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.
Largest known primes
editThese 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] | Number | Discovery date | Decimal digits |
|---|---|---|---|
| 1 | 2136279841 – 1 | 12 October 2024 | 41,024,320 |
| 2 | 282589933 – 1 | 7 December 2018 | 24,862,048 |
| 3 | 277232917 – 1 | 26 December 2017 | 23,249,425 |
| 4 | 274207281 – 1 | 7 January 2016 | 22,338,618 |
| 5 | 257885161 – 1 | 25 January 2013 | 17,425,170 |
| 6 | 243112609 – 1 | 23 August 2008 | 12,978,189 |
| 7 | 242643801 – 1 | 4 June 2009 | 12,837,064 |
| 8 | 2 October 2023 | 11,981,518 | |
| 9 | 31 May 2023 | 11,887,192 | |
| 10 | 237156667 – 1 | 6 September 2008 | 11,185,272 |
| 11 | 232582657 – 1 | 4 September 2006 | 9,808,358 |
| 12 | 10223×231172165 + 1 | 31 October 2016 | 9,383,761 |
| 13 | 230402457 – 1 | 15 December 2005 | 9,152,052 |
| 14 | 4×511786358 + 1 | 1 October 2024 | 8,238,312 |
| 15 | 225964951 – 1 | 18 February 2005 | 7,816,230 |
| 16 | 69×224612729 – 1 | 13 August 2024 | 7,409,172 |
| 17 | 224036583 – 1 | 15 May 2004 | 7,235,733 |
| 18 | 107347×223427517 – 1 | 4 August 2024 | 7,052,391 |
| 19 | 38432361048576 + 1 | 17 December 2024 | 6,904,556 |
| 20 | 3×222103376 − 1 | 30 September 2024 | 6,653,780 |
| 21 | 19637361048576 + 1 | 24 September 2022 | 6,598,776 |
| 22 | 19517341048576 + 1 | 9 August 2022 | 6,595,985 |
| 23 | 202705×221320516 + 1 | 25 November 2021 | 6,418,121 |
| 24 | 220996011 – 1 | 17 November 2003 | 6,320,430 |
| 25 | 10590941048576 + 1 | 31 October 2018 | 6,317,602 |
| 26 | 3×220928756 − 1 | 5 July 2023 | 6,300,184 |
| 27 | 9194441048576 + 1 | 29 August 2017 | 6,253,210 |
| 28 | 81×220498148 + 1 | 13 June 2023 | 6,170,560 |
| 29 | 7×220267500 + 1 | 21 July 2022 | 6,101,127 |
| 30 | 4×58431178 + 1 | 2 January 2024 | 5,893,142 |
| 31 | 168451×219375200 + 1 | 17 September 2017 | 5,832,522 |
| 32 | 69×219374980 − 1 | 3 July 2022 | 5,832,452 |
| 33 | 3×218924888 − 1 | 24 March 2022 | 5,696,990 |
| 34 | 69×218831865 − 1 | 16 December 2021 | 5,668,959 |
| 35 | 2×311879700 + 1 | 22 June 2024 | 5,668,058 |
| 36 | 97139×218397548 − 1 | 23 April 2023 | 5,538,219 |
| 37 | 7×218233956 + 1 | 1 October 2020 | 5,488,969 |
| 38 | 3×218196595 − 1 | 8 January 2022 | 5,477,722 |
| 39 | 4×311279466 + 1 | 10 September 2024 | 5,381,674 |
| 40 | 3×217748034 − 1 | 6 September 2021 | 5,342,692 |
| 41 | 23 February 2017 | 5,338,805 | |
| 42 | 3622×57558139 − 1 | 18 February 2022 | 5,282,917 |
| 43 | 7×66772401 + 1 | 9 September 2019 | 5,269,954 |
| 44 | 2×310852677 + 1 | 8 January 2023 | 5,178,044 |
| 45 | 8508301×217016603 – 1 | 21 March 2018 | 5,122,515 |
| 46 | 8×105112848 – 1 | 30 January 2024 | 5,112,848 |
| 47 | 13×216828072 + 1 | 11 October 2023 | 5,065,756 |
| 48 | 3×216819291 – 1 | 20 January 2021 | 5,063,112 |
| 49 | 5287180×310574360 – 1 | 3 November 2024 | 5,045,259 |
| 50 | 3×216408818 + 1 | 25 October 2020 | 4,939,547 |
| 51 | 2329989×216309923 – 1 | 13 February 2024 | 4,909,783 |
| 52 | 69×215866556 + 1 | 20 August 2021 | 4,776,312 |
| 53 | 2036×310009192 + 1 | 15 February 2024 | 4,775,602 |
| 54 | 2525332×732525332 + 1 | 28 August 2021 | 4,705,888 |
| 55 | 1419499×215614489 + 1 | 9 February 2024 | 4,700,436 |
| 56 | 11×215502315 + 1 | 8 January 2023 | 4,666,663 |
