List of largest known primes and probable primes

Last updated

The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the PrimePages and by Henri & Renaud Lifchitz's PRP Records. Numbers with more than 2,000,000 digits are shown.

Contents

Largest known primes

These numbers have been proved prime by computer with a primality test for their form, for example the Lucas–Lehmer primality test for Mersenne numbers. “!” is the factorial, “#” is the primorial, and is the third cyclotomic polynomial, defined as .

Rank [1] [2] NumberDiscovery dateDecimal digits
12136279841 − 1
[3]
12 October 202441,024,320
2282589933 − 1
[4]
7 December 201824,862,048
3277232917 − 1
[5]
26 December 201723,249,425
4274207281 − 1
[6]
7 January 201622,338,618
5257885161 − 1
[7]
25 January 201317,425,170
6243112609 − 1
[8]
23 August 200812,978,189
7242643801 − 1
[9]
4 June 200912,837,064
82 October 202311,981,518
931 May 202311,887,192
10237156667 − 1
[8]
6 September 200811,185,272
11232582657 − 1 4 September 20069,808,358
1210223×231172165 + 1 31 October 20169,383,761
13230402457 − 1 15 December 20059,152,052
144×511786358 + 11 October 20248,238,312
15225964951 − 1 18 February 20057,816,230
164052186×694052186 + 116 April 20257,451,366
1769×224612729 − 113 August 20247,409,172
18224036583 − 1 15 May 20047,235,733
19107347×223427517 − 14 August 20247,052,391
203×223157875 − 125 June 20256,971,216
2138432361048576 + 1 17 December 20246,904,556
223×222103376 − 130 September 20246,653,780
2319637361048576 + 1 24 September 20226,598,776
2419517341048576 + 1 9 August 20226,595,985
25202705×221320516 + 1 25 November 20216,418,121
26220996011 − 1 17 November 20036,320,430
2710590941048576 + 1 31 October 20186,317,602
283×220928756 − 15 July 20236,300,184
299194441048576 + 1 29 August 20176,253,210
3081×220498148 + 113 June 20236,170,560
317×220267500 + 121 July 20226,101,127
324×58431178 + 12 January 20245,893,142
33168451×219375200 + 1 17 September 20175,832,522
3469×219374980 − 13 July 20225,832,452
353×218924888 − 124 March 20225,696,990
3669×218831865 − 116 December 20215,668,959
372×311879700 + 122 June 20245,668,058
3897139×218397548 − 123 April 20235,538,219
397×218233956 + 11 October 20205,488,969
403×218196595 − 18 January 20225,477,722
414×311279466 + 110 September 20245,381,674
423×217748034 − 1 6 September 20215,342,692
4323 February 20175,338,805
443622×57558139 − 118 February 20225,282,917
457×66772401 + 19 September 20195,269,954
462×310852677 + 18 January 20235,178,044
478508301×217016603 − 1 21 March 20185,122,515
488×105112848 − 130 January 20245,112,848
4913×216828072 + 111 October 20235,065,756
503×216819291 − 1 20 January 20215,063,112
515287180×310574360 − 13 November 20245,045,259
523×216408818 + 1 25 October 20204,939,547
532329989×216309923 − 113 February 20244,909,783
5469×215866556 + 120 August 20214,776,312
552036×310009192 + 115 February 20244,775,602
562525332×732525332 + 128 August 20214,705,888
571419499×215614489 + 19 February 20244,700,436
5811×215502315 + 18 January 20234,666,663
59(102332974 + 1)2 − 220 February 20244,665,949
6037×215474010 + 18 November 20224,658,143
6193839×215337656 − 128 November 20224,617,100
62215317227+27658614 + 131 July 20204,610,945
6313×215294536 + 130 September 20234,604,116
646×56546983 + 113 June 20204,576,146
654788920×39577840 − 114 February 20244,569,798
6631×215145093 − 19 February 20254,559,129
6769×214977631 − 13 December 20214,508,719
68192971×214773498 − 17 March 20214,447,272
694×39214845 + 110 September 20244,396,600
709145334×39145334 + 125 December 20234,363,441
714×56181673 − 115 July 20224,320,805
72396101×214259638 − 13 February 20244,292,585
736962×312863120 − 129 February 20204,269,952
