The Top Twenty--a Prime Page Collection

Largest Known Primes

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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.

(up) Definitions and Notes

At this site we maintain a list of the 5000 largest known primes (plus selected smller primes). It is easy to show that there are infinitely many primes (in fact there are approximately x/ln(x) primes less than x, see "How Many"). This means that each of the primes below are probably separated by many millions of other (curently unkown) primes.

(up) Record Primes of this Type

rankprime digitswhowhencomment
1257885161 - 1 17425170 G13 Feb 2013 Mersenne 48??
2243112609 - 1 12978189 G10 Aug 2008 Mersenne 47??
3242643801 - 1 12837064 G12 Jun 2009 Mersenne 46??
4237156667 - 1 11185272 G11 Sep 2008 Mersenne 45?
5232582657 - 1 9808358 G9 Sep 2006 Mersenne 44?
6230402457 - 1 9152052 G9 Dec 2005 Mersenne 43?
7225964951 - 1 7816230 G8 Feb 2005 Mersenne 42
8224036583 - 1 7235733 G7 May 2004 Mersenne 41
9220996011 - 1 6320430 G6 Nov 2003 Mersenne 40
10213466917 - 1 4053946 G5 Dec 2001 Mersenne 39
1119249 · 213018586 + 1 3918990 SB10 May 2007  
123 · 211484018 - 1 3457035 L3993 Nov 2014  
133 · 210829346 + 1 3259959 L3770 Jan 2014 Divides GF(10829343, 3), GF(10829345, 5)
14475856524288 + 1 2976633 L3230 Aug 2012 Generalized Fermat
15356926524288 + 1 2911151 L3209 Jul 2012 Generalized Fermat
16341112524288 + 1 2900832 L3184 Jun 2012 Generalized Fermat
1727653 · 29167433 + 1 2759677 SB8 Jun 2005  
1890527 · 29162167 + 1 2758093 L1460 Jun 2010  
1975898524288 + 1 2558647 p334 Nov 2011 Generalized Fermat
2028433 · 27830457 + 1 2357207 SB7 Dec 2004  

(up) Related Pages

(up) References

Ribenboim95
P. Ribenboim, The new book of prime number records, 3rd edition, Springer-Verlag, 1995.  New York, NY, pp. xxiv+541, ISBN 0-387-94457-5. MR 96k:11112 [An excellent resource for those with some college mathematics. Basically a Guinness Book of World Records for primes with much of the relevant mathematics. The extensive bibliography is seventy-five pages.]
Riesel94
H. Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics Vol, 126, Birkhäuser Boston, Boston, MA, 1994.  ISBN 0-8176-3743-5. MR 95h:11142 [An excellent reference for those who want to start to program some of these algorithms. Code is provided in Pascal. Previous edition was vol. 57, 1985.]
Chris K. Caldwell © 1996-2014 (all rights reserved)