| 57 | (102332974 + 1)2-2 | 20 February 2024 | 4,665,949 |
| 58 | 37×215474010 + 1 | 8 November 2022 | 4,658,143 |
| 59 | 93839×215337656 – 1 | 28 November 2022 | 4,617,100 |
| 60 | 215317227+27658614 + 1 | 31 July 2020 | 4,610,945 |
| 61 | 13×215294536 + 1 | 30 September 2023 | 4,604,116 |
| 62 | 6×56546983 + 1 | 13 June 2020 | 4,576,146 |
| 63 | 4788920×39577840 – 1 | 14 February 2024 | 4,569,798 |
| 64 | 69×214977631 – 1 | 3 December 2021 | 4,508,719 |
| 65 | 192971×214773498 – 1 | 7 March 2021 | 4,447,272 |
| 66 | 4×39214845 + 1 | 10 September 2024 | 4,396,600 |
| 67 | 9145334×39145334 + 1 | 25 December 2023 | 4,363,441 |
| 68 | 4×56181673 – 1 | 15 July 2022 | 4,320,805 |
| 69 | 396101×214259638 – 1 | 3 February 2024 | 4,292,585 |
| 70 | 6962×312863120 – 1 | 29 February 2020 | 4,269,952 |
| 71 | 37×214166940 + 1 | 24 June 2022 | 4,264,676 |
| 72 | 99739×214019102 – 1 | 24 December 2019 | 4,220,176 |
| 73 | 69×213832885 – 1 | 17 January 2022 | 4,164,116 |
| 74 | 404849×213764867 + 1 | 10 March 2021 | 4,143,644 |
| 75 | 25×213719266 + 1 | 20 September 2022 | 4,129,912 |
| 76 | 81×213708272 + 1 | 11 October 2022 | 4,126,603 |
| 77 | 2740879×213704395 – 1 | 26 October 2019 | 4,125,441 |
| 78 | 479216×38625889 – 1 | 16 November 2019 | 4,115,601 |
| 79 | 30 January 2017 | 4,055,114 | |
| 80 | 81×213470584 + 1 | 9 October 2022 | 4,055,052 |
| 81 | 213466917 – 1 | 14 November 2001 | 4,053,946 |
| 82 | 5778486×55778486 + 1 | 15 August 2024 | 4,038,996 |
| 83 | 9×213334487 + 1 | 31 March 2020 | 4,014,082 |
| 84 | 206039×213104952 − 1 | 26 April 2021 | 3,944,989 |
| 85 | 2805222×55610444 + 1 | 2 September 2019 | 3,921,539 |
| 86 | 5128×222919993 + 1 | 5 December 2024 | 3,919,869 |
| 87 | 19249×213018586 + 1 | 26 March 2007 | 3,918,990 |
| 88 | 2293×212918431 − 1 | 13 February 2021 | 3,888,839 |
| 89 | 81×212804541 + 1 | 19 September 2022 | 3,854,553 |
| 90 | 4×55380542 + 1 | 22 February 2023 | 3,760,839 |
| 91 | 9×212406887 + 1 | 29 March 2020 | 3,734,847 |
| 92 | 12693488524288 + 1 | 6 January 2025 | 3,724,323 |
| 93 | 11937916524288 + 1 | 5 October 2024 | 3,710,349 |
| 94 | 7×212286041 − 1 | 10 June 2023 | 3,698,468 |
| 95 | 10913140524288 + 1 | 19 June 2024 | 3,689,913 |
| 96 | 69×212231580 − 1 | 27 July 2021 | 3,682,075 |
| 97 | 27×212184319 + 1 | 6 February 2021 | 3,667,847 |
| 98 | 9332124524288 + 1 | 22 June 2024 | 3,654,278 |
| 99 | 8630170524288 + 1 | 13 April 2024 | 3,636,472 |
| 100 | 863282×55179692 - 1 | 17 October 2024 | 3,620,456 |
| 101 | 670490×123352450 - 1 | 17 October 2024 | 3,617,907 |
| 102 | 4×37578378 + 1 | 9 September 2024 | 3,615,806 |
| 103 | 11×211993994 − 1 | 15 August 2024 | 3,610,554 |
| 104 | 3761×211978874 − 1 | 6 July 2022 | 3,606,004 |
| 105 | 95×211954552 − 1 | 28 May 2024 | 3,598,681 |
| 106 | 259072×55136295 − 1 | 28 October 2024 | 3,590,122 |
| 107 | 3×211895718 − 1 | 23 June 2015 | 3,580,969 |
| 108 | 37×211855148 + 1 | 30 May 2022 | 3,568,757 |
| 109 | 6339004524288 + 1 | 8 June 2023 | 3,566,218 |
| 110 | 763795×64582771 + 1 | 11 December 2023 | 3,566,095 |
| 111 | 5897794524288 + 1 | 18 December 2022 | 3,549,792 |
| 112 | 3×211731850 − 1 | 13 March 2015 | 3,531,640 |
| 113 | 69×211718455 − 1 | 4 December 2020 | 3,527,609 |
| 114 | 8629×211708579 – 1 | 19 September 2024 | 3,524,638 |
