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Proth prime table

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Overview

Automatically generated table from available Proth primes.

Explanations

The colors used in the table are defined as:

 
 : k-value is reserved
 
 : k-value is not reserved

Primes table

There are 58 sequences:

k Type Date max n Nash # Primes for n
1
2010-10-01
FermatSearch
8,589,934,591 78 5 1, 2, 4, 8, 16
3 2020-10-29
PrimeGrid
16,270,000 2132 50 1, 2, 5, 6, 8, 12, 18, 30, 36, 41, 66, 189, 201, 209, 276, 353, 408, 438, 534, 2208, 2816, 3168, 3189, 3912, 20909, 34350, 42294, 42665, 44685, 48150, 54792, 55182, 59973, 80190, 157169, 213321, 303093, 362765, 382449, 709968, 801978, 916773, 1832496, 2145353, 2291610, 2478785, 5082306, 7033641, 10829346, 16408818
5
2020-12-28
PrimeGrid (M)
7,620,000 891 25 1, 3, 7, 13, 15, 25, 39, 55, 75, 85, 127, 1947, 3313, 4687, 5947, 13165, 23473, 26607, 125413, 209787, 240937, 819739, 1282755, 1320487, 1777515
7
2020-12-28
PrimeGrid (M)
7,620,000 2144 41 2, 4, 6, 14, 20, 26, 50, 52, 92, 120, 174, 180, 190, 290, 320, 390, 432, 616, 830, 1804, 2256, 6614, 13496, 15494, 16696, 22386, 54486, 88066, 95330, 207084, 283034, 561816, 804534, 811230, 1491852, 2139912, 2167800, 2915954, 3015762, 3511774, 18233956
9 2020-12-28
PrimeGrid (M)
7,620,000 2297 66 1, 2, 3, 6, 7, 11, 14, 17, 33, 42, 43, 63, 65, 67, 81, 134, 162, 206, 211, 366, 663, 782, 1305, 1411, 1494, 2297, 2826, 3230, 3354, 3417, 3690, 4842, 5802, 6937, 7967, 9431, 13903, 22603, 24422, 39186, 43963, 47003, 49902, 67943, 114854, 127003, 145247, 147073, 149143, 304607, 384990, 412034, 435743, 461081, 834810, 1051026, 1807574, 2543551, 3497442, 5642513, 9778263, 11158963, 11366286, 11500843, 12406887, 13334487
11
2020-12-28
PrimeGrid (M)
7,620,000 1387 29 1, 3, 5, 7, 19, 21, 43, 81, 125, 127, 209, 211, 3225, 4543, 10179, 15329, 18759, 28277, 93279, 105741, 268009, 412447, 525589, 644677, 886071, 960901, 1343347, 2230369, 2476839
13
2020-12-28
PrimeGrid (M)
7,620,000 920 26 2, 8, 10, 20, 28, 82, 188, 308, 316, 1000, 28280, 38008, 43856, 88018, 109258, 114296, 521306, 562456, 684560, 1038896, 1499876, 1861732, 4998362, 5523860, 6481780, 8989858
15 2020-12-28
PrimeGrid (M)
7,620,000 2873 58 1, 2, 4, 9, 10, 12, 27, 37, 38, 44, 48, 78, 112, 168, 229, 297, 339, 517, 522, 654, 900, 1518, 2808, 2875, 3128, 3888, 4410, 6804, 7050, 7392, 19219, 21445, 21550, 24105, 24995, 34224, 34260, 43388, 48444, 61758, 184290, 294894, 300488, 403929, 483098, 635989, 701902, 734400, 1229600, 1244377, 1276177, 1368428, 1418605, 1597510, 1667744, 2393365, 7300254, 7619838
17
2020-12-28
PrimeGrid (M)
7,620,000 672 19 3, 15, 27, 51, 147, 243, 267, 347, 471, 747, 2163, 3087, 5355, 6539, 7311, 99231, 824451, 1388355, 1990299
19
2020-12-28
PrimeGrid (M)
