GIMPS

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

The GIMPS project was founded by George Woltman, who also wrote the software Prime95 and MPrime for the project. Scott Kurowski wrote the PrimeNet Internet server that supports the research to demonstrate Entropia-distributed computing software, a company he founded in 1997. GIMPS is registered as Mersenne Research, Inc. Kurowski is Executive Vice President and board director of Mersenne Research Inc. 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 fifteen Mersenne primes as of January 2016^[update], thirteen of which were the largest known prime number at their respective times of discovery. The largest known prime as of January 2016^[ref] is 2^74,207,281 − 1 (or M_74,207,281 in short). This prime was discovered on September 17, 2015 by Curtis Cooper at the University of Central Missouri.

To perform its testing, the project relies primarily on Lucas–Lehmer primality test, an algorithm that is both specialized to testing Mersenne primes and particularly efficient on binary computer architectures. They also have a trial division phase, used to rapidly eliminate Mersenne numbers with small factors which make up a large proportion of candidates. Pollard's p - 1 algorithm is also used to search for larger factors.

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