| Rank | exponent p | discovery date | discoverer (credited persons) | needed real time to prove | supporting help |
|---|---|---|---|---|---|
| 1 | 2 | < 0 | |||
| 2 | 3 | < 0 | |||
| 3 | 5 | < 0 | |||
| 4 | 7 | < 0 | |||
| 5 | 13 | 1456 | |||
| 6 | 17 | 1588 | Pietro Cataldi | ||
| 7 | 19 | 1588 | Pietro Cataldi | ||
| 8 | 31 | 1772 | Leonhard Euler | ||
| 12 | 127 | 1876 | Francois Edouard A. Lucas | ||
| 9 | 61 | 1883 | Ivane M. Pervouchine | ||
| 10 | 89 | 1911 | R. E. Powers | ||
| 11 | 107 | 1914 | R. E. Powers | ||
| 13 | 521 | 1952-01-30 | Raphael M. Robinson | ~ 80 sec | SWAC |
| 14 | 607 | 1952-01-30 | Raphael M. Robinson | ~ 2 min | SWAC |
| 15 | 1279 | 1952-06-25 | Raphael M. Robinson | 13.5 min | SWAC |
| 16 | 2203 | 1952-10-07 | Raphael M. Robinson | ~ 55 min | SWAC |
| 17 | 2281 | 1952-10-09 | Raphael M. Robinson | 1 hour | SWAC |
| 18 | 3217 | 1957-09-08 | Hans Riesel | 5.5 hours | BESK |
| 19 | 4253 | 1961-11-03 | Alexander Hurwitz & John L. Selfridge | ~ 50 min | IBM 7090 |
| 20 | 4423 | 1961-11-03 | Alexander Hurwitz & John L. Selfridge | 50 min | IBM 7090 |
| 21 | 9689 | 1963-05-11 | Donald B. Gillies | 83 min | ILLIAC II |
| 22 | 9941 | 1963-05-16 | Donald B. Gillies | 90 min | ILLIAC II |
| 23 | 11213 | 1963-06-02 | Donald B. Gillies | 135 min | ILLIAC II |
| 24 | 19937 | 1971-03-04 | Bryant Tuckerman | 35 min | IBM 360/91 |
| 25 | 21701 | 1978-10-30 | Landon Curt Noll & Laura Nickel | 7h 40m 20s | CDC Cyber 174 |
| 26 | 23209 | 1979-02-09 | Landon Curt Noll & Laura Nickel | 8h 39m 37s | CDC Cyber 174 |
| 27 | 44497 | 1979-04-08 | Harry Nelson & David Slowinski | Cray 1 | |
| 28 | 86243 | 1982-09-25 | David Slowinski | Cray 1 | |
| 30 | 132049 | 1983-09-19 | David Slowinski | Cray X-MP | |
| 31 | 216091 | 1985-09-01 | David Slowinski | Cray X-MP/24 | |
| 29 | 110503 | 1988-01-28 | Walt Colquitt & Luke Welsh | 686 sec | NEC SX/2 |
| 32 | 756839 | 1992-04-01 | David Slowinski & Paul Gage | ~ 16 hours | Cray-2 |
| 33 | 859433 | 1994-02-01 | David Slowinski & Paul Gage | 7.2 hours | Cray C90 |
| 34 | 1257787 | 1996-09-03 | David Slowinski & Paul Gage | ~ 6 hours | Cray T94 |
| 35 | 1398269 | 1996-11-23 | Joel Armengaud, Woltman, et. al. | 88 hours | 90 MHz Pentium PC |
| 36 | 2976221 | 1997-09-01 | Gordon Spence, Woltman, et. al. | 15 days | 100 MHz Pentium PC |
| 37 | 3021377 | 1998-01-27 | Roland Clarkson, Woltman, Kurowski et. al. | 46 days | 200 MHz Pentium PC |
| 38 | 6972593 | 1999-06-01 | Nayan Hajratwala, Woltman, Kurowski et. al. | 111 days | 350 MHz Pentium II IBM Aptiva PC |
| 39 | 13466917 | 2001-11-14 | Michael Cameron, Woltman, Kurowski et. al. | 45 days | 800 MHz AMD T-Bird PC |
| 40 | 20996011 | 2003-11-17 | Michael Shafer, Georg Woltman, Scott Kurowski et. al. | 19 days | 2 GHz Pentium 4 Dell Dimension PC |
| 41 | 24036583 | 2004-05-15 | Josh Findley, Georg Woltman, Scott Kurowski et. al. | 14 days | 2.4 GHz Pentium 4 PC |
