Mersenne

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The Prime Pages

GIMPS has discovered a new largest known prime number: 2^82589933-1 (24,862,048 digits)

The Prime Pages keeps a list of the 5000 largest known primes, plus a few each of certain selected archivable forms and classes. These forms are defined in this collection's home page. This page is about one of those forms. Comments and suggestions requested.

Definitions and Notes

Mersenne primes are primes of the form 2^p-1. The first few are 3, 7, 31, 127, 8191, 131071 and 524287 (with exponents p=2, 3, 5, 7, 13, 17, and 19). The Mersennes are also prime for p=31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377 and 6972593. See our page on Mersenne numbers for more information, history and theorems. Luke's web page on Marin Mersenne is also and excellent starting place.

Record Primes of this Type

rank prime digits who when comment

1 2^82589933 - 1 24862048 G16 Dec 2018 Mersenne 51??
2 2^77232917 - 1 23249425 G15 Jan 2018 Mersenne 50??
3 2^74207281 - 1 22338618 G14 Jan 2016 Mersenne 49??
4 2^57885161 - 1 17425170 G13 Feb 2013 Mersenne 48?
5 2^43112609 - 1 12978189 G10 Aug 2008 Mersenne 47
6 2^42643801 - 1 12837064 G12 Jun 2009 Mersenne 46
7 2^37156667 - 1 11185272 G11 Sep 2008 Mersenne 45
8 2^32582657 - 1 9808358 G9 Sep 2006 Mersenne 44
9 2^30402457 - 1 9152052 G9 Dec 2005 Mersenne 43
10 2^25964951 - 1 7816230 G8 Feb 2005 Mersenne 42
11 2^24036583 - 1 7235733 G7 May 2004 Mersenne 41
12 2^20996011 - 1 6320430 G6 Nov 2003 Mersenne 40
13 2^13466917 - 1 4053946 G5 Dec 2001 Mersenne 39
14 2^6972593 - 1 2098960 G4 Jun 1999 Mersenne 38
15 2^3021377 - 1 909526 G3 Jan 1998 Mersenne 37
16 2^2976221 - 1 895932 G2 Aug 1997 Mersenne 36
17 2^1398269 - 1 420921 G1 Nov 1996 Mersenne 35
18 2^1257787 - 1 378632 SG Sep 1996 Mersenne 34
19 2⁸⁵⁹⁴³³ - 1 258716 SG Jan 1994 Mersenne 33
20 2⁷⁵⁶⁸³⁹ - 1 227832 SG Feb 1992 Mersenne 32

References

BSW89
P. T. Bateman, J. L. Selfridge and Wagstaff, Jr., S. S., "The new Mersenne conjecture," Amer. Math. Monthly, 96 (1989) 125-128. MR 90c:11009
CW91
W. N. Colquitt and Welsh, Jr., L., "A new Mersenne prime," Math. Comp., 56 (1991) 867--870. MR 91h:11006 [The discovery of the 29th Mersenne prime.]
Gillies64
D. B. Gillies, "Three new Mersenne primes and a statistical theory," Math. Comp., 18 (1964) 93--95. Corrigendum in Math. Comp. 31 (1977), 1051. MR 28:2990 [The primes are 2¹¹²¹³-1, 2⁹⁹⁴¹-1 and 2⁹⁶⁸⁹-1.]
NN80
C. Noll and L. Nickel, "The 25th and 26th Mersenne primes," Math. Comp., 35 (1980) 1387-1390. MR 81k:10010
Peterson92
I. Peterson, "Striking paydirt in prime-number terrain," Science News, 141:14 (1992) 213. [Discusses the discovery of the Mersenne prime 2⁷⁵⁶⁸³⁹ -1]
Robinson54
R. M. Robinson, "Mersenne and Fermat numbers," Proc. Amer. Math. Soc., 5 (1954) 842-846. [Announces the discovery of the 13th through 17th Mersenne primes--the first Mersenne primes found by electronic computer.]
Slowinski79
D. Slowinski, "Searching for the 27th Mersenne prime," J. Recreational Math., 11 (1978-9) 258--261.
Tuckerman71
B. Tuckerman, "The 24th Mersenne prime," Proc. Nat. Acad. Sci. U. S. A., 68 (1971) 2319-2320. MR 45:166