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. The project was founded by George Woltman, who also wrote the software Prime95 and MPrime for the project. Scott Kurowski wrote the Internet PrimeNet 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 thirteen Mersenne primes as of 9 November 2011 (2011 -11-09), eleven of which were the largest known prime number at their respective times of discovery. The largest known prime as of November 2011 is 243,112,609 − 1 (or M_43,112,609 in short). This prime was discovered on 23 August 2008 by Edson Smith at the University of California, Los Angeles (UCLA)'s Mathematics Department. This prime allowed GIMPS to win the $100,000 prize from Electronic Frontier Foundation for discovering a prime with more than 10 million decimal digits. Refer to the article on Mersenne prime numbers for the complete list of GIMPS successes.

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