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Williams primes of the form (b+1)•bn-1
Primes table
There are 128 sequences:
| Base | Last update | max n | # | Primes for n |
|---|---|---|---|---|
| 2 | 2024-07-31 PrimeGrid |
21,851,244 | 66 | 1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, 827, 1274, 3276, 4204, 5134, 7559, 12676, 14898, 18123, 18819, 25690, 26459, 41628, 51387, 71783, 80330, 85687, 88171, 97063, 123630, 155930, 164987, 234760, 414840, 584995, 702038, 727699, 992700, 1201046, 1232255, 2312734, 3136255, 4235414, 6090515, 11484018, 11731850, 11895718, 16819291, 17748034, 18196595, 18924988, 20928756 |
| 3 | 2021-01-26 | 2,000,000 | 31 | 1, 3, 5, 7, 15, 45, 95, 235, 463, 733, 1437, 1583, 1677, 1803, 4163, 4765, 9219, 9959, 25477, 26059, 41539, 54195, 65057, 74977, 116589, 192289, 311835, 350767, 353635, 416337, 423253 |
| 4 | 2021-10-09 | 6,000,000 | 51 | 1, 2, 4, 5, 6, 7, 9, 16, 24, 27, 36, 74, 92, 124, 135, 137, 210, 670, 719, 761, 819, 877, 942, 1007, 1085, 1274, 1311, 1326, 1352, 6755, 10869, 12812, 20967, 25739, 26270, 26615, 86150, 122864, 175014, 597082, 1230241, 1529849, 1545430, 1632325, 1784577, 2714747, 3518594, 3877501, 5174500, 5247810, 5677882 |
| 5 | 2024-09-20 Riley Fisher |
250,000 | 29 | 1, 2, 5, 11, 28, 65, 72, 361, 479, 494, 599, 1062, 1094, 1193, 2827, 3271, 3388, 3990, 4418, 11178, 16294, 25176, 42500, 68320, 85698, 145259, 159119, 169771, 252665 |
| 6 | 2024-10-08 Riley Fisher |
250,000 | 29 | 1, 2, 3, 13, 21, 28, 30, 32, 36, 48, 52, 76, 734, 2236, 2272, 3135, 3968, 6654, 7059, 22055, 26423, 31206, 35536, 37999, 45712, 49756, 167591, 231066, 259555 |
| 7 | 2024-08-10 Riley Fisher |
250,000 | 17 | 4, 7, 10, 14, 23, 59, 1550, 1835, 2515, 3532, 3818, 8260, 19696, 46079, 49130, 53075, 83255 |
| 8 | 2024-08-10 Dmitry Domanov |
2,600,000 | 20 | 1, 5, 7, 21, 33, 53, 103, 313, 517, 1863, 2669, 3849, 4165, 27805, 34353, 91953, 128081, 336759, 473285, 1561185 |
| 9 | 2024-08-23 Riley Fisher |
250,000 | 34 | 1, 2, 4, 5, 7, 10, 11, 13, 15, 19, 27, 29, 35, 42, 51, 70, 112, 164, 179, 180, 242, 454, 621, 2312, 3553, 6565, 14026, 16083, 18493, 43289, 44970, 73654, 79638, 218669 |
| 10 | 2024-09-30 | 600,000 | 24 | 1, 9, 11, 17, 22, 29, 36, 37, 52, 166, 448, 2011, 3489, 4871, 6982, 10024, 16974, 33287, 47364, 58873, 126160, 234424, 382881, 524706 |
| 11 | 2024-09-27 | 200,000 | 24 | 1, 2, 3, 4, 11, 13, 22, 27, 48, 51, 103, 147, 280, 908, 1346, 1524, 1776, 2173, 2788, 6146, 18134, 20427, 62186, 100298 |
| 12 | 2024-10-03 | 200,000 | 20 | 2, 6, 11, 66, 196, 478, 2968, 3568, 5411, 7790, 13751, 16159, 19922, 22826, 32366, 36943, 43176, 70826, 153752, 193172 |