7,620,000 828 21 6, 10, 46, 366, 1246, 2038, 4386, 4438, 6838, 7498, 7998, 9450, 11890, 17034, 23290, 73338, 149146, 323638, 853546, 2206266, 6833086
31
2020-12-28
PrimeGrid (M)
7,620,000 839 11 8, 60, 68, 140, 216, 416, 1808, 1944, 9096, 76596, 93168
33 2020-12-28
PrimeGrid (M)
7,620,000 1960 40 1, 6, 13, 18, 21, 22, 25, 28, 66, 93, 118, 289, 412, 453, 525, 726, 828, 1420, 1630, 3076, 3118, 4452, 4941, 5236, 6346, 9133, 13401, 14214, 18766, 37249, 42685, 47805, 61372, 74178, 600270, 922782, 1130884, 2345001, 3176269, 3570132
63 2010-04-20 1,200,000 3116 67 1, 4, 5, 9, 10, 14, 17, 18, 21, 25, 37, 38, 44, 60, 65, 94, 133, 153, 228, 280, 314, 326, 334, 340, 410, 429, 626, 693, 741, 768, 1150, 1290, 1441, 2424, 2478, 3024, 3293, 4956, 5221, 6416, 8480, 20746, 24633, 30053, 34074, 88366, 121917, 125218, 130221, 131325, 141497, 151269, 222861, 263413, 270094, 425028, 448833, 521925, 775857, 892164, 898308, 1070449, 1356980, 1530888, 1625970, 1686050, 1784498
127
2010-12-13 1,140,000 1773 30 2, 12, 18, 24, 54, 72, 114, 180, 214, 504, 558, 964, 1098, 1420, 2764, 4322, 5582, 10538, 14634, 23970, 61054, 67618, 88958, 96744, 297350, 357840, 376162, 723530, 916980, 925012
129 2014-09-15 3,328,805 2357 37 3, 5, 21, 27, 59, 75, 111, 287, 414, 786, 966, 1071, 2433, 2817, 3165, 4958, 5895, 12450, 39399, 50019, 57386, 72599, 75866, 82026, 112497, 268271, 284975, 478538, 564990, 630843, 739023, 851306, 872765, 1774709, 1956915, 2255199, 3328805
255 2010-11-24 1,020,000 2629 60 2, 5, 32, 36, 38, 41, 57, 69, 71, 72, 116, 137, 156, 197, 237, 336, 353, 489, 545, 678, 1040, 1137, 1217, 1451, 1577, 1589, 1836, 3077, 4640, 4850, 5145, 7139, 7766, 8051, 9662, 11159, 13433, 13763, 15998, 16862, 19002, 25412, 35558, 47916, 48509, 86900, 88046, 116228, 161486, 253233, 265808, 373580, 411408, 463229, 668348, 883046, 884769, 942620, 1122897, 1155630
301
2019-05-12
PrimeGrid (M)
2,725,000 1328 24 4, 184, 344, 352, 392, 1060, 2452, 7360, 9736, 10324, 21316, 22752, 27272, 27744, 28068, 55628, 72864, 88472, 95872, 124628, 218584, 424448, 517960, 880792
511
2019-05-23
PrimeGrid
2,727,432 383 6 8, 264, 1392, 317328, 495800, 1777488
513 2010-11-02 940,000 2665 59 2, 4, 5, 6, 9, 10, 12, 14, 17, 22, 26, 30, 33, 45, 66, 110, 116, 126, 153, 165, 174, 220, 230, 234, 294, 362, 404, 1576, 1625, 1640, 2540, 2936, 3525, 5470, 9736, 11004, 11110, 15652, 19965, 23244, 24341, 48386, 52234, 54021, 74264, 78604, 117992, 136476, 175370, 189156, 193212, 273482, 279213, 337140, 369969, 392925, 797084, 818964, 861512
1023 2010-09-08 920,000 3931 78 2, 4, 9, 13, 14, 16, 32, 33, 81, 101, 124, 242, 272, 301, 380, 453, 469, 533, 612, 929, 1081, 1176, 1749, 1797, 1852, 2318, 2405, 3057, 3408, 3440, 4392, 5032, 6637, 9441, 9688, 11970, 13617, 15182, 15316, 17188, 19036, 33709, 34533, 34557, 34716, 37377, 38862, 43640, 47469, 63265, 109010, 111404, 131188, 132810, 183416, 203604, 216930, 253224, 270093, 287797, 289953, 301580, 358082, 367344, 490681, 550765, 611208, 620205, 641310, 681313, 797786, 868480, 943418, 1068402, 1138576, 1153248, 1177850, 1223814