7437×214166940 + 124 June 20224,264,676
7599739×214019102 + 1 24 December 20194,220,176
7669×213832885 − 117 January 20224,164,116
779562633# + 125 June 20254,151,498
78404849×213764867 + 110 March 20214,143,644
7925×213719266 + 120 September 20224,129,912
8081×213708272 + 111 October 20224,126,603
812740879×213704395 − 126 October 20194,125,441
82479216×38625889 − 116 November 20194,115,601
8313×213584543 − 130 May 20254,089,357
8431×213514933 − 19 February 20254,068,402
8530 January 20174,055,114
8681×213470584 + 19 October 20224,055,052
87213466917 − 1 14 November 20014,053,946
885778486×55778486 + 115 August 20244,038,996
899×213334487 + 131 March 20204,014,082
90206039×213104952 − 126 April 20213,944,989
912805222×55610444 + 1 2 September 20193,921,539
925128×222919993 + 15 December 20243,919,869
9319249×213018586 + 126 March 20073,918,990
942293×212918431 − 113 February 20213,888,839
9581×212804541 + 119 September 20223,854,553
9667612×55501582 + 18 April 20253,845,446
9718099898524288 + 11 September 20253,805,113
9816211276524288 + 19 August 20253,780,021
9915958750524288 + 115 July 20253,776,446
10015852200524288 + 18 July 20253,774,921
1014×55380542 + 122 February 20233,760,839
10213520762524288 + 125 February 20253,738,699
10313427472524288 + 13 March 20253,737,122
1049×212406887 + 129 March 20203,734,847
10512900356524288 + 122 January 20253,728,004
10612693488524288 + 16 January 20253,724,323
10711937916524288 + 15 October 20243,710,349
1087×212286041 − 110 June 20233,698,468
10910913140524288 + 119 June 20243,689,913
11069×212231580 − 127 July 20213,682,075
11127×212184319 + 16 February 20213,667,847
1129332124524288 + 122 June 20243,654,278
1138630170524288 + 113 April 20243,636,472
114863282×55179692 − 117 October 20243,620,456
115670490×123352450 − 117 October 20243,617,907
1164×37578378 + 19 September 20243,615,806
11711×211993994 − 115 August 20243,610,554
1183761×211978874 − 16 July 20223,606,004
11995×211954552 − 128 May 20243,598,681
120259072×55136295 − 128 October 20243,590,122
1213×211895718 − 1 23 June 20153,580,969
12237×211855148 + 130 May 20223,568,757
1236339004524288 + 18 June 20233,566,218
124763795×64582771 + 111 December 20233,566,095
1255897794524288 + 118 December 20223,549,792
1263×211731850 − 113 March 20153,531,640
12769×211718455 − 14 December 20203,527,609
1288629×211708579 − 119 September 20243,524,638
12941×211676439 + 120 June 20223,514,960
1304896418524288 + 115 May 20223,507,424
13181×211616017 + 130 August 20223,496,772
13269×211604348 − 14 December 20203,493,259
1334450871×64450871 + 117 September 20233,463,458
1349×211500843 + 113 March 20203,462,100
1353×211484018 − 122 November 20143,457,035
136193997×211452891 + 13 April 20183,447,670
13729914×54930904 + 127 September 20243,446,559
1383638450524288 + 129 May 20203,439,810
1399221×211392194 − 17 February 20213,429,397
1409×211366286 + 126 March 20203,421,594
1415×211355764 − 12 October 20213,418,427
142732050×64392301 + 19 September 20233,417,881
1433214654524288 + 124 December 20193,411,613
144632760! − 120 October 20243,395,992
145146561×211280802 − 116 November 20203,395,865
14651208×54857576 + 16 June 20243,395,305
1472985036524288 + 118 September 20193,394,739
1484591×211270837 − 12 January 20253,392,864
1496929×211255424 − 17 July 20223,388,225
1502877652524288 + 129 June 20193,386,397
1512788032524288 + 117 April 20193,379,193
1522733014524288 + 118 March 20193,374,655
1539×211158963 + 113 March 20203,359,184
1549271×211134335 − 117 January 20213,351,773
155136804×54777253 − 11 March 20243,339,162
1562312092524288 + 14 August 20183,336,572
157987324×481974648 − 112 October 20243,319,866
