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 2 − 1 (or M 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 September 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. History. The project began in early January 1996, with a program  that ran on i386 computers. The name for the project was coined by Luke Welsh, one of its earlier searchers and the co-discoverer of the 29th Mersenne prime. Within a few months, several dozen people had joined, and over a thousand by the end of the first year. Joel Armengaud, a participant, discovered the primality of M on November 13, 1996. Status. , GIMPS has a sustained average aggregate throughput of approximately 1.21 PetaFLOPS (or PFLOPS). In November 2012, GIMPS maintained 95 TFLOPS, theoretically earning the GIMPS virtual computer a rank of 330 among the TOP500 most powerful known computer  systems in the world. The preceding place was then held by an 'HP Cluster Platform 3000 BL460c G7' of Hewlett-Packard. As of July 2021 TOP500 results, the current GIMPS numbers would no longer make the list. Previously, this was approximately 50 TFLOPS in early 2010, 30 TFLOPS in mid-2008, 20 TFLOPS in mid-2006, and 14 TFLOPS in early 2004. Software license. Although the GIMPS software's source code is publicly available, technically it is not free software, since it has a restriction that users must abide by the project's distribution terms. Specifically, if the software is used to  discover a prime number with at least 100,000,000 decimal digits, the user will only win $50,000 of the $150,000 prize offered by the Electronic Frontier Foundation. Third-party programs for testing Mersenne numbers, such as Mlucas and Glucas (for non-x86 systems), do not have this restriction. GIMPS also "reserves the right to change this EULA without notice and with reasonable retroactive effect"."" Primes found. All Mersenne primes are of the form , where "p" is a prime number itself. The smallest Mersenne prime in this table is The first column is the rank of the Mersenne prime in  the (ordered) sequence of all Mersenne primes; GIMPS has found all known Mersenne primes beginning with the 35th. Whenever a possible prime is reported to the server, it is verified first (by one or more independent tests on different machines) before being announced. The importance of this was illustrated in 2003, when a false positive was reported to the server as being a Mersenne prime but verification failed. The official "discovery date" of a prime is the date that a human first noticed the result for the prime, which may differ from the date that the result was first reported  to the server. For example, M was reported to the server on September 17, 2015, but the report was overlooked until January 7, 2016.