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
1669×224612729 – 113 August 20247,409,172
17224036583 – 1 15 May 20047,235,733
18107347×223427517 – 14 August 20247,052,391
193×222103376 − 130 September 20246,653,780
2019637361048576 + 1 24 September 20226,598,776
2119517341048576 + 1 9 August 20226,595,985
22202705×221320516 + 1 25 November 20216,418,121
23220996011 – 1 17 November 20036,320,430
2410590941048576 + 1 31 October 20186,317,602
253×220928756 − 15 July 20236,300,184
269194441048576 + 1 29 August 20176,253,210
2781×220498148 + 113 June 20236,170,560
287×220267500 + 121 July 20226,101,127
294×58431178 + 12 January 20245,893,142
30168451×219375200 + 1 17 September 20175,832,522
3169×219374980 − 13 July 20225,832,452
323×218924888 − 124 March 20225,696,990
3369×218831865 − 116 December 20215,668,959
342×311879700 + 122 June 20245,668,058
3597139×218397548 − 123 April 20235,538,219
367×218233956 + 11 October 20205,488,969
373×218196595 − 18 January 20225,477,722
384×311279466 + 110 September 20245,381,674
393×217748034 − 1 6 September 20215,342,692
4023 February 20175,338,805
413622×57558139 − 118 February 20225,282,917
427×66772401 + 19 September 20195,269,954
432×310852677 + 18 January 20235,178,044
448508301×217016603 – 1 21 March 20185,122,515
458×105112848 – 130 January 20245,112,848
4613×216828072 + 111 October 20235,065,756
473×216819291 – 1 20 January 20215,063,112
485287180×310574360 – 13 November 20245,045,259
493×216408818 + 1 25 October 20204,939,547
502329989×216309923 – 113 February 20244,909,783
5169×215866556 + 120 August 20214,776,312
522036×310009192 + 115 February 20244,775,602
532525332×732525332 + 128 August 20214,705,888
541419499×215614489 + 19 February 20244,700,436
5511×215502315 + 18 January 20234,666,663
56(102332974 + 1)2-220 February 20244,665,949
5737×215474010 + 18 November 20224,658,143
5893839×215337656 – 128 November 20224,617,100
59215317227+27658614 + 131 July 20204,610,945
6013×215294536 + 130 September 20234,604,116
616×56546983 + 113 June 20204,576,146
624788920×39577840 – 114 February 20244,569,798
6369×214977631 – 13 December 20214,508,719
64192971×214773498 – 17 March 20214,447,272
654×39214845 + 110 September 20244,396,600
669145334×39145334 + 125 December 20234,363,441
674×56181673 – 115 July 20224,320,805
68396101×214259638 – 13 February 20244,292,585
696962×312863120 – 129 February 20204,269,952
7037×214166940 + 124 June 20224,264,676
7199739×214019102 – 1 24 December 20194,220,176
7269×213832885 – 117 January 20224,164,116
73404849×213764867 + 110 March 20214,143,644
7425×213719266 + 120 September 20224,129,912
7581×213708272 + 111 October 20224,126,603
762740879×213704395 – 126 October 20194,125,441
77479216×38625889 – 116 November 20194,115,601
7830 January 20174,055,114
7981×213470584 + 19 October 20224,055,052
80213466917 – 1 14 November 20014,053,946
815778486×55778486 + 115 August 20244,038,996
829×213334487 + 131 March 20204,014,082
83206039×213104952 − 126 April 20213,944,989
842805222×55610444 + 1 2 September 20193,921,539
855128×222919993 + 15 December 20243,919,869
8619249×213018586 + 126 March 20073,918,990
872293×212918431 − 113 February 20213,888,839
8881×212804541 + 119 September 20223,854,553
894×55380542 + 122 February 20233,760,839
909×212406887 + 129 March 20203,734,847
9111937916524288 + 15 October 20243,710,349
927×212286041 − 110 June 20233,698,468
9310913140524288 + 119 June 20243,689,913