1582061748524288 + 120 March 20183,310,478
1591880370524288 + 115 January 20183,289,511
16027×210902757 − 17 March 20223,282,059
1613×210829346 + 114 January 20143,259,959
16211×210803449 + 129 May 20223,252,164
16311×210797109 + 129 May 20223,250,255
1647×210612737 − 119 May 20223,194,154
1657351117# + 114 September 20243,191,401
16637×210599476 + 117 June 20223,190,762
1675×210495620 − 126 September 20213,159,498
16830 June 20233,153,105
1695×210349000 − 126 September 20213,115,361
17017 January 20173,107,335
17117×210248660 − 18 August 20253,085,156
17252922×54399812 − 13 August 20233,075,342
17314 January 20173,068,389
174177742×54386703 − 124 July 20233,066,180
1754×36402015 + 19 September 20243,054,539
176874208×541748416 − 126 September 20193,028,951
177475856524288 + 18 August 20122,976,633
1782×36236772 + 120 December 20222,975,697
17915×39830108 + 119 August 20232,959,159
1809×29778263 + 15 August 20202,943,552
181198×5581061348 + 130 August 20242,915,138
1821806676×411806676 + 111 March 20182,913,785
183356926524288 + 120 June 20122,911,151
184341112524288 + 115 June 20122,900,832
185213988×54138363 − 129 November 20222,892,597
18643×29596983 − 128 February 20222,888,982
187121×29584444 + 118 November 20202,885,208
18815×29482269 − 114 August 20242,854,449
1896533299# − 118 August 20242,835,864
19011×29381365 + 17 March 20202,824,074
19115×29312889 + 17 August 20232,803,461
19297×29305542 + 110 May 20252,801,250
19393×29235048 + 17 May 20252,780,029
19449×29187790 + 111 September 20222,765,803
1956369619# + 112 August 20242,765,105
19627653×29167433 + 18 June 20052,759,677
1976354977# − 112 August 20242,758,832
19890527×29162167 + 130 June 20102,758,093
1996795×29144320 − 131 March 20212,752,719
20031×29088085 − 127 August 20242,735,788
20175×29079482 + 125 July 20232,733,199
2021323365×1161323365 + 118 January 20182,732,038
20357×29075622 − 17 August 20222,732,037
204102718281 − 5×101631138 − 5×101087142 − 16 August 20242,718,281
20563838×53887851 − 119 June 20222,717,497
20613×28989858 + 110 March 20202,706,219
2074159×28938471 − 119 April 20222,690,752
208273809×28932416 − 113 December 20172,688,931
20993×28898285 + 14 March 20242,678,653
2102×35570081 + 114 February 20202,657,605
21125×28788628 + 11 March 20212,645,643
2122038×3661028507 − 14 April 20162,636,562
21364598×53769854 − 114 June 20222,635,020
21463×28741225 + 16 May 20242,631,373
2158×785900325 + 14 June 20222,606,325
21617×28636199 + 117 February 20212,599,757
21775898524288 + 119 November 20112,558,647
21825×28456828 + 127 January 20212,545,761
21939×28413422 + 123 January 20212,532,694
22031×28348000 + 119 January 20212,513,000
22127×28342438 − 11 February 20212,511,326
22217×28330892 − 116 July 20252,507,850
2233867×28261084 − 114 April 20212,486,838
224101×28152967 + 12 December 20232,454,290
2259×28128075 − 18 July 20252,446,796
226273662×53493296 − 1 7 December 20212,441,715
22781×28109236 + 19 September 20222,441,126
22811×28103463 + 16 March 20202,439,387
229102818×53440382 − 1 8 October 20212,404,729
2309×27979119 − 18 July 20252,401,956
23111×27971110 − 125 November 20192,399,545
23227×27963247 + 114 January 20212,397,178
2333177×27954621 − 113 June 20212,394,584
23439×27946769 + 114 January 20212,392,218
2357×63072198 + 14 August 20192,390,636
2363765×27904593 − 110 January 20212,379,524
23729×27899985 + 114 January 20212,378,134
2385113×27895471 − 127 November 20222,376,778
239861×27895451 − 121 February 20212,376,771
24075×27886683 + 14 September 20232,374,131
2412661×27861390 − 128 December 20242,366,518
24221×27838882 − 115 August 20252,359,740
24330397×27838120 + 117 August 20252,359,514
24499×27830910 + 124 April 20242,357,341