| 115 | 41×211676439 + 1 | 20 June 2022 | 3,514,960 |
| 116 | 4896418524288 + 1 | 15 May 2022 | 3,507,424 |
| 117 | 81×211616017 + 1 | 30 August 2022 | 3,496,772 |
| 118 | 69×211604348 − 1 | 4 December 2020 | 3,493,259 |
| 119 | 4450871×64450871 + 1 | 17 September 2023 | 3,463,458 |
| 120 | 9×211500843 + 1 | 13 March 2020 | 3,462,100 |
| 121 | 3×211484018 − 1 | 22 November 2014 | 3,457,035 |
| 122 | 193997×211452891 +1 | 3 April 2018 | 3,447,670 |
| 123 | 29914×54930904 +1 | 27 September 2024 | 3,446,559 |
| 124 | 3638450524288 +1 | 29 May 2020 | 3,439,810 |
| 125 | 9221×211392194 -1 | 7 February 2021 | 3,429,397 |
| 126 | 9×211366286 +1 | 26 March 2020 | 3,421,594 |
| 127 | 5×211355764 -1 | 2 October 2021 | 3,418,427 |
| 128 | 732050×64392301 +1 | 9 September 2023 | 3,417,881 |
| 129 | 3214654524288 +1 | 24 December 2019 | 3,411,613 |
| 130 | 632760! - 1 | 20 October 2024 | 3,395,992 |
| 131 | 146561×211280802 -1 | 16 November 2020 | 3,395,865 |
| 132 | 51208×54857576 +1 | 6 June 2024 | 3,395,305 |
| 133 | 2985036524288 +1 | 18 September 2019 | 3,394,739 |
| 134 | 4591×211270837 -1 | 2 January 2025 | 3,392,864 |
| 135 | 6929×211255424 -1 | 7 July 2022 | 3,388,225 |
| 136 | 2877652524288 +1 | 29 June 2019 | 3,386,397 |
| 137 | 2788032524288 +1 | 17 April 2019 | 3,379,193 |
| 138 | 2733014524288 +1 | 18 March 2019 | 3,374,655 |
| 139 | 9×211158963 +1 | 13 March 2020 | 3,359,184 |
| 140 | 9271×211134335 -1 | 17 January 2021 | 3,351,773 |
| 141 | 136804×54777253 -1 | 1 March 2024 | 3,339,162 |
| 142 | 2312092524288 + 1 | 4 August 2018 | 3,336,572 |
| 143 | 987324×481974648 - 1 | 12 October 2024 | 3,319,866 |
| 144 | 2061748524288 + 1 | 20 March 2018 | 3,310,478 |
| 145 | 1880370524288 + 1 | 15 January 2018 | 3,289,511 |
| 146 | 27×210902757 − 1 | 7 March 2022 | 3,282,059 |
| 147 | 3×210829346 + 1 | 14 January 2014 | 3,259,959 |
| 148 | 11×210803449 + 1 | 29 May 2022 | 3,252,164 |
| 149 | 11×210797109 + 1 | 29 May 2022 | 3,250,255 |
| 150 | 7×210612737 − 1 | 19 May 2022 | 3,194,154 |
| 151 | 7351117# + 1 | 14 September 2024 | 3,191,401 |
| 152 | 37×210599476 + 1 | 17 June 2022 | 3,190,762 |
| 153 | 5×210495620 − 1 | 26 September 2021 | 3,159,498 |
| 154 | 30 June 2023 | 3,153,105 | |
| 155 | 5×210349000 − 1 | 26 September 2021 | 3,115,361 |
| 156 | 17 January 2017 | 3,107,335 | |
| 157 | 52922×54399812 – 1 | 3 August 2023 | 3,075,342 |
| 158 | 14 January 2017 | 3,068,389 | |
| 159 | 177742×54386703 – 1 | 24 July 2023 | 3,066,180 |
| 160 | 4×36402015 + 1 | 9 September 2024 | 3,054,539 |
| 161 | 874208×541748416 – 1 | 26 September 2019 | 3,028,951 |
| 162 | 475856524288 + 1 | 8 August 2012 | 2,976,633 |
| 163 | 2×36236772 + 1 | 20 December 2022 | 2,975,697 |
| 164 | 15×39830108 + 1 | 19 August 2023 | 2,959,159 |
| 165 | 9×29778263 + 1 | 5 August 2020 | 2,943,552 |
| 166 | 198×5581061348 + 1 | 30 August 2024 | 2,915,138 |
| 167 | 1806676×411806676 + 1 | 11 March 2018 | 2,913,785 |
| 168 | 356926524288 + 1 | 20 June 2012 | 2,911,151 |
| 169 | 341112524288 + 1 | 15 June 2012 | 2,900,832 |
| 170 | 213988×54138363 – 1 | 29 November 2022 | 2,892,597 |
| 171 | 43×29596983 – 1 | 28 February 2022 | 2,888,982 |
| 172 | 121×29584444 + 1 | 18 November 2020 | 2,885,208 |
| 173 | 15×29482269 – 1 | 14 August 2024 | 2,854,449 |
| 174 | 6533299# - 1 | 18 August 2024 | 2,835,864 |