9469×212231580 − 127 July 20213,682,075
9527×212184319 + 16 February 20213,667,847
969332124524288 + 122 June 20243,654,278
978630170524288 + 113 April 20243,636,472
98863282×55179692 - 117 October 20243,620,456
99670490×123352450 - 117 October 20243,617,907
1004×37578378 + 19 September 20243,615,806
10111×211993994 − 115 August 20243,610,554
1023761×211978874 − 16 July 20223,606,004
10395×211954552 − 128 May 20243,598,681
104259072×55136295 − 128 October 20243,590,122
1053×211895718 − 1 23 June 20153,580,969
10637×211855148 + 130 May 20223,568,757
1076339004524288 + 18 June 20233,566,218
108763795×64582771 + 111 December 20233,566,095
1095897794524288 + 118 December 20223,549,792
1103×211731850 − 113 March 20153,531,640
11169×211718455 − 14 December 20203,527,609
1128629×211708579 – 119 September 20243,524,638
11341×211676439 + 120 June 20223,514,960
1144896418524288 + 115 May 20223,507,424
11581×211616017 + 130 August 20223,496,772
11669×211604348 − 14 December 20203,493,259
1174450871×64450871 + 117 September 20233,463,458
1189×211500843 + 113 March 20203,462,100
1193×211484018 − 122 November 20143,457,035
120193997×211452891 +13 April 20183,447,670
12129914×54930904 +127 September 20243,446,559
1223638450524288 +129 May 20203,439,810
1239221×211392194 -17 February 20213,429,397
1249×211366286 +126 March 20203,421,594
1255×211355764 -12 October 20213,418,427
126732050×64392301 +19 September 20233,417,881
1273214654524288 +124 December 20193,411,613
128632760! - 120 October 20243,395,992
129146561×211280802 -116 November 20203,395,865
13051208×54857576 +16 June 20243,395,305
1312985036524288 +118 September 20193,394,739
1326929×211255424 -17 July 20223,388,225
1332877652524288 +129 June 20193,386,397
1342788032524288 +117 April 20193,379,193
1352733014524288 +118 March 20193,374,655
1369×211158963 +113 March 20203,359,184
1379271×211134335 -117 January 20213,351,773
138136804×54777253 -11 March 20243,339,162
1392312092524288 + 14 August 20183,336,572
140987324×481974648 - 112 October 20243,319,866
1412061748524288 + 120 March 20183,310,478
1421880370524288 + 115 January 20183,289,511
14327×210902757 − 17 March 20223,282,059
1443×210829346 + 114 January 20143,259,959
14511×210803449 + 129 May 20223,252,164
14611×210797109 + 129 May 20223,250,255
1477×210612737 − 119 May 20223,194,154
1487351117# + 114 September 20243,191,401
14937×210599476 + 117 June 20223,190,762
1505×210495620 − 126 September 20213,159,498
15130 June 20233,153,105
1525×210349000 − 126 September 20213,115,361
15317 January 20173,107,335
15452922×54399812 – 13 August 20233,075,342
15514 January 20173,068,389
156177742×54386703 – 124 July 20233,066,180
1574×36402015 + 19 September 20243,054,539
158874208×541748416 – 126 September 20193,028,951
159475856524288 + 18 August 20122,976,633
1602×36236772 + 120 December 20222,975,697
16115×39830108 + 119 August 20232,959,159
1629×29778263 + 15 August 20202,943,552
163198×5581061348 + 130 August 20242,915,138
1641806676×411806676 + 111 March 20182,913,785
165356926524288 + 120 June 20122,911,151
166341112524288 + 115 June 20122,900,832
167213988×54138363 – 129 November 20222,892,597
16843×29596983 – 128 February 20222,888,982
169121×29584444 + 118 November 20202,885,208
17015×29482269 – 114 August 20242,854,449
1716533299# - 118 August 20242,835,864
17211×29381365 + 17 March 20202,824,074
17315×29312889 + 17 August 20232,803,461
17449×29187790 + 111 September 20222,765,803
1756369619# + 112 August 20242,765,105
