Mersenne Prime - List of Known Mersenne Primes

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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