24528433×27830457 + 131 December 20042,357,207
2462589×27803339 − 121 August 20222,349,043
24759×27792307 + 124 April 20242,345,720
248101×27784453 + 124 April 20242,343,356
24995×27778585 + 124 April 20242,341,590
2508401×27767655 − 124 April 20232,338,302
2519693×27767343 − 117 November 20232,338,208
2525×27755002 − 123 September 20212,334,489
2532945×27753232 − 127 November 20222,333,959
2542×836798431 + 110 September 20242,333,181
25563×27743186 + 124 April 20242,330,934
2562545×27732265 − 113 January 20212,327,648
2575539×27730709 − 115 January 20212,327,180
2584817×27719584 − 113 June 20212,323,831
259183×558842752 + 123 August 20242,314,734
2601341174×531341174 + 121 August 20172,312,561
2619467×27680034 − 120 February 20222,311,925
26245×27661004 + 113 December 20202,306,194
26315×27619838 + 16 December 20202,293,801
2643645×27610003 − 128 August 20252,290,843
2653597×27580693 − 110 January 20212,282,020
2665256037# + 16 August 20242,281,955
2673129×27545557 − 114 March 20232,271,443
2687401×27523295 − 121 February 20212,264,742
26945×27513661 + 112 November 20202,261,839
27011 January 20172,259,865
2712739×27483537 − 11 May 20252,252,773
2729×27479919 − 13 June 20232,251,681
2731875×27474308 − 121 August 20222,249,995
27469×27452023 + 123 March 20232,243,285
2751281879×27447178 + 127 December 20232,241,831
2769107×27417464 − 13 May 20252,232,884
2774×53189669 − 112 July 20222,229,484
27819×27383785 − 111 July 20252,222,743
27929×27374577 + 127 October 20202,219,971
2802653×27368343 − 118 September 20242,218,096
28121555×27364128 − 14 September 20242,216,828
2823197×27359542 − 127 November 20222,215,447
283109838×53168862 − 113 August 20202,214,945
28495×27354869 + 125 September 20232,214,039
285101×27345194 − 15 October 20192,211,126
28685×27333444 + 125 September 20232,207,589
28715×27300254 + 125 October 20202,197,597
288422429! + 121 February 20222,193,027
2891759×27284439 − 128 August 20212,192,838
2901909683×141909683 + 127 May 20232,188,748
291737×27269322 − 110 August 20172,188,287
2926909×27258896 − 118 September 20242,185,150
29393×27241494 + 125 September 20232,179,909
294118568×53112069 + 11 May 20202,175,248
2954215×27221386 − 127 December 20242,173,858
29640×257901632 + 111 September 20242,172,875
2971685×27213108 − 113 April 20252,171,366
298580633×27208783 − 115 February 20242,170,066
2996039×27207973 − 124 March 20212,169,820
300502573×27181987 − 14 October 20142,162,000
301402539×27173024 − 12 October 20142,159,301
3023343×27166019 − 129 September 20162,157,191
3034137×27132569 − 111 April 20252,147,121
304161041×27107964 + 16 January 20152,139,716
305294×213918952 − 119 September 20232,139,672
30617×27101254 − 111 July 20252,137,692
30727×27046834 + 111 October 20182,121,310
3081759×27046791 − 128 August 20212,121,299
309327×27044001 − 113 January 20212,120,459
3105×27037188 − 122 September 20212,118,406
3113×27033641 + 121 February 20112,117,338
312625783×27031319 − 110 February 20242,116,644
31333661×27031232 + 130 October 20072,116,617
3146 January 20172,114,016
315207494×53017502 − 116 March 20202,109,149
31615×26993631 − 125 August 20212,105,294
3178943501×26972593 − 18 January 20222,098,967
3186020095×26972593 − 14 September 20222,098,967
31926972593 − 1 1 June 19992,098,960
320273×26963847 − 116 November 20222,096,330
3216219×26958945 − 17 January 20212,094,855
32251×26945567 + 126 May 20202,090,826
3238×102084563 − 11 June 20252,084,564
3243323×26921196 − 118 September 20242,083,492
325238694×52979422 − 112 March 20202,082,532
3264×721119849 − 17 September 20162,079,933
327129×26900230 + 15 June 20252,077,179
32833×26894190 − 127 July 20212,075,360
3294778027# − 131 July 20242,073,926