17627653×29167433 + 18 June 20052,759,677
1776354977# − 112 August 20242,758,832
17890527×29162167 + 130 June 20102,758,093
1796795×29144320 − 131 March 20212,752,719
18031×29088085 − 127 August 20242,735,788
18175×29079482 + 125 July 20232,733,199
1821323365×1161323365 + 118 January 20182,732,038
18357×29075622 – 17 August 20222,732,037
184102718281-5×101631138-5×101087142 – 16 August 20242,718,281
18563838×53887851 – 119 June 20222,717,497
18613×28989858 + 110 March 20202,706,219
1874159×28938471 − 119 April 20222,690,752
188273809×28932416 − 113 December 20172,688,931
18993×28898285 + 14 March 20242,678,653
1902×35570081 + 114 February 20202,657,605
19125×28788628 + 11 March 20212,645,643
1922038×3661028507 − 14 April 20162,636,562
19364598×53769854 − 114 June 20222,635,020
19463×28741225 + 16 May 20242,631,373
1958×785900325 + 14 June 20222,606,325
19617×28636199 + 117 February 20212,599,757
19775898524288 + 119 November 20112,558,647
19825×28456828 + 127 January 20212,545,761
19939×28413422 + 123 January 20212,532,694
20031×28348000 + 119 January 20212,513,000
20127×28342438 − 11 February 20212,511,326
2023867×28261084 − 114 April 20212,486,838
203101×28152967 + 12 December 20232,454,290
204273662×53493296 − 1 7 December 20212,441,715
20581×28109236 + 19 September 20222,441,126
20611×28103463 + 16 March 20202,439,387
207102818×53440382 − 1 8 October 20212,404,729
20811×27971110 − 125 November 20192,399,545
20927×27963247 + 114 January 20212,397,178
2103177×27954621 − 113 June 20212,394,584
21139×27946769 + 114 January 20212,392,218
2127×63072198 + 14 August 20192,390,636
2133765×27904593 − 110 January 20212,379,524
21429×27899985 + 114 January 20212,378,134
2155113×27895471 − 127 November 20222,376,778
216861×27895451 − 121 February 20212,376,771
21775×27886683 + 14 September 20232,374,131
21899×27830910 + 124 April 20242,357,341
21928433×27830457 + 131 December 20042,357,207
2202589×27803339 − 121 August 20222,349,043
22159×27792307 + 124 April 20242,345,720
222101×27784453 + 124 April 20242,343,356
22395×27778585 + 124 April 20242,341,590
2248401×27767655 − 124 April 20232,338,302
2259693×27767343 − 117 November 20232,338,208
2265×27755002 − 123 September 20212,334,489
2272945×27753232 − 127 November 20222,333,959
2282×836798431 + 110 September 20242,333,181
22963×27743186 + 124 April 20242,330,934
2302545×27732265 − 113 January 20212,327,648
2315539×27730709 − 115 January 20212,327,180
2324817×27719584 − 113 June 20212,323,831
233183×558842752 + 123 August 20242,314,734
2341341174×531341174 + 121 August 20172,312,561
2359467×27680034 − 120 February 20222,311,925
23645×27661004 + 113 December 20202,306,194
23715×27619838 + 16 December 20202,293,801
2383597×27580693 − 110 January 20212,282,020
2395256037# + 16 August 20242,281,955
2403129×27545557 − 114 March 20232,271,443
2417401×27523295 − 121 February 20212,264,742
24245×27513661 + 112 November 20202,261,839
24311 January 20172,259,865
2449×27479919 − 13 June 20232,251,681
2451875×27474308 − 121 August 20222,249,995
24669×27452023 + 123 March 20232,243,285
2471281879×27447178 + 127 December 20232,241,831
2484×53189669 − 112 July 20222,229,484
24929×27374577 + 127 October 20202,219,971
2502653×27368343 − 118 September 20242,218,096
25121555×27364128 − 14 September 20242,216,828
2523197×27359542 − 127 November 20222,215,447
253109838×53168862 − 113 August 20202,214,945
25495×27354869 + 125 September 20232,214,039