| 13 | 2024-10-03 | 200,000 | 18 | 1, 3, 4, 9, 11, 17, 19, 21, 24, 84, 93, 564, 817, 864, 961, 1009, 1200, 148503 |
| 14 | 2024-09-25 Richard Kapek |
100,000 | 17 | 2, 8, 172, 357, 918, 1025, 1373, 2812, 3298, 4099, 4332, 6099, 7014, 7474, 15588, 47058, 58738 |
| 15 | 2024-09-25 Richard Kapek |
100,000 | 12 | 1, 9, 15, 57, 79, 221, 1105, 2265, 6471, 86925, 89071, 89605 |
| 16 | 2024-09-02 | 1,250,000 | 27 | 1, 4, 5, 9, 15, 24, 31, 63, 89, 115, 153, 166, 243, 297, 328, 1072, 1320, 2275, 5419, 6207, 11536, 15537, 29446, 52866, 77686, 736646, 1026886 |
| 17 | 2024-09-02 | 100,000 | 20 | 4, 6, 15, 18, 23, 83, 359, 420, 711, 723, 864, 1103, 2166, 4056, 6102, 9055, 13091, 19428, 40258, 97630 |
| 18 | 2024-09-04 | 100,000 | 13 | 3, 4, 5, 7, 476, 572, 684, 865, 1240, 1945, 3907, 51524, 79569 |
| 19 | 2024-09-04 | 100,000 | 9 | 1, 2, 503, 806, 1182, 6642, 8202, 9949, 46762 |
| 20 | 2024-09-09 | 100,000 | 22 | 1, 10, 26, 30, 33, 73, 80, 120, 282, 331, 662, 859, 2976, 3106, 6645, 9674, 10459, 14062, 15751, 42558, 60173, 98104 |
| 21 | 2024-09-09 | 100,000 | 18 | 1, 8, 13, 26, 355, 985, 1347, 1918, 1968, 2802, 3310, 8113, 8728, 10906, 15042, 24051, 36359, 48512 |
| 22 | 2024-09-10 | 100,000 | 16 | 2, 18, 252, 1303, 2475, 4096, 6567, 9758, 9924, 11052, 11374, 28027, 35184, 58627, 81822, 83767 |
| 23 | 2024-09-10 | 100,000 | 19 | 7, 35, 79, 117, 137, 144, 157, 481, 529, 1300, 1813, 4044, 33920, 35888, 43988, 45481, 59772, 64857, 70977 |
| 24 | 2024-09-14 | 100,000 | 15 | 1, 3, 11, 29, 171, 249, 569, 735, 1019, 2785, 4553, 7335, 7977, 29381, 52227 |
| 25 | 2024-09-14 | 100,000 | 13 | 2, 17, 18, 118, 220, 290, 988, 1544, 3065, 3695, 20828, 68207, 76808 |
| 26 | 2024-09-23 | 100,000 | 11 | 1, 2, 4, 14, 26, 49, 226, 3346, 12464, 56621, 63371 |
| 27 | 2024-09-23 | 100,000 | 13 | 2, 4, 6, 8, 46, 56, 79, 571, 1904, 2690, 3559, 4920, 11195 |
| 28 | 2024-09-25 | 100,000 | 11 | 1, 72, 153, 1131, 1175, 2175, 3215, 4055, 8961, 29391, 57651 |
| 29 | 2024-09-25 | 100,000 | 15 | 2, 4, 13, 17, 27, 189, 200, 340, 449, 1024, 1910, 4916, 15412, 29259, 48314 |
| 30 | 2018-03-17 | 25,000 | 14 | 1, 5, 11, 15, 21, 22, 129, 153, 217, 411, 855, 2820, 2900, 8707 |
| 31 | 2018-03-17 | 25,000 | 16 | 1, 4, 9, 11, 22, 34, 59, 89, 117, 127, 172, 223, 1056, 3988, 8407, 16389 |
| 32 | 2024-08-16 Ryan Propper |
1,200,000 | 20 | 2, 7, 38, 66, 72, 163, 371, 1095, 1942, 5315, 11539, 12623, 25727, 34622, 117080, 134810, 154606, 423714, 1286432, 1378838 |
| 33 | 2019-04-23 | 10,000 | 7 | 4, 13, 48, 216, 859, 1036, 1968 |
| 34 | 2019-04-23 | 10,000 | 14 | 2, 3, 4, 5, 24, 59, 64, 91, 171, 731, 784, 1084, 2642, 6187 |