| 175 | 11×29381365 + 1 | 7 March 2020 | 2,824,074 |
| 176 | 15×29312889 + 1 | 7 August 2023 | 2,803,461 |
| 177 | 49×29187790 + 1 | 11 September 2022 | 2,765,803 |
| 178 | 6369619# + 1 | 12 August 2024 | 2,765,105 |
| 179 | 27653×29167433 + 1 | 8 June 2005 | 2,759,677 |
| 180 | 6354977# − 1 | 12 August 2024 | 2,758,832 |
| 181 | 90527×29162167 + 1 | 30 June 2010 | 2,758,093 |
| 182 | 6795×29144320 − 1 | 31 March 2021 | 2,752,719 |
| 183 | 31×29088085 − 1 | 27 August 2024 | 2,735,788 |
| 184 | 75×29079482 + 1 | 25 July 2023 | 2,733,199 |
| 185 | 1323365×1161323365 + 1 | 18 January 2018 | 2,732,038 |
| 186 | 57×29075622 – 1 | 7 August 2022 | 2,732,037 |
| 187 | 102718281-5×101631138-5×101087142 – 1 | 6 August 2024 | 2,718,281 |
| 188 | 63838×53887851 – 1 | 19 June 2022 | 2,717,497 |
| 189 | 13×28989858 + 1 | 10 March 2020 | 2,706,219 |
| 190 | 4159×28938471 − 1 | 19 April 2022 | 2,690,752 |
| 191 | 273809×28932416 − 1 | 13 December 2017 | 2,688,931 |
| 192 | 93×28898285 + 1 | 4 March 2024 | 2,678,653 |
| 193 | 2×35570081 + 1 | 14 February 2020 | 2,657,605 |
| 194 | 25×28788628 + 1 | 1 March 2021 | 2,645,643 |
| 195 | 2038×3661028507 − 1 | 4 April 2016 | 2,636,562 |
| 196 | 64598×53769854 − 1 | 14 June 2022 | 2,635,020 |
| 197 | 63×28741225 + 1 | 6 May 2024 | 2,631,373 |
| 198 | 8×785900325 + 1 | 4 June 2022 | 2,606,325 |
| 199 | 17×28636199 + 1 | 17 February 2021 | 2,599,757 |
| 200 | 75898524288 + 1 | 19 November 2011 | 2,558,647 |
| 201 | 25×28456828 + 1 | 27 January 2021 | 2,545,761 |
| 202 | 39×28413422 + 1 | 23 January 2021 | 2,532,694 |
| 203 | 31×28348000 + 1 | 19 January 2021 | 2,513,000 |
| 204 | 27×28342438 − 1 | 1 February 2021 | 2,511,326 |
| 205 | 3867×28261084 − 1 | 14 April 2021 | 2,486,838 |
| 206 | 101×28152967 + 1 | 2 December 2023 | 2,454,290 |
| 207 | 273662×53493296 − 1 | 7 December 2021 | 2,441,715 |
| 208 | 81×28109236 + 1 | 9 September 2022 | 2,441,126 |
| 209 | 11×28103463 + 1 | 6 March 2020 | 2,439,387 |
| 210 | 102818×53440382 − 1 | 8 October 2021 | 2,404,729 |
| 211 | 11×27971110 − 1 | 25 November 2019 | 2,399,545 |
| 212 | 27×27963247 + 1 | 14 January 2021 | 2,397,178 |
| 213 | 3177×27954621 − 1 | 13 June 2021 | 2,394,584 |
| 214 | 39×27946769 + 1 | 14 January 2021 | 2,392,218 |
| 215 | 7×63072198 + 1 | 4 August 2019 | 2,390,636 |
| 216 | 3765×27904593 − 1 | 10 January 2021 | 2,379,524 |
| 217 | 29×27899985 + 1 | 14 January 2021 | 2,378,134 |
| 218 | 5113×27895471 − 1 | 27 November 2022 | 2,376,778 |
| 219 | 861×27895451 − 1 | 21 February 2021 | 2,376,771 |
| 220 | 75×27886683 + 1 | 4 September 2023 | 2,374,131 |
| 221 | 2661×27861390 - 1 | 28 December 2024 | 2,366,518 |
| 222 | 99×27830910 + 1 | 24 April 2024 | 2,357,341 |
| 223 | 28433×27830457 + 1 | 31 December 2004 | 2,357,207 |
| 224 | 2589×27803339 − 1 | 21 August 2022 | 2,349,043 |
| 225 | 59×27792307 + 1 | 24 April 2024 | 2,345,720 |
| 226 | 101×27784453 + 1 | 24 April 2024 | 2,343,356 |
| 227 | 95×27778585 + 1 | 24 April 2024 | 2,341,590 |
| 228 | 8401×27767655 − 1 | 24 April 2023 | 2,338,302 |
| 229 | 9693×27767343 − 1 | 17 November 2023 | 2,338,208 |
| 230 | 5×27755002 − 1 | 23 September 2021 | 2,334,489 |
| 231 | 2945×27753232 − 1 | 27 November 2022 | 2,333,959 |
| 232 | 2×836798431 + 1 | 10 September 2024 | 2,333,181 |