255101×27345194 − 15 October 20192,211,126
25685×27333444 + 125 September 20232,207,589
25715×27300254 + 125 October 20202,197,597
258422429! + 121 February 20222,193,027
2591759×27284439 − 128 August 20212,192,838
2601909683×141909683 + 127 May 20232,188,748
261737×27269322 − 110 August 20172,188,287
2626909×27258896 − 118 September 20242,185,150
26393×27241494 + 125 September 20232,179,909
264118568×53112069 + 11 May 20202,175,248
26540×257901632 + 111 September 20242,172,875
266580633×27208783 − 115 February 20242,170,066
2676039×27207973 − 124 March 20212,169,820
268502573×27181987 − 14 October 20142,162,000
269402539×27173024 − 12 October 20142,159,301
2703343×27166019 − 129 September 20162,157,191
271161041×27107964 + 16 January 20152,139,716
272294×213918952 – 119 September 20232,139,672
27327×27046834 + 111 October 20182,121,310
2741759×27046791 − 128 August 20212,121,299
275327×27044001 − 113 January 20212,120,459
2765×27037188 − 122 September 20212,118,406
2773×27033641 + 121 February 20112,117,338
278625783×27031319 − 110 February 20242,116,644
27933661×27031232 + 130 October 20072,116,617
2806 January 20172,114,016
281207494×53017502 – 116 March 20202,109,149
28215×26993631 – 125 August 20212,105,294
2838943501×26972593 – 18 January 20222,098,967
2846020095×26972593 – 14 September 20222,098,967
28526972593 – 1 1 June 19992,098,960
286273×26963847 – 116 November 20222,096,330
2876219×26958945 – 17 January 20212,094,855
28851×26945567 + 126 May 20202,090,826
2893323×26921196 – 118 September 20242,083,492
290238694×52979422 – 112 March 20202,082,532
2914×721119849 − 17 September 20162,079,933
29233×26894190 – 127 July 20212,075,360
2934778027# − 131 July 20242,073,926
2942345×26882320 – 113 April 20222,071,789
29557×26857990 + 117 August 20232,064,463
296146264×52953282 – 19 March 20202,064,261
29769×26838971 – 11 March 20202,058,738
29835816×52945294 – 15 March 20202,058,677
299127×26836153 – 125 June 20182,057,890
30019×26833086 + 124 October 20202,056,966
30165×26810465 + 122 September 20232,050,157
30240597×26808509 – 125 December 20132,049,571
303283×26804701 – 119 January 20202,048,431
3041861209×26789999 + 12 December 20202,044,000
3055817×26789459 – 19 January 20212,043,835
3068435×26786180 – 17 January 20212,042,848
30751×26753404 + 126 May 20202,032,979
30893×26750726 + 118 September 20232,032,173
30969×26745775 + 121 March 20232,030,683
3109995×26711008 – 131 December 20202,020,219
31139×26684941 + 120 October 20202,012,370
3126679881×26679881 + 125 July 20092,010,852
31337×26660841 − 130 July 20142,005,115
31443330794262144 + 13 December 20242,001,941
31539×26648997 + 120 October 20202,001,550
31642781592262144 + 118 November 20242,000,489
317102000007 – 101127194 – 10872812 – 112 January 20242,000,007
318102000005 – 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 [101] 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
17October 20232,614,858
183 June 20242,482,834
19August 20202,449,236
20August 20222,388,581
2150018654465 + 54465500186August 20242,368,940
22July 20212,358,349
23February 20222,307,015
24December 20232,239,990
251 March 20182,201,714
26December 20232,181,134
27July 20242,174,370
28 F(10367321)10 August 20242,166,642
29July 20242,166,255
3034532794 + 45327943October 20232,162,693
31 F(10317107)27 July 20242,156,148
3227 October 20172,131,318
33360834356345 + 356345360834February 20242,003,304
34360339356572 + 356572360339May 20242,000,656

