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Proth primes of the form k•2n+1, 10,000 ≤ k ≤ 100,000

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Overview

Automatically generated table from available Proth primes 10,000 < k < 100,000.

Explanations

The colors used in the table are defined as:

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

Primes table

There are 46 sequences:

k Type Date max n Nash # Primes for n
10001 2018-04-05 1,000,000 1114 30 7, 27, 33, 55, 61, 67, 85, 91, 103, 133, 159, 187, 223, 375, 727, 1179, 1933, 4267, 40915, 104887, 109213, 129183, 227169, 255391, 317107, 354861, 374461, 462753, 960399, 2172615
10003 2019-07-21 400,000 2157 45 2, 4, 6, 14, 18, 28, 42, 44, 50, 64, 74, 78, 96, 174, 212, 288, 352, 596, 642, 686, 712, 796, 1084, 1826, 3632, 3670, 4338, 4594, 5830, 7222, 8962, 12276, 15044, 15590, 22834, 31876, 34676, 37532, 77478, 96670, 177394, 384864, 479254, 528030, 1468292
10223 Low 2017 31,278,077 207 1 31172165
12321 3 2020-06-15 300,000 2495 46 4, 24, 29, 47, 61, 63, 67, 69, 87, 101, 129, 143, 153, 249, 252, 333, 408, 561, 616, 732, 929, 1349, 3467, 6156, 6919, 9244, 14413, 17128, 20059, 20169, 20512, 23479, 24076, 26208, 27189, 34113, 37648, 43893, 45537, 63107, 79527, 88752, 118701, 122844, 164961, 218753
12743 Low 2020-06-09 100,000 416 3 9, 41205, 49113
15735 315 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 3 2019-10-12 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 Low 2024-04-07
PrimeGrid Seventeen or Bust (MR16)
41,208,000 169 0
22249 Low 2020-04-10 500,000 284 2 2, 408602
22699 Low 2024-04-07
PrimeGrid Seventeen or Bust (MR16)
41,208,000 69 0
23451 3 2024-06-22 100,000 1223 17 43, 75, 147, 163, 197, 203, 709, 973, 1503, 20635, 32333, 36045, 42623, 67103, 186837, 215203, 3739388
23873 Low 2020-04-08 136,733 282 2 5, 136733
23971 Low 2020-10-06 10,000,000 108 1 8
24737 Low 2024-04-07
PrimeGrid Seventeen or Bust (MR16)
41,208,000 174 0
27697 2024-06-04 50,000 1193 17 4, 6, 12, 46, 166, 286, 582, 756, 1132, 1924, 2188, 6454, 7036, 9414, 16774, 25168, 48222
28831 Low 2020-04-09 204,580 225 2 4, 204580
32247 3 2022-03-04 100,000 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
35461 Low 2020-04-08 129,820 202 2 4, 129820
39527 Low 2020-04-08 143,055 141 2 15, 143055
42717 3Low 2024-06-22 100,000 893 7 39, 51, 59, 4671, 5931, 13479, 905792
44243 Low 2020-04-17 440,969 237 2 9, 440969
45323 Low 2020-10-17
CRUS Even Sierpiński (MR12)
10,000,000 266 1 1
48495 315 2024-05-15
(Alex_soldier)
1,100,000 3088 51 11, 13, 29, 40, 43, 49, 50, 70, 73, 82, 106, 125, 163, 251, 269, 349, 401, 479, 527, 614, 920, 1180, 2105, 2789, 3263, 3581, 4690, 6503, 8470, 10582, 12361, 14690, 16702, 20102, 23341, 28379, 44686, 81371, 81443, 87370, 105287, 109625, 112484, 113482, 115156, 137894, 138056, 142984, 189373, 569842, 805655
50777 Low 2020-10-06 10,000,000 166 1 11
50873 Low 2020-10-17
CRUS Even Sierpiński (MR12)
10,000,000 410 1 1
53133 3 2022-03-04 50,000 1475 18 14, 26, 44, 72, 144, 146, 204, 222, 404, 642, 716, 1116, 1178, 5846, 16292, 21224, 24788, 42542
54953 Low 2020-04-19 622,065 220 2 9, 622065
55459 Low 2024-04-07
PrimeGrid Seventeen or Bust (MR16)
41,208,000 242 0
57377 Low 2020-04-09 447,439 155 2 7, 447439
60357 3 2024-06-22 100,000 2209 34 2, 6, 8, 14, 18, 24, 26, 80, 218, 270, 378, 410, 450, 572, 774, 1712, 2660, 2712, 2994, 3500, 4040, 4326, 7766, 8832, 13406, 15578, 31524, 39830, 47186, 48948, 49124, 66804, 95954, 1676907
60849 3 2024-06-22 100,000 1368 22 9, 129, 147, 181, 225, 337, 549, 597, 1177, 1327, 2685, 11019, 18397, 19539, 66889, 77959, 90405, 95647, 97497, 246691, 390015, 3067914
66741 3Low 2020-07-05 50,000 811 9 5, 51, 95, 117, 237, 357, 2231, 3767, 6837
67275 315 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 Low 2024-04-07
PrimeGrid Seventeen or Bust (MR16)
41,208,000 56 0
68221 Low 2020-04-09 200,944 326 2 16, 200944
68633 Low 2020-06-02 2,715,609 250 2 9, 2715609
71657 Low 2020-05-01 1,146,175 327 2 15, 1146175
76877 Low 2020-10-06 10,000,000 96 1 11
77297 Low 2020-04-08 118,499 257 2 3, 118499
77777 Low 2023-05-28
(Alex_soldier)
2,100,000 374 6 15, 103, 223, 1063, 34087, 2013487
78557 Low 1962 0 0 0 No primes possible!
79309 Low 2024-04-07
PrimeGrid Prime Sierpiński Problem (MR18)
30,935,000 56 0
79817 Low 2024-04-07
PrimeGrid Prime Sierpiński Problem (MR18)
30,935,000 146 0
84363 3 2024-06-22 100,000 1624 28 2, 4, 16, 20, 26, 34, 38, 328, 346, 610, 628, 656, 700, 800, 866, 1160, 1198, 1334, 1654, 2558, 4462, 6032, 9044, 9796, 11782, 43534, 87308, 2222321
85287 3 2024-06-22 100,000 1630 20 14, 22, 26, 58, 182, 190, 274, 416, 524, 1426, 1790, 5440, 5536, 10682, 13958, 15656, 20906, 34784, 52390, 1890011
95283 3 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
Proth primes