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

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Primes table

There are 128 sequences:

Base Last update max n # Primes for n
2 2024-10-13
PrimeGrid
22,021,811 67 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, 22103376
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 2024-11-04
Riley Fisher
250,000 30 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, 277330
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 2024-10-12 200,000 20 2, 8, 172, 357, 918, 1025, 1373, 2812, 3298, 4099, 4332, 6099, 7014, 7474, 15588, 47058, 58738, 122992, 131824, 151845
15 2024-10-12 200,000 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 2024-10-24 200,000 20 4, 6, 15, 18, 23, 83, 359, 420, 711, 723, 864, 1103, 2166, 4056, 6102, 9055, 13091, 19428, 40258, 97630
18 2024-10-24 200,000 13 3, 4, 5, 7, 476, 572, 684, 865, 1240, 1945, 3907, 51524, 79569
19 2024-11-04 200,000 10 1, 2, 503, 806, 1182, 6642, 8202, 9949, 46762, 175283
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 2024-11-04 200,000 17 2, 18, 252, 1303, 2475, 4096, 6567, 9758, 9924, 11052, 11374, 28027, 35184, 58627, 81822, 83767, 192875
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 2024-11-04 200,000 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 2024-11-04 200,000 13 1, 72, 153, 1131, 1175, 2175, 3215, 4055, 8961, 29391, 57651, 122988, 158589
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 2024-12-05
Kevin Würth
140,000 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 2024-12-05
Kevin Würth
57,000 5 3, 4, 24, 67, 43920
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 2024-12-05
Kevin Würth
100,000 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 2024-12-05
Kevin Würth
82,000 19 1, 2, 7, 22, 37, 40, 62, 231, 266, 352, 372, 537, 2428, 3099, 4634, 7047, 35880, 43977, 80543
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 2024-10-26
Richard Kapek
300,000 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 2024-12-05
Kevin Würth
100,000 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 2024-10-11 100,000 13 1, 13, 24, 39, 57, 91, 137, 265, 269, 1134, 5686, 15112, 61272
67 2024-10-14 100,000 10 24, 123, 144, 166, 398, 3240, 3250, 4068, 20855, 96551
68 2024-10-18 100,000 9 1, 7, 13, 37, 40, 65, 71, 2381, 3809
69 2024-10-18 100,000 15 2, 4, 5, 8, 19, 39, 60, 224, 344, 6107, 9377, 10384, 20262, 60379, 69485
70 2024-10-14 100,000 15 1, 2, 4, 47, 52, 60, 106, 352, 670, 3247, 4246, 4610, 8171, 51012, 52402
71 2024-10-24 100,000 17 2, 11, 35, 60, 119, 120, 1248, 1401, 1447, 3990, 5574, 7259, 7295, 11912, 16102, 19551, 26620
72 2024-10-24 100,000 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 2024-11-13
No Prime Left Behind
400,000 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 2024-11-13
No Prime Left Behind
350,000 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 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