See also

Related Research Articles

<span class="mw-page-title-main">Great Internet Mersenne Prime Search</span> Volunteer project using software to search for Mersenne prime numbers

The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers.

In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form Mp = 2p − 1 for some prime p.

<span class="mw-page-title-main">Prime number</span> Number divisible only by 1 or itself

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.

In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes and safe primes have applications in public key cryptography and primality testing. It has been conjectured that there are infinitely many Sophie Germain primes, but this remains unproven.

In mathematics, a Fermat number, named after Pierre de Fermat (1607–1665), the first known to have studied them, is a positive integer of the form: where n is a non-negative integer. The first few Fermat numbers are: 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ....

<span class="mw-page-title-main">Prime95</span> Freeware application to search for primes

Prime95, also distributed as the command-line utility mprime for FreeBSD and Linux, is a freeware application written by George Woltman. It is the official client of the Great Internet Mersenne Prime Search (GIMPS), a volunteer computing project dedicated to searching for Mersenne primes. It is also used in overclocking to test for system stability.

127 is the natural number following 126 and preceding 128. It is also a prime number.

In mathematics, a double Mersenne number is a Mersenne number of the form

In number theory, a Wagstaff prime is a prime number of the form

Ralph Ernest Powers was an American amateur mathematician who worked on prime numbers.

<span class="mw-page-title-main">Largest known prime number</span>

The largest known prime number is 2136,279,841 − 1, a number which has 41,024,320 digits when written in the decimal system. It was found on October 12, 2024, on a cloud-based virtual machine volunteered by Luke Durant to the Great Internet Mersenne Prime Search (GIMPS).

In number theory, a Pierpont prime is a prime number of the form for some nonnegative integers u and v. That is, they are the prime numbers p for which p − 1 is 3-smooth. They are named after the mathematician James Pierpont, who used them to characterize the regular polygons that can be constructed using conic sections. The same characterization applies to polygons that can be constructed using ruler, compass, and angle trisector, or using paper folding.

<span class="mw-page-title-main">PrimeGrid</span> BOINC based volunteer computing project researching prime numbers

PrimeGrid is a volunteer computing project that searches for very large prime numbers whilst also aiming to solve long-standing mathematical conjectures. It uses the Berkeley Open Infrastructure for Network Computing (BOINC) platform. PrimeGrid offers a number of subprojects for prime-number sieving and discovery. Some of these are available through the BOINC client, others through the PRPNet client. Some of the work is manual, i.e. it requires manually starting work units and uploading results. Different subprojects may run on different operating systems, and may have executables for CPUs, GPUs, or both; while running the Lucas–Lehmer–Riesel test, CPUs with Advanced Vector Extensions and Fused Multiply-Add instruction sets will yield the fastest results for non-GPU accelerated workloads.

In number theory, a Leyland number is a number of the form

In mathematics, the Mersenne conjectures concern the characterization of a kind of prime numbers called Mersenne primes, meaning prime numbers that are a power of two minus one.

Curtis Niles Cooper is an American mathematician who was a professor at the University of Central Missouri, in the Department of Mathematics and Computer Science.

<span class="mw-page-title-main">Megaprime</span> Prime number with at least one million digits

A megaprime is a prime number with at least one million decimal digits.

In mathematics, the Lucas–Lehmer–Riesel test is a primality test for numbers of the form N = k ⋅ 2n − 1 with odd k < 2n. The test was developed by Hans Riesel and it is based on the Lucas–Lehmer primality test. It is the fastest deterministic algorithm known for numbers of that form. For numbers of the form N = k ⋅ 2n + 1, either application of Proth's theorem or one of the deterministic proofs described in Brillhart–Lehmer–Selfridge 1975 are used.

