The prime numbers among the Mersenne numbers are called Mersenne primes.
Mersenne primes are rare: so far (December 2018) only 51 of them have been found.
NR. | P | NUMBER OF DIGITS FROM M(P) | YEAR | EXPLORER |
---|---|---|---|---|
1 | 2 | 1 | – | – |
2 | 3 | 1 | – | – |
3 | 5 | 2 | – | – |
4 | 7 | 3 | – | – |
5 | 13 | 4 | 1456 | – |
6 | 17 | 6 | 1555 | Johann Scheubel |
7 | 19 | 6 | 1555 | Johann Scheubel |
8 | 31 | 10 | 1772 | Leonhard Euler |
9 | 61 | 19 | 1883 | Iwan Perwuschin |
10 | 89 | 27 | 1911 | Ralph E. Powers |
11 | 107 | 33 | 1914 | Powers |
12 | 127 | 39 | 1876 | Édouard Lucas |
13 | 521 | 157 | 1952 | Raphael Robinson |
14 | 607 | 183 | 1952 | Raphael Robinson |
15 | 1279 | 386 | 1952 | Raphael Robinson |
16 | 2203 | 664 | 1952 | Raphael Robinson |
17 | 2281 | 687 | 1952 | Raphael Robinson |
18 | 3217 | 969 | 1957 | Hans Riesel |
19 | 4253 | 1281 | 1961 | Alexander Hurwitz |
20 | 4423 | 1332 | 1961 | Alexander Hurwitz |
21 | 9689 | 2917 | 1963 | Donald B. Gillies |
22 | 9941 | 2993 | 1963 | Donald B. Gillies |
23 | 11.213 | 3376 | 1963 | Donald B. Gillies |
24 | 19.937 | 6002 | 1971 | Bryant Tuckerman |
25 | 21.701 | 6533 | 1978 | Landon Curt Noll, Laura Nickel |
26 | 23.209 | 6987 | 1979 | Landon CurtNoll |
27 | 44.497 | 13.395 | 1979 | David Slowinski, Harry L. Nelson |
28 | 86.243 | 25.962 | 1982 | David Slowinski |
29 | 110.503 | 33.265 | 1988 | Walter Colquitt, Luther Welsh Jr. |
30 | 132.049 | 39.751 | 1983 | David Slowinski |
31 | 216.091 | 65.050 | 1985 | David Slowinski |
32 | 756.839 | 227.832 | 1992 | David Slowinski, Paul Gage |
33 | 859.433 | 258.716 | 1994 | David Slowinski, Paul Gage |
34 | 1.257.787 | 378.632 | 1996 | David Slowinski, Paul Gage |
35 | 1.398.269 | 420.921 | 1996 | GIMPS/Joel Armengaud |
36 | 2.976.221 | 895.932 | 1997 | GIMPS/Gordon Spence |
37 | 3.021.377 | 909.526 | 1998 | GIMPS/Roland Clarkson |
38 | 6.972.593 | 2.098.960 | 1999 | GIMPS/Nayan Hajratwala |
39 | 13.466.917 | 4.053.946 | 2001 | GIMPS/Michael Cameron |
40 | 20.996.011 | 6.320.430 | 2003 | GIMPS/Michael Shafer |
41 | 24.036.583 | 7.235.733 | 2004 | GIMPS/Josh Findley |
42 | 25.964.951 | 7.816.230 | 2005 | GIMPS/Martin Nowak |
43 | 30.402.457 | 9.152.052 | 2005 | GIMPS/Curtis Cooper, Steven Boone |
44 | 32.582.657 | 9.808.358 | 2006 | GIMPS/Curtis Cooper, Steven Boone |
45 | 37.156.667 | 11.185.272 | 2008 | GIMPS/Hans-Michael Elvenich |
46 | 42.643.801 | 12.837.064 | 2009 | GIMPS/Odd M. Strindmo |
47 | 43.112.609 | 12.978.189 | 2008 | GIMPS/Edson Smith |
48? | 57.885.161 | 17.425.170 | 2013 | GIMPS/Curtis Cooper |
49? | 74.207.281 | 22.338.618 | 2016 | GIMPS/Curtis Cooper |
50? | 77.232.917 | 23.249.425 | 2017 | GIMPS/Jonathan Pace |
51? | 82.589.933 | 24.862.048 | 2018 | GIMPS/Patrick Laroche |
As of March 13, 2020, however, it cannot be ruled out that there are other, as yet undiscovered Mersenne primes between n = 43,112,609 and n = 82,589,933; therefore, the numbering from No. 48 onward is still uncertain (and marked with a “?”).