9267 2020-05-16
Jean Penné
200,000 498 10 100, 1556, 1966, 2660, 4342, 4468, 5372, 39538, 65386, 142426
10223
2017 31,278,077 207 1 31172165
12743
2020-06-09 100,000 416 3 9, 41205, 49113
15735 2020-10-11 50,000 2954 35 4, 7, 10, 94, 95, 98, 110, 128, 136, 200, 215, 334, 559, 676, 740, 856, 935, 1159, 1463, 1468, 1763, 1795, 3274, 4037, 4162, 6139, 6857, 9893, 10228, 14915, 18815, 22903, 28555, 29278, 36490
19683 2019-10-08 4,000,000 1802 32 1, 5, 8, 32, 50, 400, 536, 592, 676, 866, 1157, 1300, 1661, 1730, 2440, 7046, 9698, 16180, 16226, 22330, 26990, 206005, 238780, 278941, 366665, 485845, 493846, 901745, 1797997, 1868828, 2033900, 2265896
21181
2020-09-25
PrimeGrid (M)
32,698,000 169 0
22249
2020-04-10 500,000 284 2 2, 408602
22699
2020-09-25
PrimeGrid (M)
32,698,000 69 0
23971
2020-10-17
PrimeGrid (M)
10,000,000 108 1 8
24737
2020-09-25
PrimeGrid (M)
32,698,000 174 0
32247 2020-07-04
Conjectures 'R Us (M)
6,620,000 1736 23 10, 18, 40, 94, 114, 190, 234, 240, 300, 538, 922, 1224, 6514, 8740, 13438, 19692, 23764, 43894, 48862, 49774, 60148, 75202, 75780
45323
2020-11-25 10,000,000 266 1 1
48495 2020-10-08 1,000 3088 21 11, 13, 29, 40, 43, 49, 50, 70, 73, 82, 106, 125, 163, 251, 269, 349, 401, 479, 527, 614, 920
50777
2020-10-17
PrimeGrid (M)
10,000,000 166 1 11
50873
2020-11-25 10,000,000 410 1 1
53133 2020-07-04
Conjectures 'R Us (M)
6,620,000 1475 18 14, 26, 44, 72, 144, 146, 204, 222, 404, 642, 716, 1116, 1178, 5846, 16292, 21224, 24788, 42542
55459
2020-09-25
PrimeGrid (M)
32,698,000 242 0
66741 2020-07-05 50,000 811 9 5, 51, 95, 117, 237, 357, 2231, 3767, 6837
67275 2020-10-08 1,000 3481 25 3, 4, 7, 9, 13, 15, 22, 33, 36, 37, 49, 64, 69, 72, 78, 93, 102, 109, 145, 211, 216, 277, 325, 348, 457
67607
2020-09-25
PrimeGrid (M)
32,698,000 56 0
68633
2020-06-02 2,715,609 250 2 9, 2715609
76877
2020-10-17
PrimeGrid (M)
10,000,000 96 1 11
78557
1962 0 0 0
79309
2020-10-04
PrimeGrid (M)
22,600,000 56 0
79817
2020-10-04
PrimeGrid (M)
22,600,000 146 0
95283 2020-07-05 50,000 1489 27 4, 14, 22, 28, 34, 148, 230, 274, 304, 352, 446, 616, 652, 1214, 1796, 2632, 4516, 4888, 4918, 7852, 9314, 13096, 17908, 25124, 25828, 29912, 40228
152267
2020-10-04
PrimeGrid (M)
22,600,000 92 0
156511
2020-10-04
PrimeGrid (M)
22,600,000 58 0
168451
2017-09-17 19,395,180 99 1 19375200
222113
2020-10-04
PrimeGrid (M)
22,600,000 248 0
225931
2020-10-04
PrimeGrid (M)
22,600,000 124 0
237019
2020-10-04
PrimeGrid (M)
22,600,000 155 0
271129
0 0 0
84966861 2020-06-17 150,000 2140 30 4, 40, 60, 157, 179, 233, 252, 287, 303, 332, 427, 807, 1068, 1259, 1288, 1289, 1432, 1983, 2812, 4229, 8187, 29719, 35020, 38357, 55544, 58392, 62860, 100489, 140219, 148073