A Proth number is a natural number N of the form where k and n are positive integers, k is odd and . A Proth prime is a Proth number that is prime. They are named after the French mathematician François Proth. The first few Proth primes are

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 press release of 41st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  17. ↑ Official announcement of discovery of 3×222103376 − 1, PrimeGrid
  18. ↑ Official announcement of discovery of 19637361048576 + 1, PrimeGrid
  19. ↑ Official announcement of discovery of 19517341048576 + 1, PrimeGrid
  20. ↑ Official announcement of discovery of 202705×221320516 + 1, PrimeGrid
  21. ↑ "Official press release of 40th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  22. ↑ Official announcement of discovery of 10590941048576 + 1, PrimeGrid
  23. ↑ Official announcement of discovery of 3×220928756 − 1, PrimeGrid
  24. ↑ Official announcement of discovery of 9194441048576 + 1, PrimeGrid
  25. ↑ Official announcement of discovery of 168451×219375200 + 1, PrimeGrid
  26. ↑ Official announcement of discovery of 3×218924888 − 1, PrimeGrid
  27. ↑ Official announcement of discovery of 3×218196595 − 1, PrimeGrid
  28. ↑ Official announcement of discovery of 3×217748034 − 1, PrimeGrid
  29. ↑ Official announcement of discovery of 8508301×217016603 – 1, PrimeGrid
  30. ↑ Official announcement of discovery of 3×216819291 – 1, PrimeGrid
  31. ↑ Official announcement of discovery of 3×216408818 + 1, PrimeGrid
  32. ↑ Official announcement of discovery of 2525332×732525332 + 1, PrimeGrid
  33. ↑ Official announcement of discovery of 99739×214019102 – 1, PrimeGrid
  34. ↑ "Official press release of 39th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
  35. ↑ Official announcement of discovery of 2805222×55610444 + 1, PrimeGrid
  36. 1 2 3 4 5 6 7 8 9 10 11 Chris Caldwell, The Largest Known Primes at The PrimePages.
  37. ↑ Official announcement of discovery of 11937916524288 + 1, PrimeGrid
  38. ↑ Official announcement of discovery of 10913140524288 + 1, PrimeGrid
  39. ↑ Official announcement of discovery of 9332124524288 + 1, PrimeGrid
  40. ↑ Official announcement of discovery of 8630170524288 + 1, PrimeGrid
  41. ↑ Official announcement of discovery of 3×211895718−1, PrimeGrid
  42. ↑ Official announcement of discovery of 6339004524288 + 1, PrimeGrid
  43. ↑ Official announcement of discovery of 3×211731850 − 1, PrimeGrid
  44. ↑ Official announcement of discovery of 4896418524288 + 1, PrimeGrid
  45. ↑ Official announcement of discovery of 3×211484018 − 1, PrimeGrid
  46. ↑ Official announcement of discovery of 193997×211452891 + 1, PrimeGrid
  47. ↑ Official announcement of discovery of 3638450524288 + 1, PrimeGrid
  48. ↑ Official announcement of discovery of 9221×211392194 -1, PrimeGrid
  49. ↑ Official announcement of discovery of 3214654524288 + 1, PrimeGrid
  50. ↑ Official announcement of discovery of 146561×211280802 -1, PrimeGrid
  51. ↑ Official announcement of discovery of 2985036524288 + 1, PrimeGrid
  52. ↑ Official announcement of discovery of 2877652524288 + 1, PrimeGrid
  53. ↑ Official announcement of discovery of 2788032524288 + 1, PrimeGrid
  54. ↑ Official announcement of discovery of 2733014524288 + 1, PrimeGrid
