Great Internet Mersenne Prime Search

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The Great Internet Mersenne Prime Search, or GIMPS, is a collaborative project of volunteers, who use Prime95 and MPrime, software that can be downloaded from the Internet for free, in order to search for Mersenne prime numbers. The project was founded and the prime testing software was written by George Woltman. Scott Kurowski wrote the PrimeNet Server that supports the research to demonstrate Entropia distributed computing software, a company he founded in 1997.

This project has been successful: it has found a total of ten Mersenne primes, each of which was the largest known prime at the time of discovery. The largest known prime as of September 2006 is 2^32,582,657 − 1 (or M_32,582,657 in short). This prime was discovered on September 4, 2006 on a 700 PC cluster operated by Steven Boone and Curtis Cooper at the University of Central Missouri. Refer to the article on Mersenne prime numbers for the complete list of GIMPS successes.

To perform its testing, the project relies primarily on the Lucas–Lehmer test for Mersenne numbers,^[1] 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. Pollard's p − 1 algorithm is also used to search for larger factors.

As of May 2008, GIMPS has a sustained throughput of approximately 29 TFLOPS, earning the GIMPS virtual computer a place among the most powerful supercomputers in the world.

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^[2] if the software is used to discover a prime number with at least 10,000,000 decimal digits and wins the $100,000 bounty offered by the EFF^[3].

For free software alternatives, Glucas^[4] and Mlucas^[5] are both licensed under the GPL.

1 Primes found
2 See also
3 References
4 External links

[edit] Primes found

All primes are in the form M_n, where n is the exponent. The prime number itself is 2ⁿ - 1, so the first prime number in this table is 2^32582657 - 1.

Discovery date	Prime	Digits
4 September 2006	M_32582657	9808358
15 December 2005	M_30402457	9152052
18 February 2005	M_25964951	7816230
15 May 2004	M_24036583	7235733
17 November 2003	M_20996011	6320430
14 November 2001	M_13466917	4053946
1 June 1999	M_6972593	2098960
27 January 1998	M_3021377	909526
24 August 1997	M_2976221	895932
13 November 1996	M_1398269	420921

The number M_32582657 has 9,808,358 digits. To help visualize the size of this number, a standard word processor layout (50 lines per page, 75 digits per line) would require 2,616 pages to display it.