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.

Definitions and Notes

At this site we maintain a list of the 5000 largest known primes (plus selected smaller 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 (currently unknown) primes.

Record Primes of this Type

rank prime digits who when comment 1 2136279841 - 1 41024320 MP1 Oct 2024 Mersenne 52?? 2 282589933 - 1 24862048 G16 Dec 2018 Mersenne 51? 3 277232917 - 1 23249425 G15 Jan 2018 Mersenne 50? 4 274207281 - 1 22338618 G14 Jan 2016 Mersenne 49? 5 257885161 - 1 17425170 G13 Feb 2013 Mersenne 48 6 243112609 - 1 12978189 G10 Aug 2008 Mersenne 47 7 242643801 - 1 12837064 G12 Jun 2009 Mersenne 46 8 5166932097152 - 5166931048576 + 1 11981518 L4561 Oct 2023 Generalized unique 9 4658592097152 - 4658591048576 + 1 11887192 L4561 May 2023 Generalized unique 10 237156667 - 1 11185272 G11 Sep 2008 Mersenne 45 11 232582657 - 1 9808358 G9 Sep 2006 Mersenne 44 12 10223 · 231172165 + 1 9383761 SB12 Nov 2016   13 230402457 - 1 9152052 G9 Dec 2005 Mersenne 43 14 4 · 511786358 + 1 8238312 A2 Oct 2024 Generalized Fermat 15 225964951 - 1 7816230 G8 Feb 2005 Mersenne 42 16 4052186 · 694052186 + 1 7451366 A61 Apr 2025 Generalized Cullen 17 69 · 224612729 - 1 7409172 A2 Aug 2024   18 224036583 - 1 7235733 G7 May 2004 Mersenne 41 19 107347 · 223427517 - 1 7052391 A2 Aug 2024   20 38432361048576 + 1 6904556 L6094 Dec 2024 Generalized Fermat

Related Pages

• The Largest Known Primes
• Largest Known Prime by Year
• The chronology of prime number records

References

Ribenboim95

P. Ribenboim, The new book of prime number records, 3rd edition, Springer-Verlag, New York, NY, 1995.  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.]