GIMPS

Great Internet Mersenne Prime Search (GIMPS) is a distributed computing project aimed at finding Mersenne primes, primes of the form 2^p-1 with p prime. Started in 1996 by George Woltman, it relies on volunteers who donate computing power to test large exponents using specialized software such as Prime95. The primality tests used are based on the Lucas-Lehmer test, the standard method for testing Mersenne numbers.

Operation and workflow: Participants run the test on their personal computers or servers. The project assigns candidate p values to test; when a candidate appears promising, the Lucas-Lehmer test is performed to determine primality. Because hardware can yield incorrect results, every claimed prime is independently verified by other volunteers on different machines or with different software before it is officially recorded.

Impact and milestones: GIMPS has yielded many of the known Mersenne primes and has contributed to setting records for prime size. In 2018, GIMPS announced the discovery of 2^82,589,933-1, a Mersenne prime with about 24.8 million digits, illustrating the scale of computations involved.

Current status: The project continues to operate as a long-running public experiment in distributed computing, drawing participants worldwide who run Prime95 in the background to contribute to mathematics and numerical analysis.