Largest known prime number


The largest known prime number as of 2026 is, a number which has 41,024,320 digits when written in the decimal system. It was found on October 12, 2024, on a cloud-based virtual machine volunteered by Luke Durant, a 36-year-old researcher from San Jose, California, to the Mersenne Prime Search">Mersenne prime">Mersenne Prime Search.
A prime number is a natural number greater than 1 with no divisors other than 1 and itself. Euclid's theorem proves that for any given prime number, there will always be a higher one, and thus there are infinitely many; there is no largest prime.
Many of the largest known primes are Mersenne primes, numbers that are one less than a power of two, because they can utilize a specialized primality test that is faster than the general one., the seven largest known primes are Mersenne primes. The last eighteen record primes were Mersenne primes. The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2k − 1 is simply k ones.
Finding larger prime numbers is sometimes presented as a means to stronger encryption, but this is not the case. Primes with millions of digits are not useful for cryptography.

Current record

The record is currently held by with 41,024,320 digits, found by GIMPS on October 12, 2024. The first and last 120 digits of its value are:

Prizes

There are several prizes offered by the Electronic Frontier Foundation for record primes. A prime with one million digits was found in 1999, earning the discoverer a US$50,000 prize. In 2008, a ten-million-digit prime won a US$100,000 prize and a Cooperative Computing Award from the EFF. Time called this prime the 29th top invention of 2008.
Both of these primes were discovered through the Great Internet Mersenne Prime Search, which coordinates long-range search efforts among tens of thousands of computers and thousands of volunteers. The $50,000 prize went to the discoverer and the $100,000 prize went to GIMPS. GIMPS will split the US$150,000 prize for the first prime of over 100 million digits with the winning participant. A further US$250,000 prize is offered for the first prime with at least one billion digits.
GIMPS also offers a US$3,000 research discovery award for participants who discover a new Mersenne prime of less than 100 million digits.

History

The following table lists the progression of the largest known prime number in ascending order. Here is the Mersenne number with exponent p, where p is a prime number. The longest record-holder known was, which was the largest known prime for 184 years.
The primes up to and including are found without a computer, while the primes starting with 180×2+1 are found using computers.
GIMPS volunteers found the sixteen latest records, all of them Mersenne primes. They were found on ordinary personal computers until the most recent one, found by ex-Nvidia employee Luke Durant using a network of thousands of dedicated graphics processing units. Durant spent about one year and US$2 million on the hunt. This is the first time a Mersenne prime has been discovered using GPUs instead of central processing units.
NumberDigitsYear foundDiscoverer
M1761588Pietro Cataldi
M1961588Pietro Cataldi
M31101772Leonhard Euler
131867Fortuné Landry
M127391876Édouard Lucas
441951Aimé Ferrier, with a mechanical calculator. The largest record not set by computer.
180×2+1791951J. C. P. Miller & D. J. Wheeler using Cambridge's EDSAC computer
M5211571952Raphael M. Robinson
M6071831952Raphael M. Robinson
M12793861952Raphael M. Robinson
M22036641952Raphael M. Robinson
M22816871952Raphael M. Robinson
M32179691957Hans Riesel
M44231,3321961Alexander Hurwitz
M96892,9171963Donald B. Gillies
M99412,9931963Donald B. Gillies
M112133,3761963Donald B. Gillies
M199376,0021971Bryant Tuckerman
M217016,5331978Laura A. Nickel and Landon Curt Noll
M232096,9871979Landon Curt Noll
M4449713,3951979David Slowinski and Harry L. Nelson
M8624325,9621982David Slowinski
M13204939,7511983David Slowinski
M21609165,0501985David Slowinski
391581×2216193−165,0871989The "Amdahl Six": John Brown, Landon Curt Noll, B. K. Parady, Gene Ward Smith, Joel F. Smith, Sergio E. Zarantonello.
Largest non-Mersenne prime that was the largest known prime when it was discovered.
M756839227,8321992David Slowinski and Paul Gage
M859433258,7161994David Slowinski and Paul Gage
M1257787378,6321996David Slowinski and Paul Gage
M1398269420,9211996GIMPS, Joel Armengaud
M2976221895,9321997GIMPS, Gordon Spence
M3021377909,5261998GIMPS, Roland Clarkson
M69725932,098,9601999GIMPS, Nayan Hajratwala
M134669174,053,9462001GIMPS, Michael Cameron
M209960116,320,4302003GIMPS, Michael Shafer
M240365837,235,7332004GIMPS, Josh Findley
M259649517,816,2302005GIMPS, Martin Nowak
M304024579,152,0522005GIMPS, University of Central Missouri professors Curtis Cooper and Steven Boone
M325826579,808,3582006GIMPS, Curtis Cooper and Steven Boone
M4311260912,978,1892008GIMPS, Edson Smith
M5788516117,425,1702013GIMPS, Curtis Cooper
M7420728122,338,6182016GIMPS, Curtis Cooper
M7723291723,249,4252017GIMPS, Jonathan Pace
M8258993324,862,0482018GIMPS, Patrick Laroche
M13627984141,024,3202024GIMPS, Luke Durant

Twenty largest

A list of the 5,000 largest known primes is maintained by the PrimePages, of which the twenty largest are listed below.
RankNumberDiscoveredDigitsFormRef
12136279841 − 12024-10-1241,024,320Mersenne
2282589933 − 12018-12-0724,862,048Mersenne
3277232917 − 12017-12-2623,249,425Mersenne
4274207281 − 12016-01-0722,338,618Mersenne
5257885161 − 12013-01-2517,425,170Mersenne
625241902097152 + 12025-10-1213,426,224Generalized Fermat
7243112609 − 12008-08-2312,978,189Mersenne
8242643801 − 12009-06-0412,837,064Mersenne
9Φ32023-10-0211,981,518Generalized unique
10Φ32023-05-3111,887,192Generalized unique
11237156667 − 12008-09-0611,185,272Mersenne
12232582657 − 12006-09-049,808,358Mersenne
1310223 × 231172165 + 12016-10-319,383,761Proth
14230402457 − 12005-12-159,152,052Mersenne
154 × 511786358 + 12024-10-018,238,312Generalized Proth
16225964951 − 12005-02-187,816,230Mersenne
174052186 × 694052186 + 12025-04-177,451,366Generalized Cullen
1869 × 224612729 − 12024-08-137,409,102Riesel
19224036583 − 12004-05-157,235,733Mersenne
2053362841048576 + 12025-11-027,054,022Generalized Fermat