330105×26884697 + 12 June 20252,072,503
3312345×26882320 − 113 April 20222,071,789
33257×26857990 + 117 August 20232,064,463
333146264×52953282 − 19 March 20202,064,261
33469×26838971 − 11 March 20202,058,738
33535816×52945294 − 15 March 20202,058,677
336127×26836153 − 125 June 20182,057,890
337105×26835099 + 126 May 20252,057,572
33819×26833086 + 124 October 20202,056,966
33969170386262144 + 113 September 20252,055,189
34068717884262144 + 130 August 20252,054,441
34168000464262144 + 110 August 20252,053,246
34267886950262144 + 19 August 20252,053,056
34367673558262144 + 15 August 20252,052,698
34467535128262144 + 12 August 20252,052,465
34567433562262144 + 12 August 20252,052,293
34667167678262144 + 124 July 20252,051,844
34767141518262144 + 124 July 20252,051,799
34867062340262144 + 122 July 20252,051,665
34966498472262144 + 18 July 20252,050,704
35066342922262144 + 14 July 20252,050,437
35166266188262144 + 13 July 20252,050,305
35265×26810465 + 122 September 20232,050,157
35340597×26808509 − 125 December 20132,049,571
354283×26804701 − 119 January 20202,048,431
35565136498262144 + 120 June 20252,048,348
35664989720262144 + 118 June 20252,048,091
35764074894262144 + 130 May 20252,046,447
35864010198262144 + 130 May 20252,046,362
35963833640262144 + 127 May 20252,046,047
3608×102045966 − 131 May 20252,045,967
36163784742262144 + 126 May 20252,045,960
36263558122262144 + 127 May 20252,045,555
36363448958262144 + 122 May 20252,045,359
36463286690262144 + 119 May 20252,045,068
36562767176262144 + 19 May 20252,044,129
36662747994262144 + 19 May 20252,044,095
3671861209×26789999 + 12 December 20202,044,000
3685817×26789459 − 19 January 20212,043,835
36962311952262144 + 13 May 20252,043,301
37062199610262144 + 15 May 20252,043,095
37162152830262144 + 11 May 20252,043,010
37262136706262144 + 12 May 20252,042,980
3738435×26786180 − 17 January 20212,042,848
37461238184262144 + 121 April 20252,041,322
375119×26777781 + 118 May 20252,040,318
37659145944262144 + 129 March 20252,037,364
37758936230262144 + 128 March 20252,036,960
37858870004262144 + 128 March 20252,036,832
37958846688262144 + 128 March 20252,036,787
38058333324262144 + 128 March 20252,035,789
38158288282262144 + 128 March 20252,035,701
38257643582262144 + 128 March 20252,034,435
38357594478262144 + 128 March 20252,034,338
38457478518262144 + 128 March 20252,034,108
38557429230262144 + 127 March 20252,034,111
38651×26753404 + 126 May 20202,032,979
38793×26750726 + 118 September 20232,032,173
38856303352262144 + 127 March 20252,031,757
38956295176262144 + 126 March 20252,031,740
39055952434262144 + 126 March 20252,031,045
39155892864262144 + 127 March 20252,030,920
39269×26745775 + 121 March 20232,030,683
39355702322262144 + 127 March 20252,030,535
39455695224262144 + 125 March 20252,030,520
39555169618262144 + 125 March 20252,029,441
39655007338262144 + 125 March 20252,029,105
39754852328262144 + 125 March 20252,028,784
39854528918262144 + 126 March 20252,028,111
39954044092262144 + 124 March 20252,027,094
40053903472262144 + 124 March 20252,026,797
40153750036262144 + 124 March 20252,026,473
40253616962262144 + 128 March 20252,026,191
40353311612262144 + 124 March 20252,025,540
4044681×26728157 − 125 August 20252,025,381
40553008094262144 + 123 March 20252,024,890
40652648144262144 + 121 March 20252,024,115
40752599274262144 + 120 March 20252,024,009
40852592976262144 + 121 March 20252,023,995
409117×26719464 + 110 May 20252,022,763
41051992174262144 + 116 March 20252,022,687
41151852794262144 + 114 March 20252,022,382
41251714136262144 + 113 March 20252,022,077
41351283286262144 + 19 March 20252,021,124
41451125138262144 + 17 March 20252,020,773
4159995×26711008 − 131 December 20202,020,219
