −7 2*, 3, 107, 197, 2843, 3571, 4451, ..., 31517, ... A301369 9 −8 3, 7, 13, 19, 307, 619, 2089, 7297, 75571, 76103, 98897, ... A187819 10 9 2, 3, 7, 11, 19, 29, 401, 709, 2531, 15787, 66949, 282493, ... A062576 10 7 2, 31, 103, 617, 10253, 10691, ... A273403 10 3 2, 3, 5, 37, 599, 38393, 51431, ... A128026 10 1 2, 19, 23, 317, 1031, 49081, 86453, 109297, 270343, ... A004023 10 −1 5, 7, 19, 31, 53, 67, 293, 641, 2137, 3011, 268207, ... A001562 10 −3 2*, 3, 19, 31, 101, 139, 167, 1097, 43151, 60703, 90499, ... A128069 10 −7 2*, 3, 5, 11, 19, 1259, 1399, 2539, 2843, 5857, 10589, ... 10 −9 4*, 7, 67, 73, 1091, 1483, 10937, ... A217095 11 10 3, 5, 19, 311, 317, 1129, 4253, 7699, 18199, 35153, 206081, ... A062577 11 9 5, 31, 271, 929, 2789, 4153, ... A273601 11 8 2, 7, 11, 17, 37, 521, 877, 2423, ... A273600 11 7 5, 19, 67, 107, 593, 757, 1801, 2243, 2383, 6043, 10181, 11383, 15629, ... A273599 11 6 2, 3, 11, 163, 191, 269, 1381, 1493, ... A273598 11 5 5, 41, 149, 229, 263, 739, 3457, 20269, 98221, ... A128347 11 4 3, 5, 11, 17, 71, 89, 827, 22307, 45893, 63521, ... A216181 11 3 3, 5, 19, 31, 367, 389, 431, 2179, 10667, 13103, 90397, ... A128027 11 2 2, 5, 11, 13, 331, 599, 18839, 23747, 24371, 29339, 32141, 67421, ... A210506 11 1 17, 19, 73, 139, 907, 1907, 2029, 4801, 5153, 10867, 20161, 293831, ... A005808 11 −1 5, 7, 179, 229, 439, 557, 6113, 223999, 327001, ... A057177 11 −2 3, 5, 17, 67, 83, 101, 1373, 6101, 12119, 61781, ... A125957 11 −3 3, 103, 271, 523, 23087, 69833, ... A128070 11 −4 2*, 7, 53, 67, 71, 443, 26497, ... A224501 11 −5 7, 11, 181, 421, 2297, 2797, 4129, 4139, 7151, 29033, ... A128340 11 −6 2*, 5, 7, 107, 383, 17359, 21929, 26393, ... 11 −7 7, 1163, 4007, 10159, ... 11 −8 2*, 3, 13, 31, 59, 131, 223, 227, 1523, ... 11 −9 2*, 3, 17, 41, 43, 59, 83, ... 11 −10 53, 421, 647, 1601, 35527, ... A185239 12 11 2, 3, 7, 89, 101, 293, 4463, 70067, ... A062578 12 7 2, 3, 7, 13, 47, 89, 139, 523, 1051, ... A273814 12 5 2, 3, 31, 41, 53, 101, 421, 1259, 4721, 45259, ... A128348 12 1 2, 3, 5, 19, 97, 109, 317, 353, 701, 9739, 14951, 37573, 46889, 769543, ... A004064 12 −1 2*, 5, 11, 109, 193, 1483, 11353, 21419, 21911, 24071, 106859, 139739, ... A057178 12 −5 2*, 3, 5, 13, 347, 977, 1091, 4861, 4967, 34679, ... A128341 12 −7 2*, 3, 7, 67, 79, 167, 953, 1493, 3389, 4871, ... 12 −11 47, 401, 509, 8609, ... A213216
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