List of known Mersenne primes
From Mersennewiki
# | n | Digits in M_{n} | Digits in P_{n} | Date of discovery | Discoverer |
---|---|---|---|---|---|
1 | 2 | 1 | 1 | c. 430 BCE | Ancient Greek mathematicians |
2 | 3 | 1 | 2 | c. 430 BCE | Ancient Greek mathematicians |
3 | 5 | 2 | 3 | c. 300 BCE | Ancient Greek mathematicians |
4 | 7 | 3 | 4 | c. 300 BCE | Ancient Greek mathematicians |
5 | 13 | 4 | 8 | 1456 | anonymous |
6 | 17 | 6 | 10 | 1588 | Cataldi |
7 | 19 | 6 | 12 | 1588 | Cataldi |
8 | 31 | 10 | 19 | 1772 | Euler |
9 | 61 | 19 | 37 | 1883 | Pervushin |
10 | 89 | 27 | 54 | 1911 | Powers |
11 | 107 | 33 | 65 | 1914 | Powers |
12 | 127 | 39 | 77 | 1876 | Lucas |
13 | 521 | 157 | 314 | January 30 1952 | Robinson |
14 | 607 | 183 | 366 | January 30 1952 | Robinson |
15 | 1,279 | 386 | 770 | June 25 1952 | Robinson |
16 | 2,203 | 664 | 1,327 | October 7 1952 | Robinson |
17 | 2,281 | 687 | 1,373 | October 9 1952 | Robinson |
18 | 3,217 | 969 | 1,937 | September 8 1957 | Riesel |
19 | 4,253 | 1,281 | 2,561 | November 3 1961 | Hurwitz |
20 | 4,423 | 1,332 | 2,663 | November 3 1961 | Hurwitz |
21 | 9,689 | 2,917 | 5,834 | May 11 1963 | Gillies |
22 | 9,941 | 2,993 | 5,985 | May 16 1963 | Gillies |
23 | 11,213 | 3,376 | 6,751 | June 2 1963 | Gillies |
24 | 19,937 | 6,002 | 12,003 | March 4 1971 | Tuckerman |
25 | 21,701 | 6,533 | 13,066 | October 30 1978 | Noll & Nickel |
26 | 23,209 | 6,987 | 13,973 | February 9 1979 | Noll |
27 | 44,497 | 13,395 | 26,790 | April 8 1979 | Nelson & Slowinski |
28 | 86,243 | 25,962 | 51,924 | September 25 1982 | Slowinski |
29 | 110,503 | 33,265 | 66,530 | January 28 1988 | Colquitt & Welsh |
30 | 132,049 | 39,751 | 79,502 | September 20 1983 | Slowinski |
31 | 216,091 | 65,050 | 130,100 | September 6 1985 | Slowinski |
32 | 756,839 | 227,832 | 455,663 | February 19 1992 | Slowinski, Gage & Harwell |
33 | 859,433 | 258,716 | 517,430 | January 10 1994 | Slowinski & Gage |
34 | 1,257,787 | 378,632 | 757,263 | September 3 1996 | Slowinski & Gage |
35 | 1,398,269 | 420,921 | 841,842 | November 13 1996 | Armengaud, Woltman et. al. GIMPS |
36 | 2,976,221 | 895,932 | 1,791,864 | August 24 1997 | Spence, Woltman et. al. GIMPS |
37 | 3,021,377 | 909,526 | 1,819,050 | January 27 1998 | Clarkson, Woltman, Kurowski et. al. GIMPS & PrimeNet |
38 | 6,972,593 | 2,098,960 | 4,197,919 | June 1 1999 | Hajratwala, Woltman, Kurowski et. al. GIMPS & PrimeNet |
39 | 13,466,917 | 4,053,946 | 8,107,892 | November 14 2001 | Cameron, Woltman, Kurowski et. al. GIMPS & PrimeNet |
40 | 20,996,011 | 6,320,430 | 12,640,858 | November 17 2003 | Shafer, Woltman, Kurowski et. al. GIMPS & PrimeNet |
41 | 24,036,583 | 7,235,733 | 14,471,465 | May 15 2004 | Findley, Woltman, Kurowski et. al. GIMPS & PrimeNet |
42 | 25,964,951 | 7,816,230 | 15,632,458 | February 18 2005 | Nowak, Woltman, Kurowski et. al. GIMPS & PrimeNet |
43 | 30,402,457 | 9,152,052 | 18,304,103 | December 15 2005 | Cooper, Boone, Woltman, Kurowski et. al. GIMPS & PrimeNet |
44 | 32,582,657 | 9,808,358 | 19,616,714 | September 4 2006 | Cooper, Boone, Woltman, Kurowski et. al. GIMPS & PrimeNet |
45^{*} | 37,156,667 | 11,185,272 | 22,370,543 | September 6 2008 | Elvenich, Woltman, Kurowski, et al. GIMPS & PrimeNet |
46^{*} | 42,643,801 | 12,837,064 | 25,674,127 | April 12 2009 | Strindmo, Woltman, Kurowski, et al. GIMPS & PrimeNet |
47^{*} | 43,112,609 | 12,978,189 | 25,957,378 | August 23 2008 | Smith, Woltman, Kurowski, et al. GIMPS & PrimeNet |
48^{*} | 57,885,161 | 17,425,170 | 34,850,340 | January 25 2013 | Cooper, Woltman, Kurowski et. al. GIMPS & PrimeNet |
49^{*} | 74,207,281 | 22,338,618 | 44,677,236 | January 7 2016 | Cooper, Woltman, Kurowski, Blosser et. al. GIMPS & PrimeNet |
^{*}It is not known whether any undiscovered Mersenne primes exist between the 45th () and the 49th () on this chart; the ranking is therefore provisional.
[edit]
See also
[edit]
External links
- Great Internet Mersenne Prime Search (GIMPS) - home page of mersenne.org
- prime Mersenne Numbers - History, Theorems and Lists Explanation
- GIMPS Mersenne Prime - status page gives various statistics on search progress, some parts are updated automatically, others typically updated every week, including progress towards proving the ordering of primes 41-47ff
- Mersenne numbers - Wolfram Research/Mathematica
- prime Mersenne numbers - Wolfram Research/Mathematica
- M_{q} = (8x)^2 - (3qy)^2 Mersenne Proof (pdf)
- M_{q} = x^2 + d.y^2 Math Thesis (pdf)
- Mersenne Prime Bibliography with Hyperlinks to original publications
- dpa - reportage about prime mersenne number - detection in detail (German)