  55. ↑ Official announcement of discovery of 2312092524288 + 1, PrimeGrid
  56. ↑ Official announcement of discovery of 2061748524288 + 1, PrimeGrid
  57. ↑ Official announcement of discovery of 1880370524288 + 1, PrimeGrid
  58. ↑ Official announcement of discovery of 3×210829346 + 1, PrimeGrid
  59. ↑ Official announcement of discovery of 475856524288 + 1, PrimeGrid
  60. ↑ Official announcement of discovery of 356926524288 + 1, PrimeGrid
  61. ↑ Official announcement of discovery of 341112524288 + 1, PrimeGrid
  62. ↑ Official announcement of discovery of 121×29584444 + 1, PrimeGrid
  63. ↑ Official announcement of discovery of 1323365×1161323365 + 1, PrimeGrid
  64. ↑ Official announcement of discovery of 63838×53887851 – 1, PrimeGrid
  65. ↑ Official announcement of discovery of 273809×28932416 -1, PrimeGrid
  66. ↑ Official announcement of discovery of 25×28788628 + 1, PrimeGrid
  67. 1 2 3 "CRUS - Proven Conjectures". www.noprimeleftbehind.net.
  68. ↑ Official announcement of discovery of 17×28636199 + 1, PrimeGrid
  69. ↑ Official announcement of discovery of 75898524288 + 1, PrimeGrid
  70. ↑ Official announcement of discovery of 25×28456828 + 1, PrimeGrid
  71. ↑ Official announcement of discovery of 39×28413822 + 1, PrimeGrid
  72. ↑ Official announcement of discovery of 31×28348000 + 1, PrimeGrid
  73. ↑ Official announcement of discovery of 27×28342438 − 1, PrimeGrid
  74. ↑ Official announcement of discovery of 273662×53493296 + 1, PrimeGrid
  75. ↑ 102818×53440382 – 1, PrimeGrid
  76. ↑ Official announcement of discovery of 27×27963247 + 1, PrimeGrid
  77. ↑ Official announcement of discovery of 39×27946769 + 1, PrimeGrid
  78. ↑ Official announcement of discovery of 29×27899985 + 1, PrimeGrid
  79. ↑ Official announcement of discovery of 1341174×531341174 + 1, PrimeGrid
  80. ↑ Official announcement of discovery of 45×27661004 + 1, PrimeGrid
  81. ↑ Official announcement of discovery of 15×27619838 + 1, PrimeGrid
  82. ↑ Official announcement of discovery of 45×27513661 + 1, PrimeGrid
  83. ↑ Official announcement of discovery of 29×27374577 + 1, PrimeGrid
  84. ↑ 109838×53168862 – 1, PrimeGrid
  85. ↑ Official announcement of discovery of 29×27300254 + 1, PrimeGrid
  86. ↑ 118568×53112069 + 1, PrimeGrid
  87. ↑ Official announcement of discovery of 502573×27181987 − 1, PrimeGrid
  88. ↑ Official announcement of discovery of 402539×27173024 − 1, PrimeGrid
  89. ↑ Official announcement of discovery of 161041×27107964 + 1, PrimeGrid
  90. ↑ Official announcement of discovery of 27×27046834 + 1, PrimeGrid
  91. ↑ Official announcement of discovery of 3×27033641 + 1, PrimeGrid
  92. ↑ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
  93. ↑ 238694×52979422 – 1, PrimeGrid
  94. ↑ 146264×52953282 – 1, PrimeGrid
  95. ↑ 35816×52945294 – 1, PrimeGrid
  96. ↑ Official announcement of discovery of 19×26833086 + 1, PrimeGrid
  97. ↑ Official announcement of discovery of 40597×26808509 – 1, PrimeGrid
  98. ↑ Official announcement of discovery of 39×26684941 + 1, PrimeGrid
  99. ↑ Official announcement of discovery of 6679881×26679881 + 1, PrimeGrid
  100. ↑ Official announcement of discovery of 39×26648997 + 1, PrimeGrid
  101. 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 Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.