| 42 | 25964951 | 2005-02-18 | Martin Nowak, Georg Woltman, Scott Kurowski et. al. | 50 days | 2.4 GHz Pentium 4 PC |
| 43 | 30402457 | 2005-12-15 | Curtis Cooper and Steven Boone, Georg Woltman, Scott Kurowski et. al. | ~ 50 days | PC network of 700 PC |
| 44 | 32582657 | 2006-09-04 | Curtis Cooper and Steven Boone, Georg Woltman, Scott Kurowski et. al. | ~ 9 months | PC network of 700 PC |
| 47 | 43112609 | 2008-08-23 | Edson Smith, Georg Woltman, Scott Kurowski et. al. | 35 days | 2.4 GHz Intel Core 2 Duo E6600 Dell Optiplex 745 PC |
| 45 | 37156667 | 2008-09-06 | Hans-Michael Elvenich, Georg Woltman, Scott Kurowski et. al. | 218 days | 2.83 GHz Intel Core 2 Duo E8300 PC |
| 46 | 42643801 | 2009-04-12 | Odd Magnar Strindmo, Georg Woltman, Scott Kurowski et. al. | 29 days | 3.0 GHz Intel Core 2 PC |
| 48 | 57885161 | 2013-01-25 | Curtis Cooper, Georg Woltman, Scott Kurowski et. al. | 39 days | 3.0 GHz Intel Core2 Duo E8400 CPU PC |
| 49 | 74207281 | 2016-01-07 | Curtis Cooper, Georg Woltman, Scott Kurowski et. al. | 31 days | 3.6 GHz Intel I7-4790 CPU PC |
| 50 | 77232917 | 2017-12-26 | Jonathan Pace, Georg Woltman, Scott Kurowski et. al. | 6 days | 3.3 GHz Intel I5-6600 CPU PC |
| 51 | 82589933 | 2018-12-07 | Patrick Laroche, Georg Woltman, Scott Kurowski et. al. | 12 days | 2.0 GHz Intel I5-4590T CPU PC |
| 52 | 136279841 | 2024-10-12 | Luke Durant, Georg Woltman, Scott Kurowski et. al. | NVIDIA A100 GPU |
| time range | count | who | how | why | importants |
|---|---|---|---|---|---|
| Antiquity | 4 | philosophs (?) | reflecting by mind | philosophy / culture | discovery of meaning |
| Middle Ages | 3 | hobby numberists | trial divisions by hand calculations | culture/fashion in Italy | disproof of tradition 211-1 must be prime |
| 18-th century until mid 20-th century (~ 220 years) | 5 | first professional mathematicians | hand calculations (Lucas sequences) | arise of scientific precise culture | important theoretical insights achieved |
| 1951-1954 | 5 | a mathematician | Lucas-Lehmer test used | scientific culture | first reliable electronic calculators |
| 1954 - 1979 (27 years) | 9 | different mathematicians | LL-test on date-typical computers | proud of record breaking | |
| 1979 - 1996 (17 years) | 8 | mainly a single programmer | LL-test on special vector-computers (Cray) | proud of record breaking (making history) | |
| January 1996 - October 2024 (28 years) | 17 | mainly one, later two, fixed programmer(s) and random people | coordinated distributed search on common computers for interested people (LL-test with FFT-multiplication) | proud of record breaking (making history) | social/info culture (GIMPS) |
| October 2024 - today (1.5 years) | 1 | one expert GPU-programmer | thousands of GPUs on distibuted servers (LL-test with FFT-multiplication on GPUs) | proud of record breaking (making history) |
Historical information about Mersenne number discoveries before 1963.
More details on History of Mersenne Primes
GIMPS (Distributed search for Mersenne Primes