| 233 | 63×27743186 + 1 | 24 April 2024 | 2,330,934 |
| 234 | 2545×27732265 − 1 | 13 January 2021 | 2,327,648 |
| 235 | 5539×27730709 − 1 | 15 January 2021 | 2,327,180 |
| 236 | 4817×27719584 − 1 | 13 June 2021 | 2,323,831 |
| 237 | 183×558842752 + 1 | 23 August 2024 | 2,314,734 |
| 238 | 1341174×531341174 + 1 | 21 August 2017 | 2,312,561 |
| 239 | 9467×27680034 − 1 | 20 February 2022 | 2,311,925 |
| 240 | 45×27661004 + 1 | 13 December 2020 | 2,306,194 |
| 241 | 15×27619838 + 1 | 6 December 2020 | 2,293,801 |
| 242 | 3597×27580693 − 1 | 10 January 2021 | 2,282,020 |
| 243 | 5256037# + 1 | 6 August 2024 | 2,281,955 |
| 244 | 3129×27545557 − 1 | 14 March 2023 | 2,271,443 |
| 245 | 7401×27523295 − 1 | 21 February 2021 | 2,264,742 |
| 246 | 45×27513661 + 1 | 12 November 2020 | 2,261,839 |
| 247 | 11 January 2017 | 2,259,865 | |
| 248 | 9×27479919 − 1 | 3 June 2023 | 2,251,681 |
| 249 | 1875×27474308 − 1 | 21 August 2022 | 2,249,995 |
| 250 | 69×27452023 + 1 | 23 March 2023 | 2,243,285 |
| 251 | 1281879×27447178 + 1 | 27 December 2023 | 2,241,831 |
| 252 | 4×53189669 − 1 | 12 July 2022 | 2,229,484 |
| 253 | 29×27374577 + 1 | 27 October 2020 | 2,219,971 |
| 254 | 2653×27368343 − 1 | 18 September 2024 | 2,218,096 |
| 255 | 21555×27364128 − 1 | 4 September 2024 | 2,216,828 |
| 256 | 3197×27359542 − 1 | 27 November 2022 | 2,215,447 |
| 257 | 109838×53168862 − 1 | 13 August 2020 | 2,214,945 |
| 258 | 95×27354869 + 1 | 25 September 2023 | 2,214,039 |
| 259 | 101×27345194 − 1 | 5 October 2019 | 2,211,126 |
| 260 | 85×27333444 + 1 | 25 September 2023 | 2,207,589 |
| 261 | 15×27300254 + 1 | 25 October 2020 | 2,197,597 |
| 262 | 422429! + 1 | 21 February 2022 | 2,193,027 |
| 263 | 1759×27284439 − 1 | 28 August 2021 | 2,192,838 |
| 264 | 1909683×141909683 + 1 | 27 May 2023 | 2,188,748 |
| 265 | 737×27269322 − 1 | 10 August 2017 | 2,188,287 |
| 266 | 6909×27258896 − 1 | 18 September 2024 | 2,185,150 |
| 267 | 93×27241494 + 1 | 25 September 2023 | 2,179,909 |
| 268 | 118568×53112069 + 1 | 1 May 2020 | 2,175,248 |
| 269 | 4215×27221386 − 1 | 27 December 2024 | 2,173,858 |
| 270 | 40×257901632 + 1 | 11 September 2024 | 2,172,875 |
| 271 | 580633×27208783 − 1 | 15 February 2024 | 2,170,066 |
| 272 | 6039×27207973 − 1 | 24 March 2021 | 2,169,820 |
| 273 | 502573×27181987 − 1 | 4 October 2014 | 2,162,000 |
| 274 | 402539×27173024 − 1 | 2 October 2014 | 2,159,301 |
| 275 | 3343×27166019 − 1 | 29 September 2016 | 2,157,191 |
| 276 | 161041×27107964 + 1 | 6 January 2015 | 2,139,716 |
| 277 | 294×213918952 – 1 | 19 September 2023 | 2,139,672 |
| 278 | 27×27046834 + 1 | 11 October 2018 | 2,121,310 |
| 279 | 1759×27046791 − 1 | 28 August 2021 | 2,121,299 |
| 280 | 327×27044001 − 1 | 13 January 2021 | 2,120,459 |
| 281 | 5×27037188 − 1 | 22 September 2021 | 2,118,406 |
| 282 | 3×27033641 + 1 | 21 February 2011 | 2,117,338 |
| 283 | 625783×27031319 − 1 | 10 February 2024 | 2,116,644 |
| 284 | 33661×27031232 + 1 | 30 October 2007 | 2,116,617 |
| 285 | 6 January 2017 | 2,114,016 | |
| 286 | 207494×53017502 – 1 | 16 March 2020 | 2,109,149 |
| 287 | 15×26993631 – 1 | 25 August 2021 | 2,105,294 |
| 288 | 8943501×26972593 – 1 | 8 January 2022 | 2,098,967 |
| 289 | 6020095×26972593 – 1 | 4 September 2022 | 2,098,967 |
| 290 | 26972593 – 1 | 1 June 1999 | 2,098,960 |
