Great Internet Mersenne Prime Search
The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers.

GIMPS was founded in 1996 by George Woltman, who also wrote the Prime95 client and its Linux port MPrime. Scott Kurowski wrote the back end PrimeNet server to demonstrate distributed computing software by Entropia, a company he founded in 1997. GIMPS is registered as Mersenne Research, Inc. with Kurowski as Executive Vice President and board director. GIMPS is said to be one of the first large scale distributed computing projects over the Internet for research purposes.

, the project has found a total of seventeen Mersenne primes, fifteen of which were the largest known prime number at their respective times of discovery. The largest known prime is 282,589,933 − 1 (or M82,589,933 for short) and was discovered on December 7, 2018, by Patrick Laroche. On December 4, 2020, the project passed a major milestone after all exponents below 100 million were checked at least once.

The project relies primarily on the Lucas–Lehmer primality test as it is an algorithm that is both specialized for testing Mersenne primes and particularly efficient on binary computer architectures. There is also a trial division phase, used to rapidly eliminate many Mersenne numbers with small factors. Pollard's "p" − 1 algorithm is also used to search for smooth factors. In 2017, GIMPS adopted the Fermat primality test as an alternative option for primality testing. In 2020, GIMPS has started using PRP proofs, which together with the very reliable error-check, devised by Robert Gerbicz, provide a complete confidence in the correctness of the test result, and thus eliminating the need for double checks.
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Great Internet Mersenne Prime Search
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