| 35 | 2019-04-23 | 10,000 | 7 | 1, 19, 23, 45, 103, 113, 1749 |
| 36 | 2024-10-03 | 25,000 | 13 | 2, 5, 7, 9, 13, 23, 35, 110, 137, 345, 712, 927, 2779 |
| 37 | 2019-04-23 | 10,000 | 7 | 2, 22, 92, 172, 712, 2054, 2602 |
| 38 | 2018-04-01 | 25,000 | 14 | 1, 3, 4, 12, 16, 157, 361, 419, 427, 523, 647, 8537, 11051, 18093 |
| 39 | 2024-10-11 Kevin Würth |
113,000 | 22 | 1, 3, 4, 6, 69, 101, 139, 163, 188, 432, 473, 512, 606, 1238, 2420, 2852, 3464, 8138, 11305, 23836, 49406, 103569 |
| 40 | 2019-04-23 | 10,000 | 8 | 2, 4, 10, 88, 134, 644, 712, 8026 |
| 41 | 2019-04-23 | 10,000 | 12 | 1, 5, 7, 49, 100, 134, 167, 542, 1877, 2104, 2329, 8983 |
| 42 | 2019-04-23 | 10,000 | 11 | 8, 14, 26, 72, 80, 160, 455, 484, 3983, 4156, 7728 |
| 43 | 2019-04-23 | 10,000 | 4 | 3, 4, 24, 67 |
| 44 | 2019-04-23 | 10,000 | 13 | 1, 2, 16, 40, 108, 119, 295, 468, 986, 1803, 2043, 8940, 9809 |
| 45 | 2019-04-23 | 10,000 | 10 | 1, 6, 40, 49, 58, 78, 366, 1009, 2091, 3009 |
| 46 | 2019-04-23 | 10,000 | 10 | 1, 6, 36, 79, 107, 475, 2065, 3667, 3677, 8798 |
| 47 | 2019-04-23 | 10,000 | 8 | 2, 4, 12, 19, 3018, 3544, 5843, 8399 |
| 48 | 2019-04-23 | 10,000 | 6 | 1, 5, 11, 35, 39, 1589 |
| 49 | 2024-10-11 Kevin Würth |
87,000 | 21 | 2, 3, 5, 10, 11, 13, 14, 45, 78, 82, 152, 158, 243, 401, 456, 768, 1763, 7713, 11174, 23576, 84605 |
| 50 | 2019-04-23 | 10,000 | 12 | 1, 4, 64, 82, 111, 124, 152, 239, 371, 404, 411, 6563 |
| 51 | 2019-04-23 | 10,000 | 14 | 5, 8, 12, 16, 18, 84, 119, 214, 219, 443, 1333, 2024, 4548, 4576 |
| 52 | 2019-04-23 | 10,000 | 8 | 3, 7, 46, 52, 90, 359, 3702, 8986 |
| 53 | 2019-04-23 | 10,000 | 5 | 1, 8, 21, 1437, 2635 |
| 54 | 2019-04-23 | 10,000 | 10 | 1, 5, 7, 23, 28, 42, 264, 359, 721, 1655 |
| 55 | 2024-10-11 Kevin Würth |
45,000 | 18 | 1, 2, 7, 22, 37, 40, 62, 231, 266, 352, 372, 537, 2428, 3099, 4634, 7047, 35880, 43977 |
| 56 | 2019-04-23 | 10,000 | 14 | 1, 7, 10, 28, 76, 87, 103, 256, 410, 626, 851, 885, 3050, 3909 |
| 57 | 2019-04-23 | 10,000 | 12 | 3, 4, 24, 28, 50, 71, 106, 127, 206, 586, 655, 5580 |
| 58 | 2019-04-23 | 10,000 | 8 | 3, 15, 72, 99, 133, 669, 2125, 3429 |
| 59 | 2024-09-27 Richard Kapek |
200,000 | 14 | 1, 4, 9, 10, 94, 136, 305, 814, 1015, 1476, 3841, 7234, 34006, 70716 |
| 60 | 2019-04-23 | 10,000 | 10 | 1, 2, 7, 11, 52, 84, 1413, 1933, 2188, 7758 |
| 61 | 2019-04-23 | 10,000 | 5 | 5, 11, 25, 26, 5015 |
| 62 | 2019-04-23 | 10,000 | 3 | 2, 15, 198 |
| 63 | 2018-02-02 | 25,000 | 2 | 1483, 14651 |
| 64 | 2020-11-12 Riesel Prime Search |