41650454356262144 + 11 March 20252,019,269
41750449664262144 + 128 February 20252,019,259
41850366208262144 + 128 February 20252,019,070
41950121532262144 + 127 February 20252,018,516
42049536902262144 + 125 February 20252,017,180
42149235348262144 + 123 February 20252,016,485
42249209090262144 + 123 February 20252,016,424
42348055302262144 + 118 February 20252,013,723
42447707672262144 + 116 February 20252,012,896
42539×26684941 + 120 October 20202,012,370
42647351862262144 + 115 February 20252,012,044
42747281922262144 + 113 February 20252,011,876
42847255958262144 + 113 February 20252,011,813
4296679881×26679881 + 125 July 20092,010,852
43046831458262144 + 111 February 20252,010,786
43146378776262144 + 18 February 20252,009,680
43245073202262144 + 121 January 20252,006,469
43345007104262144 + 119 January 20252,006,202
43444819108262144 + 114 January 20252,005,786
43544666524262144 + 112 January 20252,005,397
43637×26660841 − 130 July 20142,005,115
43744144624262144 + 129 December 20242,004,059
43844030166262144 + 130 December 20242,003,764
43943330794262144 + 13 December 20242,001,941
44039×26648997 + 120 October 20202,001,550
44142781592262144 + 118 November 20242,000,489
442102000007 − 101127194 − 10872812 − 112 January 20242,000,007
443102000005 − 101051046 − 10948958 − 16 January 20242,000,005

Largest known probable primes (PRPs)

These are probable primes. Primality has not been proven because it is too hard for general numbers of this size but they are expected to be primes. F(n) is the nth Fibonacci number.

Rank [112] NumberDiscovery dateDecimal digits
18 May 20218,177,207
220 April 20215,794,777
3June 20214,556,209
4November 20234,069,900
5213380298 − 27March 20214,027,872
6September 20134,025,533
7September 20134,017,941
83 July 20223,829,294
9November 20233,804,150
1010 April 20233,789,365
11July 20203,763,995
12February 20243,602,847
13January 20243,452,542
14December 20243,356,362
159 July 20203,143,811
1629092392 + 40291February 20112,737,083
17June 20252,644,652
18October 20232,614,858
19 F(11964299)28 June 20252,500,391
203 June 20242,482,834
21August 20202,449,236
22August 20222,388,581
2350018654465 + 54465500186August 20242,368,940
24July 20212,358,349
25February 20222,307,015
26December 20232,239,990
271 March 20182,201,714
28December 20232,181,134
29July 20242,174,370
30 F(10367321)10 August 20242,166,642
31July 20242,166,255
3234532794 + 45327943October 20232,162,693
33 F(10317107)27 July 20242,156,148
3427 October 20172,131,318
35360834356345 + 356345360834February 20242,003,304
36360339356572 + 356572360339May 20242,000,656

See also

References

  1. ↑ Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)" . Retrieved 23 November 2018.
  2. ↑ The known primes with 2,000,000 digits or more
  3. ↑ "Official press release of 52nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 21 October 2024.
  4. ↑ "Official press release of 51st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 December 2018.
  5. ↑ "Official press release of 50th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 26 December 2017.
  6. ↑ "Official press release of 49th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 January 2016.
  7. ↑ "Official press release of 48th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  8. 1 2 "Official press release of 45th and 46th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 10 September 2008.
  9. ↑ "Official press release of 47th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  10. ↑ "PrimePage Primes: Phi(3, - 516693^1048576)". t5k.org. Retrieved 18 October 2024.
  11. ↑ "PrimePage Primes: Phi(3, - 465859^1048576)". t5k.org. Retrieved 18 October 2024.
