| The largest known k-simultaneous primes | ||||||
| k | Primes | Type | Digits | When | Discoverer | Record History |
|---|---|---|---|---|---|---|
| 1 | 2136279841 − 1 | Mersenne | 41024320 | 12 Oct 2024 | Luke Durant, GIMPS |  |
| 2 | 2996863034895 • 21290000 ± 1 | Tuplet (twin) | 388342 | 14 Sep 2016 | Tom Greer, PrimeGrid, TwinGen, LLR | |
| 3 | 4404139952163 • 267002 − 5 + d, d = 0, 4, 6 | Tuplet | 20183 | 11 Jul 2024 | Serge Batalov, Polysieve, OpenPFGW, CM | |
4 | 667674063382677 • 233608 − 1 + d, d = 0, 2, 6, 8 | Tuplet | 10132 | 25 Feb 2019 | Peter Kaiser, PolySieve, LLR, Primo | |
| 5 | 585150568069684836 • 7757# / 85085 + 5 + d, d = 0, 2, 6, 8, 12 | Tuplet | 3344 | 6 Mar 2022 | Peter Kaiser, OpenPFGW, Primo | |
| 6 | 23700 + 33888977692820810260792517451 + d, d = 0, 4, 6, 10, 12, 16 | Tuplet | 1114 | 21 Nov 2021 | Vidar Nakling, Primo, Sixfinder | |
| 7 | 113225039190926127209 • 2339# / 57057 + 1 + d, d = 0, 2, 6, 8, 12, 18, 20 | Tuplet | 1002 | 27 Jan 2021 | Peter Kaiser | |
| 8 | 362079385668757696008683096558661746463 • 863# + 114023297140211 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 |
Tuplet | 401 | 10 Sep 2023 | Michalis Christou, rieMiner | |
| 9 | x93 • 541# + 145933845312371 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 | Tuplet | 312 | 22 Apr 2023 | Bielawski Mathematicians | |
| 10 | x98 • 449# + 226554621544607 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 | Tuplet | 282 | 12 Sep 2021 | Riecoin #1579367 | |
| 11 | 341841671431409652891648 • 311# • 2n + 1, n = 0..10 | CC, 2nd kind | 151 | 3 Nov 2016 | Andrey Balyakin | |
| 12 | 906644189971753846618980352 • 233# • 2n + 1, n = 0..11 | CC, 2nd kind | 123 | 15 May 2015 | Andrey Balyakin | |
| 13 | x84 • 61# • 2n − 1, n = 0..12 | CC, 1st kind | 108 | 20 Jan 2014 | Primecoin | |
| 14 | x82 • 47# • 2n + 1, n = 0..13 | CC, 2nd kind | 102 | 16 May 2014 | Primecoin | |
| 15 | 14354792166345299956567113728 • 43# • 2n − 1, n = 0..14 | CC, 1st kind | 47 | 31 Dec 2015 | Andrey Balyakin | |
| 16 | 322255 • 73# + 1354238543317302647 + d, d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60 | Tuplet | 35 | 18 Nov 2016 | Roger Thompson | |
| 17 | 3684 • 73# + 880858118723497737821 + d, d = 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66 |
Tuplet | 33 | 5 Feb 2021 | Roger Thompson | |
| 18 | 658189097608811942204322720 • 2n + 1, n = 0..17 | CC, 2nd kind | 30 | 9 Mar 2014 | Raanan Chermoni & Jaroslaw Wroblewski | |
| 19 | 622803914376064301858782434517 + d, d = 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76 |
Tuplet | 30 | 27 Dec 2018 | Raanan Chermoni & Jaroslaw Wroblewski | |
| 20 | 1236637204227022808686214288579 + d, d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80 |
Tuplet | 31 | 23 May 2021 | Raanan Chermoni & Jaroslaw Wroblewski | |
| 21 | 622803914376064301858782434517 + d, d = 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84 |
Tuplet | 30 | 27 Dec 2018 | Raanan Chermoni & Jaroslaw Wroblewski | |
| Big constants
x82 = 5819411283298069803200936040662511327268486153212216998535044251830806354124236416
x84 = 106680560818292299253267832484567360951928953599522278361651385665522443588804123392
x93 = 182075127245948453356763852678412657384571384320476086323955359028566228121357180020362596219
x98 = 14315614956030418747867488895208199566750873528908316976274174208238191434937011407287479676495550 |