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Proth primes of the form k•2n+1, k < 300

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Overview

Automatically generated table from available Proth primes k < 300.

Explanations

The colors used in the table are defined as:

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

Primes table

There are 23 sequences:

k Type Date max n Nash # Primes for n
1 Low 2010-10-01
FermatSearch
8,589,934,591 78 5 1, 2, 4, 8, 16
3 3 2021-06-20
PrimeGrid 321 Prime Search (MR22)
17,310,000 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 Low 2021-04-01 9,000,000 891 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 2021-04-01 9,000,000 2144 42 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, 5775996, 18233956
9 3 2021-04-01 4,000,000 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 2021-04-01 9,000,000 1387 34 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, 2691961, 2897409, 3771821, 8103463, 9381365
13 Low 2021-04-01 9,000,000 920 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
15 315 2021-04-01 9,000,000 2873 63 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, 2785940, 2988834, 3162659, 4246384, 4800315, 7300254, 7619838
17 Low 2021-04-01 9,000,000 672 20 3, 15, 27, 51, 147, 243, 267, 347, 471, 747, 2163, 3087, 5355, 6539, 7311, 99231, 824451, 1388355, 1990299, 8636199
19 Low 2021-04-01 9,000,000 828 21 6, 10, 46, 366, 1246, 2038, 4386, 4438, 6838, 7498, 7998, 9450, 11890, 17034, 23290, 73338, 149146, 323638, 853546, 2206266, 6833086
21 3 2021-04-01 9,000,000 2374 48 1, 4, 5, 7, 9, 12, 16, 17, 41, 124, 128, 129, 187, 209, 276, 313, 397, 899, 1532, 1613, 1969, 2245, 2733, 4585, 4644, 6712, 6981, 13344, 17524, 27124, 29769, 47337, 55828, 91008, 94801, 164901, 179457, 191337, 200568, 220992, 686632, 856865, 1022168, 1240067, 1421741, 1830919, 3065701, 6048861
23 Low 2021-04-01 9,000,000 826 19 1, 9, 13, 29, 41, 49, 69, 73, 341, 381, 389, 649, 1961, 3929, 977541, 1399841, 1448461, 2425641, 4300741
25 2021-04-01 9,000,000 2198 45 2, 4, 6, 10, 20, 22, 52, 64, 78, 184, 232, 268, 340, 448, 554, 664, 740, 748, 1280, 1328, 1640, 3314, 3904, 3938, 5152, 9522, 57488, 66872, 148060, 154254, 216092, 302194, 367294, 627710, 966414, 1211488, 1258562, 1298186, 2141884, 2583690, 2927222, 3733144, 4481024, 8456828, 8788628
27 3 2021-07-26
PrimeGrid 27121 Prime Search (MR23)
8,850,000 2142 49 2, 4, 7, 16, 19, 20, 22, 26, 40, 44, 46, 47, 50, 56, 59, 64, 92, 175, 215, 275, 407, 455, 1076, 1090, 3080, 3322, 6419, 7639, 19360, 30500, 38770, 44164, 50696, 114760, 117784, 153847, 160874, 178739, 379880, 405514, 672007, 974752, 1164664, 1476347, 2218064, 5213635, 7046834, 7963247, 12184319
29 2021-04-01 9,000,000 2120 45 1, 3, 5, 11, 27, 43, 57, 75, 77, 93, 103, 143, 185, 231, 245, 391, 1053, 1175, 2027, 3627, 4727, 5443, 7927, 8533, 9067, 14185, 25723, 88117, 96947, 144937, 219317, 252227, 261031, 339123, 343601, 627167, 742191, 800191, 1152765, 1416873, 1574753, 3964697, 4532463, 7374577, 7899985
31 Low 2021-04-01 9,000,000 839 14 8, 60, 68, 140, 216, 416, 1808, 1944, 9096, 76596, 93168, 4673544, 5560820, 8348000
33 3 2021-04-01 9,000,000 1960 41 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, 3649810
35 2021-04-01 9,000,000 2115 43 1, 3, 7, 9, 13, 15, 31, 45, 47, 49, 55, 147, 245, 327, 355, 663, 1423, 1443, 2493, 3627, 4737, 6541, 9667, 22645, 27321, 61963, 68281, 144397, 151741, 187859, 191509, 273251, 494607, 696935, 768063, 831411, 1040005, 1357881, 1765449, 2099769, 2241049, 3570777, 3587843
63 3 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
121 2021-07-26
PrimeGrid 27121 Prime Search (MR23)
8,850,000 1004 25 8, 12, 44, 84, 96, 228, 264, 320, 732, 788, 1808, 7928, 12264, 37784, 59196, 91112, 112208, 168716, 251184, 264632, 272052, 513020, 636564, 674360, 9584444
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 3 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
255 315 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
Proth primes