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Williams primes of the form (b+1)bn-1

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Primes table

There are 87 sequences:

Base Last update max n # Primes for n
2 2021-06-20 17.310.000 62 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
3 2019-03-01
Borys Jaworski
1.840.000 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 2021-03-21 2.625.000 46 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
5 2015-05-08 200.000 28 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
6 2018-03-26 25.000 20 1, 2, 3, 13, 21, 28, 30, 32, 36, 48, 52, 76, 734, 2236, 2272, 3135, 3968, 6654, 7059, 22055
7 2018-03-26 25.000 13 4, 7, 10, 14, 23, 59, 1550, 1835, 2515, 3532, 3818, 8260, 19696
8 2021-03-21 2.166.666 20 1, 5, 7, 21, 33, 53, 103, 313, 517, 1863, 2669, 3849, 4165, 27805, 34353, 91953, 128081, 336759, 473285, 1561185
9 2014-03-16 100.000 33 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
10 2013-09-17 126.000 21 1, 9, 11, 17, 22, 29, 36, 37, 52, 166, 448, 2011, 3489, 4871, 6982, 10024, 16974, 33287, 47364, 58873, 126160
11 2018-03-27 25.000 22 1, 2, 3, 4, 11, 13, 22, 27, 48, 51, 103, 147, 280, 908, 1346, 1524, 1776, 2173, 2788, 6146, 18134, 20427
12 2018-03-27 25.000 14 2, 6, 11, 66, 196, 478, 2968, 3568, 5411, 7790, 13751, 16159, 19922, 22826
13 2018-03-26 25.000 17 1, 3, 4, 9, 11, 17, 19, 21, 24, 84, 93, 564, 817, 864, 961, 1009, 1200
14 2018-03-27 25.000 15 2, 8, 172, 357, 918, 1025, 1373, 2812, 3298, 4099, 4332, 6099, 7014, 7474, 15588
15 2018-03-27 25.000 9 1, 9, 15, 57, 79, 221, 1105, 2265, 6471
16 2021-03-21 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 2018-03-09 25.000 18 4, 6, 15, 18, 23, 83, 359, 420, 711, 723, 864, 1103, 2166, 4056, 6102, 9055, 13091, 19428
18 2018-03-09 25.000 11 3, 4, 5, 7, 476, 572, 684, 865, 1240, 1945, 3907
19 2018-03-09 25.000 8 1, 2, 503, 806, 1182, 6642, 8202, 9949
20 2018-03-09 25.000 19 1, 10, 26, 30, 33, 73, 80, 120, 282, 331, 662, 859, 2976, 3106, 6645, 9674, 10459, 14062, 15751
21 2018-03-17 25.000 16 1, 8, 13, 26, 355, 985, 1347, 1918, 1968, 2802, 3310, 8113, 8728, 10906, 15042, 24051
22 2018-03-17 25.000 11 2, 18, 252, 1303, 2475, 4096, 6567, 9758, 9924, 11052, 11374
23 2018-03-17 25.000 12 7, 35, 79, 117, 137, 144, 157, 481, 529, 1300, 1813, 4044
24 2018-03-17 25.000 13 1, 3, 11, 29, 171, 249, 569, 735, 1019, 2785, 4553, 7335, 7977
25 2018-03-17 25.000 11 2, 17, 18, 118, 220, 290, 988, 1544, 3065, 3695, 20828
26 2018-03-17 25.000 9 1, 2, 4, 14, 26, 49, 226, 3346, 12464
27 2018-03-17 25.000 13 2, 4, 6, 8, 46, 56, 79, 571, 1904, 2690, 3559, 4920, 11195
28 2018-03-17 25.000 9 1, 72, 153, 1131, 1175, 2175, 3215, 4055, 8961
29 2018-03-17 25.000 13 2, 4, 13, 17, 27, 189, 200, 340, 449, 1024, 1910, 4916, 15412
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 2021-07-27 1.200.000 19 2, 7, 38, 66, 72, 163, 371, 1095, 1942, 5315, 11539, 12623, 25727, 34622, 117080, 134810, 154606, 423714, 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 2019-04-23 10.000 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 2019-04-23 10.000 18 1, 3, 4, 6, 69, 101, 139, 163, 188, 432, 473, 512, 606, 1238, 2420, 2852, 3464, 8138
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 2019-04-23 10.000 18 2, 3, 5, 10, 11, 13, 14, 45, 78, 82, 152, 158, 243, 401, 456, 768, 1763, 7713
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 2019-04-23 10.000 16 1, 2, 7, 22, 37, 40, 62, 231, 266, 352, 372, 537, 2428, 3099, 4634, 7047
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 2019-04-23 10.000 12 1, 4, 9, 10, 94, 136, 305, 814, 1015, 1476, 3841, 7234
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 2020-11-12 516.666 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
71 2018-04-01 25.000 16 2, 11, 35, 60, 119, 120, 1248, 1401, 1447, 3990, 5574, 7259, 7295, 11912, 16102, 19551
83 2018-04-14 25.000 12 1, 23, 24, 91, 289, 395, 681, 3469, 5320, 7003, 9755, 19469
88 2018-04-08 25.000 4 1704, 11111, 11393, 14399
93 2018-04-08 25.000 7 1, 4, 7, 521, 865, 1959, 2325
107 2018-04-08 25.000 6 2, 3, 4, 7, 620, 1376
113 2018-04-08 25.000 10 3, 13, 32, 107, 177, 387, 1599, 1695, 5793, 18635
128 2020-01-15 314.571 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 2021-04-21 275.000 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 2020-11-26 178.444 9 2, 15, 34, 55, 62, 2546, 2668, 6219, 136599
575 2020-05-29
Karsten Bonath
247.000 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