2003663613 2010-08-26 195,000 2762 39 21, 29, 45, 64, 80, 94, 150, 184, 293, 428, 478, 580, 704, 1501, 1518, 1532, 1628, 1925, 2422, 3845, 4294, 5488, 12381, 13662, 16940, 32741, 36909, 38613, 46868, 49589, 69317, 87910, 97740, 129397, 132632, 145134, 154988, 183092, 195000
1527888802614951 2019-04-20 10,000 2929 28 3, 4, 11, 16, 17, 52, 63, 75, 76, 120, 145, 175, 352, 420, 641, 721, 841, 1073, 1147, 1192, 1361, 1617, 2316, 3379, 3600, 3673, 4711, 7673
30562993973479965532402725
2012-08-27 340,000 7833 180 5, 15, 16, 26, 36, 38, 51, 55, 59, 66, 68, 69, 86, 93, 94, 105, 106, 136, 150, 152, 153, 160, 161, 171, 198, 199, 232, 233, 244, 246, 269, 291, 297, 307, 330, 368, 385, 394, 427, 439, 482, 485, 491, 497, 509, 532, 567, 572, 583, 596, 599, 640, 660, 736, 776, 796, 799, 818, 913, 925, 942, 1047, 1146, 1184, 1253, 1284, 1400, 1501, 1558, 1612, 1626, 1667, 1828, 1875, 1945, 1976, 2043, 2444, 2884, 3108, 3296, 3353, 3439, 3511, 3727, 4037, 4099, 4145, 4318, 4403, 4437, 4551, 4788, 4866, 5002, 5272, 5434, 5449, 6558, 6560, 6837, 7068, 8540, 8747, 9252, 9314, 9673, 10107, 10939, 11101, 11689, 11717, 12879, 12969, 13107, 13239, 14878, 14900, 16000, 16658, 16923, 18345, 18573, 18791, 19248, 19619, 20924, 21043, 21363, 22167, 22882, 27581, 28518, 28940, 29126, 29242, 29577, 29665, 34156, 35212, 39581, 40232, 43213, 43984, 45644, 62423, 63511, 65622, 69778, 72369, 72969, 79932, 85510, 89404, 94708, 95795, 98533, 100821, 104136, 109400, 116063, 121799, 127419, 131976, 146515, 157616, 177343, 182109, 198262, 205792, 209356, 211962, 222095, 250108, 294496, 295197, 299354, 302174, 335908, 338615
32268186233370440249391495 2012-08-27 340,000 7953 177 1, 3, 6, 12, 29, 39, 46, 62, 76, 79, 90, 91, 101, 106, 113, 117, 119, 127, 139, 142, 145, 165, 166, 168, 180, 190, 223, 225, 232, 253, 276, 284, 344, 353, 366, 374, 394, 421, 437, 458, 463, 465, 476, 485, 497, 510, 532, 560, 590, 595, 605, 607, 608, 694, 719, 730, 740, 772, 806, 811, 869, 886, 967, 978, 1003, 1029, 1084, 1092, 1104, 1169, 1365, 1466, 1834, 1965, 1999, 2264, 2293, 2441, 2520, 2622, 2635, 3037, 3090, 3212, 3246, 3262, 3588, 3935, 3981, 3992, 4475, 4550, 4594, 5039, 5079, 5152, 5654, 5708, 5804, 5990, 6075, 6242, 6315, 6563, 6594, 6633, 6945, 7329, 7638, 7719, 8872, 8949, 9406, 10349, 11056, 11210, 11333, 12141, 13843, 13893, 14416, 15345, 15589, 16760, 17567, 18304, 18338, 19059, 19679, 19855, 20094, 20410, 21175, 23955, 25585, 27511, 30584, 31727, 33031, 33312, 34812, 35185, 35367, 44099, 46412, 47563, 50137, 51671, 52689, 53254, 60133, 62729, 64714, 69716, 85275, 89868, 92711, 94168, 110103, 113637, 115183, 121404, 140140, 141404, 146348, 164796, 173217, 187066, 194250, 217947, 219946, 246920, 251085, 254045, 287037, 288194, 323172