  12. ↑ "Official press release of 44th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  13. ↑ Official announcement of discovery of 10223×231172165 + 1, PrimeGrid
  14. ↑ "Official press release of 43rd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  15. ↑ "Official press release of 42nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  16. ↑ Official announcement of discovery of 4052186×694052186 + 1, PrimeGrid
  17. ↑ "Official press release of 41st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  18. ↑ Official announcement of discovery of 3×223157875 − 1, PrimeGrid
  19. ↑ Official announcement of discovery of 38432361048576 + 1, PrimeGrid
  20. ↑ Official announcement of discovery of 3×222103376 − 1, PrimeGrid
  21. ↑ Official announcement of discovery of 19637361048576 + 1, PrimeGrid
  22. ↑ Official announcement of discovery of 19517341048576 + 1, PrimeGrid
  23. ↑ Official announcement of discovery of 202705×221320516 + 1, PrimeGrid
  24. ↑ "Official press release of 40th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  25. ↑ Official announcement of discovery of 10590941048576 + 1, PrimeGrid
  26. ↑ Official announcement of discovery of 3×220928756 − 1, PrimeGrid
  27. ↑ Official announcement of discovery of 9194441048576 + 1, PrimeGrid
  28. ↑ Official announcement of discovery of 168451×219375200 + 1, PrimeGrid
  29. ↑ Official announcement of discovery of 3×218924888 − 1, PrimeGrid
  30. ↑ Official announcement of discovery of 3×218196595 − 1, PrimeGrid
  31. ↑ Official announcement of discovery of 3×217748034 − 1, PrimeGrid
  32. ↑ Official announcement of discovery of 8508301×217016603 − 1, PrimeGrid
  33. ↑ Official announcement of discovery of 3×216819291 − 1, PrimeGrid
  34. ↑ Official announcement of discovery of 3×216408818 + 1, PrimeGrid
  35. ↑ Official announcement of discovery of 2525332×732525332 + 1, PrimeGrid
  36. ↑ Official announcement of discovery of 99739×214019102 + 1, PrimeGrid
  37. ↑ "Official press release of 39th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  38. ↑ Official announcement of discovery of 2805222×55610444 + 1, PrimeGrid
  39. 1 2 3 4 5 6 7 8 9 10 11 Chris Caldwell, The Largest Known Primes at The PrimePages.
  40. ↑ Official announcement of discovery of 67612×55501582 + 1, PrimeGrid
  41. ↑ Official announcement of discovery of 16211276524288 + 1, PrimeGrid
  42. ↑ Official announcement of discovery of 15958750524288 + 1, PrimeGrid
  43. ↑ Official announcement of discovery of 15852200524288 + 1, PrimeGrid
  44. ↑ Official announcement of discovery of 13520762524288 + 1, PrimeGrid
  45. ↑ Official announcement of discovery of 13427472524288 + 1, PrimeGrid
  46. ↑ Official announcement of discovery of 12900356524288 + 1, PrimeGrid
  47. ↑ Official announcement of discovery of 12693488524288 + 1, PrimeGrid
  48. ↑ Official announcement of discovery of 11937916524288 + 1, PrimeGrid
  49. ↑ Official announcement of discovery of 10913140524288 + 1, PrimeGrid
  50. ↑ Official announcement of discovery of 9332124524288 + 1, PrimeGrid
  51. ↑ Official announcement of discovery of 8630170524288 + 1, PrimeGrid
  52. ↑ Official announcement of discovery of 3×211895718−1, PrimeGrid
  53. ↑ Official announcement of discovery of 6339004524288 + 1, PrimeGrid
  54. ↑ Official announcement of discovery of 3×211731850 − 1, PrimeGrid
  55. ↑ Official announcement of discovery of 4896418524288 + 1, PrimeGrid
  56. ↑ Official announcement of discovery of 3×211484018 − 1, PrimeGrid
  57. ↑ Official announcement of discovery of 193997×211452891 + 1, PrimeGrid
  58. ↑ Official announcement of discovery of 3638450524288 + 1, PrimeGrid
  59. ↑ Official announcement of discovery of 9221×211392194 − 1, PrimeGrid