| 291 | 273×26963847 – 1 | 16 November 2022 | 2,096,330 |
| 292 | 6219×26958945 – 1 | 7 January 2021 | 2,094,855 |
| 293 | 51×26945567 + 1 | 26 May 2020 | 2,090,826 |
| 294 | 3323×26921196 – 1 | 18 September 2024 | 2,083,492 |
| 295 | 238694×52979422 – 1 | 12 March 2020 | 2,082,532 |
| 296 | 4×721119849 − 1 | 7 September 2016 | 2,079,933 |
| 297 | 33×26894190 – 1 | 27 July 2021 | 2,075,360 |
| 298 | 4778027# − 1 | 31 July 2024 | 2,073,926 |
| 299 | 2345×26882320 – 1 | 13 April 2022 | 2,071,789 |
| 300 | 57×26857990 + 1 | 17 August 2023 | 2,064,463 |
| 301 | 146264×52953282 – 1 | 9 March 2020 | 2,064,261 |
| 302 | 69×26838971 – 1 | 1 March 2020 | 2,058,738 |
| 303 | 35816×52945294 – 1 | 5 March 2020 | 2,058,677 |
| 304 | 127×26836153 – 1 | 25 June 2018 | 2,057,890 |
| 305 | 19×26833086 + 1 | 24 October 2020 | 2,056,966 |
| 306 | 65×26810465 + 1 | 22 September 2023 | 2,050,157 |
| 307 | 40597×26808509 – 1 | 25 December 2013 | 2,049,571 |
| 308 | 283×26804701 – 1 | 19 January 2020 | 2,048,431 |
| 309 | 1861209×26789999 + 1 | 2 December 2020 | 2,044,000 |
| 310 | 5817×26789459 – 1 | 9 January 2021 | 2,043,835 |
| 311 | 8435×26786180 – 1 | 7 January 2021 | 2,042,848 |
| 312 | 51×26753404 + 1 | 26 May 2020 | 2,032,979 |
| 313 | 93×26750726 + 1 | 18 September 2023 | 2,032,173 |
| 314 | 69×26745775 + 1 | 21 March 2023 | 2,030,683 |
| 315 | 9995×26711008 – 1 | 31 December 2020 | 2,020,219 |
| 316 | 39×26684941 + 1 | 20 October 2020 | 2,012,370 |
| 317 | 6679881×26679881 + 1 | 25 July 2009 | 2,010,852 |
| 318 | 44819108262144 + 1 | 14 January 2025 | 2,005,786 |
| 319 | 44666524262144 + 1 | 12 January 2025 | 2,005,397 |
| 320 | 37×26660841 − 1 | 30 July 2014 | 2,005,115 |
| 321 | 44144624262144 + 1 | 29 December 2024 | 2,004,059 |
| 322 | 44030166262144 + 1 | 30 December 2024 | 2,003,764 |
| 323 | 43330794262144 + 1 | 3 December 2024 | 2,001,941 |
| 324 | 39×26648997 + 1 | 20 October 2020 | 2,001,550 |
| 325 | 42781592262144 + 1 | 18 November 2024 | 2,000,489 |
| 326 | 102000007 – 101127194 – 10872812 – 1 | 12 January 2024 | 2,000,007 |
| 327 | 102000005 – 101051046 – 10948958 – 1 | 6 January 2024 | 2,000,005 |
Largest known probable primes (PRPs)
editThese 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[103] | Number | Discovery date | Decimal digits |
|---|---|---|---|
| 1 | 8 May 2021 | 8,177,207 | |
| 2 | 20 April 2021 | 5,794,777 | |
| 3 | June 2021 | 4,556,209 | |
| 4 | November 2023 | 4,069,900 | |
| 5 | 213380298 – 27 | March 2021 | 4,027,872 |
| 6 | September 2013 | 4,025,533 | |
| 7 | September 2013 | 4,017,941 | |
| 8 | 3 July 2022 | 3,829,294 | |
| 9 | November 2023 | 3,804,150 | |
| 10 | 10 April 2023 | 3,789,365 | |
| 11 | July 2020 | 3,763,995 | |
| 12 | February 2024 | 3,602,847 | |
| 13 | January 2024 | 3,452,542 | |
| 14 | December 2024 | 3,356,362 | |
| 15 | 9 July 2020 | 3,143,811 | |
| 16 | 29092392 + 40291 | February 2011 | 2,737,083 |
| 17 | October 2023 | 2,614,858 | |
| 18 | 3 June 2024 | 2,482,834 | |
| 19 | August 2020 | 2,449,236 | |
| 20 | August 2022 | 2,388,581 | |
| 21 | 50018654465 + 54465500186 | August 2024 | 2,368,940 |
| 22 | July 2021 | 2,358,349 | |
| 23 | February 2022 | 2,307,015 | |
| 24 | December 2023 | 2,239,990 | |
| 25 | 1 March 2018 | 2,201,714 | |
| 26 | December 2023 | 2,181,134 | |