516,666 | 28 | 1, 2, 13, 27, 29, 32, 34, 155, 162, 296, 428, 732, 788, 1341, 2079, 4476, 4526, 7540, 8671, 22433, 29943, 30991, 107855, 236848, 250940, 430620, 479453, 513492 |
| 65 | 2024-10-11 Kevin Würth |
52,000 | 25 | 1, 2, 4, 5, 9, 33, 59, 62, 78, 328, 546, 806, 996, 1293, 2048, 4445, 9934, 10508, 16044, 22757, 27142, 28428, 32857, 33740, 36983 |
| 66 | 2024-10-03 | 25,000 | 12 | 1, 13, 24, 39, 57, 91, 137, 265, 269, 1134, 5686, 15112 |
| 67 | 2024-09-29 | 25,000 | 9 | 24, 123, 144, 166, 398, 3240, 3250, 4068, 20855 |
| 68 | 2024-10-03 | 25,000 | 9 | 1, 7, 13, 37, 40, 65, 71, 2381, 3809 |
| 69 | 2024-10-03 | 25,000 | 13 | 2, 4, 5, 8, 19, 39, 60, 224, 344, 6107, 9377, 10384, 20262 |
| 70 | 2024-09-29 | 25,000 | 13 | 1, 2, 4, 47, 52, 60, 106, 352, 670, 3247, 4246, 4610, 8171 |
| 71 | 2018-04-01 | 25,000 | 16 | 2, 11, 35, 60, 119, 120, 1248, 1401, 1447, 3990, 5574, 7259, 7295, 11912, 16102, 19551 |
| 72 | 2024-10-03 | 25,000 | 5 | 6, 964, 1622, 1871, 15200 |
| 73 | 2024-09-29 | 25,000 | 5 | 3, 9, 1409, 3717, 13379 |
| 74 | 2024-10-03 | 25,000 | 12 | 3, 7, 10, 15, 20, 21, 71, 286, 816, 6371, 6850, 8756 |
| 75 | 2024-10-03 | 25,000 | 11 | 36, 125, 184, 636, 2237, 2420, 2425, 3745, 4993, 15983, 17033 |
| 76 | 2024-09-29 | 25,000 | 12 | 1, 4, 5, 29, 31, 79, 86, 132, 1456, 1572, 2952, 4060 |
| 77 | 2024-10-03 | 25,000 | 10 | 10, 19, 27, 42, 152, 260, 820, 1646, 2111, 3108 |
| 78 | 2024-10-03 | 25,000 | 7 | 8, 20, 73, 205, 304, 1447, 10656 |
| 79 | 2024-09-29 | 25,000 | 8 | 3, 15, 17, 24, 60, 231, 301, 15458 |
| 80 | 2024-10-03 | 25,000 | 4 | 7, 13, 49, 165 |
| 81 | 2024-10-03 | 25,000 | 11 | 2, 4, 5, 362, 717, 1427, 3397, 4716, 14440, 16456, 18450 |
| 82 | 2024-09-29 | 25,000 | 10 | 2, 7, 30, 48, 67, 338, 556, 2411, 4339, 16622 |
| 83 | 2018-04-14 | 25,000 | 12 | 1, 23, 24, 91, 289, 395, 681, 3469, 5320, 7003, 9755, 19469 |
| 84 | 2024-10-03 | 25,000 | 14 | 2, 19, 20, 25, 34, 135, 932, 1254, 2168, 2314, 3225, 4165, 10068, 15067 |
| 85 | 2024-09-29 | 25,000 | 12 | 1, 11, 20, 30, 31, 49, 91, 192, 295, 2856, 3120, 11899 |
| 86 | 2024-10-03 | 25,000 | 8 | 1, 5, 52, 76, 135, 142, 274, 1173 |
| 87 | 2024-10-03 | 25,000 | 5 | 7, 63, 2850, 2910, 4463 |
| 88 | 2018-04-08 | 25,000 | 4 | 1704, 11111, 11393, 14399 |
| 89 | 2024-10-03 | 25,000 | 14 | 1, 2, 4, 5, 16, 55, 554, 1004, 1066, 1595, 1964, 3283, 18456, 20614 |
| 90 | 2024-10-01 | 25,000 | 14 | 3, 4, 5, 8, 9, 110, 148, 220, 359, 720, 1444, 3967, 7263, 16239 |
| 91 | 2024-09-29 | 25,000 | 8 | 9, 12, 28, 30, 243, 2560, 14390, 19288 |
| 92 | 2024-10-01 | 25,000 | 4 | 4, 36, 136, 2934 |
| 93 | 2018-04-08 | 25,000 | 7 | 1, 4, 7, 521, 865, 1959, 2325 |
