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, special 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 rather successful: it has already 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 M32,582,657 in short). This prime was discovered on September 4, 2006 on a 700 PC cluster operated by Steven Boone and Curtis Cooper at the Central Missouri State University. Refer to the article on Mersenne prime numbers for the complete list of GIMPS successes.

As of June 2006, GIMPS has a sustained throughput of over 20 TFLOPS, earning the GIMPS virtual computer a firm place among the most powerful supercomputers in the world.

Although the GIMPS software is open source, technically it is not free software, since it has a restriction that users must abide by the projects distribution terms[1] 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 Cooperative Computing Awards.

For open source alternatives, Glucas and Mlucas are both licensed under the GPL.

[edit] Primes found

All primes are in the form Mn, 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	M32582657	9808358
15 December 2005	M30402457	9152052
18 February 2005	M25964951	7816230
15 May 2004	M24036583	7235733
17 November 2003	M20996011	6320430
14 November 2001	M13466917	4053946
1 June 1999	M6972593	2098960
27 January 1998	M3021377	909526
24 August 1997	M2976221	895932
13 November 1996	M1398269	420921

To help visualize the size of M32582657, a standard word processor layout (12pt Times New Roman, 1" margins) would require 2,616 pages to display the number (considering a page contains 50 lines, each line containing 75 digits). In other words this is a number with approximately 9 million eight hundred and 10 thousand (9,810,000) digits. Another way of expressing this is comparing this number to one of the largest numbers that has any "real" meaning in science: 10⁸⁰, which is a number with 80 digits in it. 10⁸⁰ is a rough estimate of the number of atoms that form the entire visible universe. Compare this number, with its 80 digits, to M32582657, which has over 9.8 million digits.