| 27 | July 2024 | 2,174,370 | |
| 28 | F(10367321) | 10 August 2024 | 2,166,642 |
| 29 | July 2024 | 2,166,255 | |
| 30 | 34532794 + 45327943 | October 2023 | 2,162,693 |
| 31 | F(10317107) | 27 July 2024 | 2,156,148 |
| 32 | 27 October 2017 | 2,131,318 | |
| 33 | 360834356345 + 356345360834 | February 2024 | 2,003,304 |
| 34 | 360339356572 + 356572360339 | May 2024 | 2,000,656 |
See also
editReferences
edit- ^ Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.
- ^ The known primes with 2,000,000 digits or more
- ^ "Official press release of 52nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 21 October 2024.
- ^ "Official press release of 51st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 December 2018.
- ^ "Official press release of 50th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 26 December 2017.
- ^ "Official press release of 49th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 7 January 2016.
- ^ "Official press release of 48th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
- ^ a b "Official press release of 45th and 46th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 10 September 2008.
- ^ "Official press release of 47th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
- ^ "PrimePage Primes: Phi(3, - 516693^1048576)". t5k.org. Retrieved 18 October 2024.
- ^ "PrimePage Primes: Phi(3, - 465859^1048576)". t5k.org. Retrieved 18 October 2024.
- ^ "Official press release of 44th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
- ^ Official announcement of discovery of 10223×231172165 + 1, PrimeGrid
- ^ "Official press release of 43rd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
- ^ "Official press release of 42nd Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
- ^ "Official press release of 41st Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
- ^ Official announcement of discovery of 38432361048576 + 1, PrimeGrid
- ^ Official announcement of discovery of 3×222103376 − 1, PrimeGrid
- ^ Official announcement of discovery of 19637361048576 + 1, PrimeGrid
- ^ Official announcement of discovery of 19517341048576 + 1, PrimeGrid
- ^ Official announcement of discovery of 202705×221320516 + 1, PrimeGrid
- ^ "Official press release of 40th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
- ^ Official announcement of discovery of 10590941048576 + 1, PrimeGrid
- ^ Official announcement of discovery of 3×220928756 − 1, PrimeGrid
- ^ Official announcement of discovery of 9194441048576 + 1, PrimeGrid
- ^ Official announcement of discovery of 168451×219375200 + 1, PrimeGrid
- ^ Official announcement of discovery of 3×218924888 − 1, PrimeGrid
- ^ Official announcement of discovery of 3×218196595 − 1, PrimeGrid
- ^ Official announcement of discovery of 3×217748034 − 1, PrimeGrid
- ^ Official announcement of discovery of 8508301×217016603 – 1, PrimeGrid
- ^ Official announcement of discovery of 3×216819291 – 1, PrimeGrid
- ^ Official announcement of discovery of 3×216408818 + 1, PrimeGrid
- ^ Official announcement of discovery of 2525332×732525332 + 1, PrimeGrid
- ^ Official announcement of discovery of 99739×214019102 – 1, PrimeGrid
- ^ "Official press release of 39th Mersenne prime number". Great Internet Mersenne Prime Search. Retrieved 25 January 2013.
