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

## 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 36 sequences:

k Type Date max n Nash # Primes for n
1 Low 2010-10-01
FermatSearch
8,589,934,591 39 5 1, 2, 4, 8, 16
3 3 2021-12-02
PrimeGrid 321 Prime Search (MR22)
18,000,000 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 37 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, 10797109, 10803449, 15502315
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 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
37 2021-04-01 9,000,000 2532 53 2, 4, 8, 10, 12, 16, 22, 26, 68, 82, 84, 106, 110, 166, 236, 254, 286, 290, 712, 1240, 1706, 1804, 1904, 2240, 2632, 3104, 5870, 8750, 11514, 11972, 14434, 16322, 18044, 19050, 23014, 32424, 59354, 62350, 120196, 157128, 167326, 211056, 218550, 230716, 233968, 239902, 256954, 331144, 548012, 551830, 939364, 2128328, 4046360
39 3 2021-04-01 9,000,000 3219 88 1, 2, 3, 5, 7, 10, 11, 13, 14, 18, 21, 22, 31, 42, 67, 70, 71, 73, 251, 370, 375, 389, 407, 518, 818, 865, 1057, 1602, 2211, 3049, 4802, 4865, 5317, 7583, 8061, 9853, 10217, 12103, 13721, 14927, 15441, 15931, 16709, 18907, 20221, 21882, 25654, 28437, 30325, 31485, 33593, 37393, 46362, 62429, 66971, 77242, 82191, 94449, 105063, 107778, 113490, 113549, 138009, 204681, 378861, 421590, 510595, 512997, 529642, 534973, 555902, 587850, 634441, 778233, 1612681, 1824871, 2188855, 2705367, 2978894, 3240990, 3961129, 4657951, 5119458, 6164630, 6648997, 6684941, 7946769, 8413422
41 Low 2021-04-01 9,000,000 893 17 1, 11, 19, 215, 289, 379, 1991, 7607, 8411, 12493, 13235, 13823, 274897, 364861, 462023, 1530313, 5651731
43 2021-04-01 9,000,000 1641 37 2, 6, 12, 18, 26, 32, 94, 98, 104, 144, 158, 252, 778, 1076, 2974, 3022, 3528, 4344, 5322, 10416, 10422, 29862, 33526, 163354, 167618, 175542, 217584, 762212, 835934, 894766, 1087992, 1235298, 1795628, 1799016, 2795582, 2994958, 3063674
45 2021-04-01 9,000,000 2581 57 2, 9, 12, 14, 23, 24, 29, 60, 189, 200, 333, 372, 443, 464, 801, 1374, 6146, 6284, 6359, 6923, 12293, 16679, 18660, 19301, 29240, 32018, 38457, 48612, 56754, 67394, 76416, 79160, 91403, 97116, 110303, 129731, 159318, 202304, 243321, 426653, 458712, 574506, 949353, 1086062, 1111703, 1134357, 1365167, 1427666, 1779971, 2014557, 2347187, 2507894, 2711732, 3677787, 5308037, 7513661, 7661004
47 Low 2021-04-01 9,000,000 197 3 583, 1483, 6115
49 2021-04-01 9,000,000 1209 25 2, 6, 10, 30, 42, 54, 66, 118, 390, 594, 1202, 2334, 6242, 7446, 11858, 48666, 68050, 72210, 88090, 113022, 406814, 501238, 1103430, 1646042, 3837090
63 3 2013? 3,322,000 3116 69 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, 2807130, 2898957
121 2021-04-08 10,000,000 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 2021-08-15
PrimeGrid Proth Prime Search (MR1)
3,070,000 1773 32 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, 1472718, 1817862
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
177 3 2021-08-15
PrimeGrid Proth Prime Search (MR1)
3,070,000 3473 75 2, 4, 6, 12, 16, 20, 23, 32, 38, 48, 54, 60, 100, 116, 118, 119, 140, 150, 163, 170, 190, 244, 271, 294, 299, 320, 334, 414, 439, 442, 468, 724, 794, 842, 864, 1032, 1750, 2050, 3980, 4010, 4756, 5096, 5963, 5966, 6836, 14160, 16748, 16844, 19814, 25398, 37702, 41148, 62159, 65806, 143626, 151308, 210340, 269320, 324326, 332846, 333364, 358114, 365164, 385438, 419600, 434336, 463598, 490500, 501106, 657458, 751028, 798443, 1121720, 2816050, 3411847
207 3 2021-08-15
PrimeGrid Proth Prime Search (MR1)
3,070,000 3570 69 2, 3, 4, 6, 7, 10, 14, 15, 16, 34, 42, 44, 46, 62, 66, 106, 127, 130, 171, 202, 231, 232, 238, 248, 256, 296, 314, 412, 604, 956, 1023, 1287, 1454, 1564, 1766, 2036, 5215, 5911, 6092, 9190, 9916, 10410, 13456, 14336, 14444, 15490, 30835, 32558, 34770, 41218, 46666, 56590, 58720, 62966, 63595, 70250, 128850, 141556, 186754, 288591, 317203, 555422, 755470, 1249252, 1471290, 1913067, 2649810, 2903535, 3095391
255 2021-08-15
PrimeGrid Proth Prime Search (MR1)
3,070,000 2629 66 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, 1275596, 1675403, 1765113, 2488562, 2668448, 3395661
259 Low 2021-08-15
PrimeGrid Proth Prime Search (MR1)
3,070,000 431 7 38, 70, 3230, 62918, 82878, 1282582, 3094582
261 3 2021-08-15
PrimeGrid Proth Prime Search (MR1)
3,070,000 4016 95 1, 3, 4, 5, 7, 9, 11, 27, 29, 37, 57, 59, 67, 71, 73, 101, 117, 155, 157, 160, 193, 195, 208, 273, 303, 328, 357, 433, 443, 444, 479, 587, 1095, 1101, 1149, 1291, 1319, 1580, 2065, 2137, 2225, 2796, 3025, 3195, 4396, 6309, 6396, 6933, 6955, 8271, 8691, 10688, 11709, 11711, 12993, 15120, 16509, 18105, 20115, 21685, 22213, 24411, 27227, 41868, 42201, 56939, 57371, 61444, 62445, 96360, 100677, 107639, 119447, 152951, 165575, 231025, 258179, 260997, 271361, 345171, 492999, 715965, 768815, 806980, 895203, 933869, 1331356, 1586347, 1751160, 1848217, 1995105, 2152805, 2671677, 2879941, 3066009
289 Low 2021-08-15
PrimeGrid Proth Prime Search (MR1)
3,070,000 990 20 10, 22, 34, 42, 150, 1758, 6706, 11634, 18502, 52614, 102150, 194830, 207546, 252858, 333406, 638902, 989182, 1117182, 1317378, 1522650
297 3 2021-08-15
PrimeGrid Proth Prime Search (MR1)
3,070,000 1682 34 3, 6, 14, 15, 20, 27, 38, 123, 276, 327, 380, 411, 546, 819, 1155, 1274, 1800, 1875, 3135, 3411, 7514, 9446, 12615, 23400, 23564, 99344, 108258, 148988, 153818, 157623, 306596, 622800, 2660048, 3087543
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