  60. ↑ Official announcement of discovery of 3214654524288 + 1, PrimeGrid
  61. ↑ Official announcement of discovery of 146561×211280802 − 1, PrimeGrid
  62. ↑ Official announcement of discovery of 2985036524288 + 1, PrimeGrid
  63. ↑ Official announcement of discovery of 2877652524288 + 1, PrimeGrid
  64. ↑ Official announcement of discovery of 2788032524288 + 1, PrimeGrid
  65. ↑ Official announcement of discovery of 2733014524288 + 1, PrimeGrid
  66. ↑ Official announcement of discovery of 2312092524288 + 1, PrimeGrid
  67. ↑ Official announcement of discovery of 2061748524288 + 1, PrimeGrid
  68. ↑ Official announcement of discovery of 1880370524288 + 1, PrimeGrid
  69. ↑ Official announcement of discovery of 3×210829346 + 1, PrimeGrid
  70. ↑ Official announcement of discovery of 475856524288 + 1, PrimeGrid
  71. ↑ Official announcement of discovery of 356926524288 + 1, PrimeGrid
  72. ↑ Official announcement of discovery of 341112524288 + 1, PrimeGrid
  73. ↑ Official announcement of discovery of 121×29584444 + 1, PrimeGrid
  74. ↑ Official announcement of discovery of 1323365×1161323365 + 1, PrimeGrid
  75. ↑ Official announcement of discovery of 63838×53887851 − 1, PrimeGrid
  76. ↑ Official announcement of discovery of 273809×28932416 − 1, PrimeGrid
  77. ↑ Official announcement of discovery of 25×28788628 + 1, PrimeGrid
  78. 1 2 3 "CRUS - Proven Conjectures". www.noprimeleftbehind.net.
  79. ↑ Official announcement of discovery of 17×28636199 + 1, PrimeGrid
  80. ↑ Official announcement of discovery of 75898524288 + 1, PrimeGrid
  81. ↑ Official announcement of discovery of 25×28456828 + 1, PrimeGrid
  82. ↑ Official announcement of discovery of 39×28413822 + 1, PrimeGrid
  83. ↑ Official announcement of discovery of 31×28348000 + 1, PrimeGrid
  84. ↑ Official announcement of discovery of 27×28342438 − 1, PrimeGrid
  85. ↑ Official announcement of discovery of 273662×53493296 + 1, PrimeGrid
  86. ↑ 102818×53440382 − 1, PrimeGrid
  87. ↑ Official announcement of discovery of 27×27963247 + 1, PrimeGrid
  88. ↑ Official announcement of discovery of 39×27946769 + 1, PrimeGrid
  89. ↑ Official announcement of discovery of 29×27899985 + 1, PrimeGrid
  90. ↑ Official announcement of discovery of 1341174×531341174 + 1, PrimeGrid
  91. ↑ Official announcement of discovery of 45×27661004 + 1, PrimeGrid
  92. ↑ Official announcement of discovery of 15×27619838 + 1, PrimeGrid
  93. ↑ Official announcement of discovery of 45×27513661 + 1, PrimeGrid
  94. ↑ Official announcement of discovery of 29×27374577 + 1, PrimeGrid
  95. ↑ 109838×53168862 − 1, PrimeGrid
  96. ↑ Official announcement of discovery of 29×27300254 + 1, PrimeGrid
  97. ↑ 118568×53112069 + 1, PrimeGrid
  98. ↑ Official announcement of discovery of 502573×27181987 − 1, PrimeGrid
  99. ↑ Official announcement of discovery of 402539×27173024 − 1, PrimeGrid
  100. ↑ Official announcement of discovery of 161041×27107964 + 1, PrimeGrid
  101. ↑ Official announcement of discovery of 27×27046834 + 1, PrimeGrid
  102. ↑ Official announcement of discovery of 3×27033641 + 1, PrimeGrid
  103. ↑ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
  104. ↑ 238694×52979422 − 1, PrimeGrid
  105. ↑ 146264×52953282 − 1, PrimeGrid
  106. ↑ 35816×52945294 − 1, PrimeGrid
  107. ↑ Official announcement of discovery of 19×26833086 + 1, PrimeGrid
  108. ↑ Official announcement of discovery of 40597×26808509 − 1, PrimeGrid
  109. ↑ Official announcement of discovery of 39×26684941 + 1, PrimeGrid
  110. ↑ Official announcement of discovery of 6679881×26679881 + 1, PrimeGrid
  111. ↑ Official announcement of discovery of 39×26648997 + 1, PrimeGrid
  112. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
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