Largest Known Primes

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.

(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
1282589933 - 1 24862048 G16 Dec 2018 Mersenne 51??
2277232917 - 1 23249425 G15 Jan 2018 Mersenne 50??
3274207281 - 1 22338618 G14 Jan 2016 Mersenne 49??
4257885161 - 1 17425170 G13 Feb 2013 Mersenne 48
5243112609 - 1 12978189 G10 Aug 2008 Mersenne 47
6242643801 - 1 12837064 G12 Jun 2009 Mersenne 46
7237156667 - 1 11185272 G11 Sep 2008 Mersenne 45
8232582657 - 1 9808358 G9 Sep 2006 Mersenne 44
910223 · 231172165 + 1 9383761 SB12 Nov 2016  
10230402457 - 1 9152052 G9 Dec 2005 Mersenne 43
11225964951 - 1 7816230 G8 Feb 2005 Mersenne 42
12224036583 - 1 7235733 G7 May 2004 Mersenne 41
1319517341048576 + 1 6595985 L5583 Aug 2022 Generalized Fermat
14202705 · 221320516 + 1 6418121 L5181 Dec 2021  
15220996011 - 1 6320430 G6 Nov 2003 Mersenne 40
1610590941048576 + 1 6317602 L4720 Nov 2018 Generalized Fermat
179194441048576 + 1 6253210 L4286 Sep 2017 Generalized Fermat
187 · 220267500 + 1 6101127 L4965 Jul 2022  
19168451 · 219375200 + 1 5832522 L4676 Sep 2017  
2069 · 219374980 - 1 5832452 L4965 Jul 2022  

(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.]
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