| 94 | 2024-09-29 | 25,000 | 12 | 1, 6, 16, 30, 43, 280, 474, 606, 901, 1974, 8041, 17615 |
| 95 | 2024-10-01 | 25,000 | 13 | 2, 4, 5, 9, 15, 17, 44, 117, 134, 143, 876, 2468, 24913 |
| 96 | 2024-10-01 | 25,000 | 12 | 1, 11, 20, 23, 164, 6172, 6954, 9666, 10247, 12590, 17106, 19273 |
| 97 | 2024-09-29 | 25,000 | 9 | 2, 36, 47, 96, 238, 2792, 3604, 17599, 19959 |
| 98 | 2024-10-01 | 25,000 | 7 | 24, 55, 95, 140, 403, 2613, 4428 |
| 99 | 2024-10-01 | 25,000 | 6 | 25, 35, 71, 299, 903, 3865 |
| 100 | 2024-09-29 | 25,000 | 11 | 1, 18, 91, 181, 301, 384, 571, 1505, 1534, 3505, 5413 |
| 101 | 2024-09-29 | 25,000 | 11 | 1, 5, 219, 244, 360, 539, 877, 1241, 2755, 13723, 16149 |
| 102 | 2024-09-29 | 25,000 | 9 | 3, 12, 34, 40, 74, 388, 502, 7160, 16172 |
| 103 | 2024-09-29 | 25,000 | 5 | 1, 4, 47, 77, 1289 |
| 104 | 2024-09-29 | 25,000 | 14 | 3, 8, 9, 11, 21, 22, 24, 50, 56, 213, 521, 4452, 14728, 14787 |
| 105 | 2024-09-29 | 25,000 | 11 | 6, 9, 26, 60, 114, 153, 240, 616, 1114, 1874, 5459 |
| 106 | 2024-09-29 | 25,000 | 14 | 2, 6, 26, 35, 63, 90, 124, 125, 345, 537, 735, 5122, 7119, 14687 |
| 107 | 2018-04-08 | 25,000 | 6 | 2, 3, 4, 7, 620, 1376 |
| 108 | 2024-09-29 | 25,000 | 7 | 39, 228, 611, 1020, 1420, 3753, 22311 |
| 109 | 2024-09-29 | 25,000 | 10 | 4, 5, 15, 32, 53, 81, 229, 648, 2289, 3909 |
| 110 | 2024-09-29 | 25,000 | 8 | 13, 37, 48, 434, 2257, 2394, 6109, 10082 |
| 113 | 2018-04-08 | 25,000 | 10 | 3, 13, 32, 107, 177, 387, 1599, 1695, 5793, 18635 |
| 128 | 2024-10-04 No Prime Left Behind |
385,714 | 9 | 4, 8, 15, 6485, 11195, 21544, 36425, 44884, 98699 |
| 158 | 2018-01-25 | 25,000 | 6 | 1, 316, 1035, 4644, 8707, 22144 |
| 208 | 2018-04-16 | 30,000 | 1 | 26680 |
| 256 | 2024-10-04 No Prime Left Behind |
337,500 | 10 | 2, 3, 23, 32, 53, 79, 109, 483, 24289, 35854 |
| 316 | 2018-04-23 | 10,000 | 2 | 1492, 3963 |
| 318 | 2018-04-23 | 10,000 | 3 | 2175, 3396, 4713 |
| 488 | 2018-04-24 | 10,000 | 1 | 1085 |
| 503 | 2018-04-24 | 10,000 | 2 | 2292, 2660 |
| 512 | 2024-03-09 No Prime Left Behind |
313,333 | 9 | 2, 15, 34, 55, 62, 2546, 2668, 6219, 136599 |
| 575 | 2024-08-21 Karsten Bonath |
458,000 | 0 | |
| 577 | 2018-04-25 | 10,000 | 1 | 4620 |
| 607 | 2018-04-24 | 15,000 | 1 | 11030 |
| 631 | 2018-04-24 | 10,000 | 2 | 1112, 3191 |
| 828 | 2018-04-25 | 20,000 | 1 | 19657 |
| 852 | 2018-04-25 | 10,000 | 1 | 1026 |
| 883 | 2018-04-25 | 10,000 | 1 | 1179 |
| 953 | 2018-04-25 | 10,000 | 1 | 5580 |
| 1024 | 2014-10-22 | 190,000 | 10 | 1, 16, 111, 339, 1025, 2356, 3564, 7484, 8190, 10588 |
Williams primes
| Main |
| Type MM: (b-1)•bn-1 |
| Type MP: (b-1)•bn+1 |
| Type PM: (b+1)•bn-1 |
| Type PP: (b+1)•bn+1 |
