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 volunteer 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 volunteer 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. From its inception until 2018, the project relied 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. Before applying it to a given Mersenne number, there was 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 2018, GIMPS adopted the Fermat primality test as an alternative option for primality testing, while keeping the Lucas-Lehmer test as a double-check for Mersenne numbers detected as probable primes by the Fermat test. (While the Lucas-Lehmer test is deterministic and the Fermat test is only probabilistic, the probability of the Fermat test finding a Fermat pseudoprime that is not prime is vastly lower than the error rate of the Lucas-Lehmer test due to computer hardware errors.) In September 2020, GIMPS began to support primality proofs based on verifiable delay functions.

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Supercomputer

A supercomputer is a computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). Since 2017, there have existed supercomputers which can perform over 1017 FLOPS (a hundred quadrillion FLOPS, 100 petaFLOPS or 100 PFLOPS). For comparison, a desktop computer has performance in the range of hundreds of gigaFLOPS (1011) to tens of teraFLOPS (1013).

FLOPS

In computing, floating point operations per second (FLOPS, flops or flop/s) is a measure of computer performance, useful in fields of scientific computations that require floating-point calculations. For such cases, it is a more accurate measure than measuring instructions per second. Floating-point arithmetic is needed for very large or very small real numbers, or computations that require a large dynamic range. Floating-point representation is similar to scientific notation, except everything is carried out in base two, rather than base ten.

Great Internet Mersenne Prime Search

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