- ^ Official announcement of discovery of 2805222×55610444 + 1, PrimeGrid
- ^ a b c d e f g h i j k Chris Caldwell, The Largest Known Primes at The PrimePages.
- ^ Official announcement of discovery of 12693488524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 11937916524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 10913140524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 9332124524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 8630170524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 3×211895718−1, PrimeGrid
- ^ Official announcement of discovery of 6339004524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 3×211731850 − 1, PrimeGrid
- ^ Official announcement of discovery of 4896418524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 3×211484018 − 1, PrimeGrid
- ^ Official announcement of discovery of 193997×211452891 + 1, PrimeGrid
- ^ Official announcement of discovery of 3638450524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 9221×211392194 -1, PrimeGrid
- ^ Official announcement of discovery of 3214654524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 146561×211280802 -1, PrimeGrid
- ^ Official announcement of discovery of 2985036524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 2877652524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 2788032524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 2733014524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 2312092524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 2061748524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 1880370524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 3×210829346 + 1, PrimeGrid
- ^ Official announcement of discovery of 475856524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 356926524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 341112524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 121×29584444 + 1, PrimeGrid
- ^ Official announcement of discovery of 1323365×1161323365 + 1, PrimeGrid
- ^ Official announcement of discovery of 63838×53887851 – 1, PrimeGrid
- ^ Official announcement of discovery of 273809×28932416 -1, PrimeGrid
- ^ Official announcement of discovery of 25×28788628 + 1, PrimeGrid
- ^ a b c "CRUS - Proven Conjectures". www.noprimeleftbehind.net.
- ^ Official announcement of discovery of 17×28636199 + 1, PrimeGrid
- ^ Official announcement of discovery of 75898524288 + 1, PrimeGrid
- ^ Official announcement of discovery of 25×28456828 + 1, PrimeGrid
- ^ Official announcement of discovery of 39×28413822 + 1, PrimeGrid
- ^ Official announcement of discovery of 31×28348000 + 1, PrimeGrid
- ^ Official announcement of discovery of 27×28342438 − 1, PrimeGrid
- ^ Official announcement of discovery of 273662×53493296 + 1, PrimeGrid
- ^ 102818×53440382 – 1, PrimeGrid
- ^ Official announcement of discovery of 27×27963247 + 1, PrimeGrid
- ^ Official announcement of discovery of 39×27946769 + 1, PrimeGrid
- ^ Official announcement of discovery of 29×27899985 + 1, PrimeGrid
- ^ Official announcement of discovery of 1341174×531341174 + 1, PrimeGrid
- ^ Official announcement of discovery of 45×27661004 + 1, PrimeGrid
- ^ Official announcement of discovery of 15×27619838 + 1, PrimeGrid
- ^ Official announcement of discovery of 45×27513661 + 1, PrimeGrid
- ^ Official announcement of discovery of 29×27374577 + 1, PrimeGrid
- ^ 109838×53168862 – 1, PrimeGrid
- ^ Official announcement of discovery of 29×27300254 + 1, PrimeGrid
- ^ 118568×53112069 + 1, PrimeGrid
- ^ Official announcement of discovery of 502573×27181987 − 1, PrimeGrid
- ^ Official announcement of discovery of 402539×27173024 − 1, PrimeGrid
- ^ Official announcement of discovery of 161041×27107964 + 1, PrimeGrid
- ^ Official announcement of discovery of 27×27046834 + 1, PrimeGrid
- ^ Official announcement of discovery of 3×27033641 + 1, PrimeGrid
- ^ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
- ^ 238694×52979422 – 1, PrimeGrid
- ^ 146264×52953282 – 1, PrimeGrid
- ^ 35816×52945294 – 1, PrimeGrid
- ^ Official announcement of discovery of 19×26833086 + 1, PrimeGrid
- ^ Official announcement of discovery of 40597×26808509 – 1, PrimeGrid
- ^ Official announcement of discovery of 39×26684941 + 1, PrimeGrid
- ^ Official announcement of discovery of 6679881×26679881 + 1, PrimeGrid
- ^ Official announcement of discovery of 39×26648997 + 1, PrimeGrid
- ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
External links
edit- Chris Caldwell, The Largest Known Primes Database at The PrimePages
- The 5000 largest known primes at The PrimePages
- The 10,000 largest known probable primes at primenumbers.net
- PrimeGrid’s 321 Prime Search, about the discovery of 3×26090515−1