List of Known Mersenne Primes
The table below lists all known Mersenne primes (sequence A000668 in OEIS):
# | p | Mp | Mp digits | Date of discovery | Discoverer | Method used |
---|---|---|---|---|---|---|
1 | 2 | 3 | 1 | c. 430 BCE | Ancient Greek mathematicians | |
2 | 3 | 7 | 1 | c. 430 BCE | Ancient Greek mathematicians | |
3 | 5 | 31 | 2 | c. 300 BCE | Ancient Greek mathematicians | |
4 | 7 | 127 | 3 | c. 300 BCE | Ancient Greek mathematicians | |
5 | 13 | 8191 | 4 | 1456 | Anonymous | Trial division |
6 | 17 | 131071 | 6 | 1588 | Pietro Cataldi | Trial division |
7 | 19 | 524287 | 6 | 1588 | Pietro Cataldi | Trial division |
8 | 31 | 2147483647 | 10 | 1772 | Leonhard Euler | Enhanced trial division |
9 | 61 | 2305843009213693951 | 19 | 1883 November | I. M. Pervushin | Lucas sequences |
10 | 89 | 618970019…449562111 | 27 | 1911 June | R. E. Powers | Lucas sequences |
11 | 107 | 162259276…010288127 | 33 | 1914 June 1 | R. E. Powers | Lucas sequences |
12 | 127 | 170141183…884105727 | 39 | 1876 January 10 | Édouard Lucas | Lucas sequences |
13 | 521 | 686479766…115057151 | 157 | 1952 January 30 | Raphael M. Robinson | LLT / SWAC |
14 | 607 | 531137992…031728127 | 183 | 1952 January 30 | Raphael M. Robinson | LLT / SWAC |
15 | 1,279 | 104079321…168729087 | 386 | 1952 June 25 | Raphael M. Robinson | LLT / SWAC |
16 | 2,203 | 147597991…697771007 | 664 | 1952 October 7 | Raphael M. Robinson | LLT / SWAC |
17 | 2,281 | 446087557…132836351 | 687 | 1952 October 9 | Raphael M. Robinson | LLT / SWAC |
18 | 3,217 | 259117086…909315071 | 969 | 1957 September 8 | Hans Riesel | LLT / BESK |
19 | 4,253 | 190797007…350484991 | 1,281 | 1961 November 3 | Alexander Hurwitz | LLT / IBM 7090 |
20 | 4,423 | 285542542…608580607 | 1,332 | 1961 November 3 | Alexander Hurwitz | LLT / IBM 7090 |
21 | 9,689 | 478220278…225754111 | 2,917 | 1963 May 11 | Donald B. Gillies | LLT / ILLIAC II |
22 | 9,941 | 346088282…789463551 | 2,993 | 1963 May 16 | Donald B. Gillies | LLT / ILLIAC II |
23 | 11,213 | 281411201…696392191 | 3,376 | 1963 June 2 | Donald B. Gillies | LLT / ILLIAC II |
24 | 19,937 | 431542479…968041471 | 6,002 | 1971 March 4 | Bryant Tuckerman | LLT / IBM 360/91 |
25 | 21,701 | 448679166…511882751 | 6,533 | 1978 October 30 | Landon Curt Noll & Laura Nickel | LLT / CDC Cyber 174 |
26 | 23,209 | 402874115…779264511 | 6,987 | 1979 February 9 | Landon Curt Noll | LLT / CDC Cyber 174 |
27 | 44,497 | 854509824…011228671 | 13,395 | 1979 April 8 | Harry Lewis Nelson & David Slowinski | LLT / Cray 1 |
28 | 86,243 | 536927995…433438207 | 25,962 | 1982 September 25 | David Slowinski | LLT / Cray 1 |
29 | 110,503 | 521928313…465515007 | 33,265 | 1988 January 29 | Walter Colquitt & Luke Welsh | LLT / NEC SX-2 |
30 | 132,049 | 512740276…730061311 | 39,751 | 1983 September 19 | David Slowinski | LLT / Cray X-MP |
31 | 216,091 | 746093103…815528447 | 65,050 | 1985 September 1 | David Slowinski | LLT / Cray X-MP/24 |
32 | 756,839 | 174135906…544677887 | 227,832 | 1992 February 17 | David Slowinski & Paul Gage | LLT / Maple on Harwell Lab Cray-2 |
33 | 859,433 | 129498125…500142591 | 258,716 | 1994 January 4 | David Slowinski & Paul Gage | LLT / Cray C90 |
34 | 1,257,787 | 412245773…089366527 | 378,632 | 1996 September 3 | David Slowinski & Paul Gage | LLT / Cray T94 |
35 | 1,398,269 | 814717564…451315711 | 420,921 | 1996 November 13 | GIMPS / Joel Armengaud | LLT / Prime95 on 90 MHz Pentium PC |
36 | 2,976,221 | 623340076…729201151 | 895,932 | 1997 August 24 | GIMPS / Gordon Spence | LLT / Prime95 on 100 MHz Pentium PC |
37 | 3,021,377 | 127411683…024694271 | 909,526 | 1998 January 27 | GIMPS / Roland Clarkson | LLT / Prime95 on 200 MHz Pentium PC |
38 | 6,972,593 | 437075744…924193791 | 2,098,960 | 1999 June 1 | GIMPS / Nayan Hajratwala | LLT / Prime95 on 350 MHz Pentium II IBM Aptiva |
39 | 13,466,917 | 924947738…256259071 | 4,053,946 | 2001 November 14 | GIMPS / Michael Cameron | LLT / Prime95 on 800 MHz Athlon T-Bird |
40 | 20,996,011 | 125976895…855682047 | 6,320,430 | 2003 November 17 | GIMPS / Michael Shafer | LLT / Prime95 on 2 GHz Dell Dimension |
41 | 24,036,583 | 299410429…733969407 | 7,235,733 | 2004 May 15 | GIMPS / Josh Findley | LLT / Prime95 on 2.4 GHz Pentium 4 PC |
42 | 25,964,951 | 122164630…577077247 | 7,816,230 | 2005 February 18 | GIMPS / Martin Nowak | LLT / Prime95 on 2.4 GHz Pentium 4 PC |
43 | 30,402,457 | 315416475…652943871 | 9,152,052 | 2005 December 15 | GIMPS / Curtis Cooper & Steven Boone | LLT / Prime95 on 2 GHz Pentium 4 PC |
44 | 32,582,657 | 124575026…053967871 | 9,808,358 | 2006 September 4 | GIMPS / Curtis Cooper & Steven Boone | LLT / Prime95 on 3 GHz Pentium 4 PC |
45 | 37,156,667 | 202254406…308220927 | 11,185,272 | 2008 September 6 | GIMPS / Hans-Michael Elvenich | LLT / Prime95 on 2.83 GHz Core 2 Duo PC |
46 | 42,643,801 | 169873516…562314751 | 12,837,064 | 2009 April 12 | GIMPS / Odd M. Strindmo | LLT / Prime95 on 3 GHz Core 2 PC |
47 | 43,112,609 | 316470269…697152511 | 12,978,189 | 2008 August 23 | GIMPS / Edson Smith | LLT / Prime95 on Dell Optiplex 745 |
^ *
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To help visualize the size of the 47th known Mersenne prime, it would require 3,461 pages to display the number in base 10 with 75 digits per line and 50 lines per page.
The largest known Mersenne prime (243,112,609 − 1) is also the largest known prime number, and was the first discovered prime number with more than 10 million base-10 digits.
In modern times, the largest known prime has almost always been a Mersenne prime.
Read more about this topic: Mersenne Prime
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