Great Internet Mersenne Prime Search

File:GIMPS logo.png

GIMPS logo

Not to be confused with GIMP.

The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers.

The GIMPS project was founded by George Woltman, who also wrote the software Prime95 and MPrime for the project. Scott Kurowski wrote the PrimeNet Internet server that supports the research to demonstrate Entropia-distributed computing software, a company he founded in 1997. GIMPS is registered as Mersenne Research, Inc. Kurowski is Executive Vice President and board director of Mersenne Research Inc. 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 fourteen Mersenne Primes as of April 2014, twelve of which were the largest known prime number at their respective times of discovery. The largest known prime as of April 2014 is 2^57,885,161 − 1 (or M_57,885,161 in short). This prime was discovered on January 25, 2013 by Curtis Cooper at the University of Central Missouri.

To perform its testing, the project relies primarily on Lucas–Lehmer primality test, an algorithm that is both specialized to testing Mersenne primes and particularly efficient on binary computer architectures. They also have a trial division phase, 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.

History

The project began in early January 1996, with a program that ran on i386 computers. The name for the project was coined by Luther Welsh, one of its earlier searchers and the 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_1,398,269 on November 13, 1996.

Status

As of March 2013, GIMPS has a sustained aggregate throughput of approximately 137.023 TFLOP/s. In November 2012, GIMPS maintained 95 TFLOP/s, theoretically earning the GIMPS virtual computer a place among the TOP500 most powerful known computer systems in the world. Also theoretically, in November 2012, the GIMPS held a rank of 330 in the TOP500. The preceding place was then held by an 'HP Cluster Platform 3000 BL460c G7' of Hewlett-Packard. As of November 2014 TOP500 results, these old GIMPS numbers would no longer make the list.

Previously, this was approximately 50 TFLOP/s in early 2010, 30 TFLOP/s in mid-2008, 20 TFLOP/s in mid-2006, and 14 TFLOP/s 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 if the software is used to discover a prime number with at least 100 million decimal digits and wins the $150,000 USD bounty offered by the Electronic Frontier Foundation, and a bounty of $250,000 USD for a prime number with at least 1 billion decimal digits.

Third-party programs for testing Mersenne numbers, such as Mlucas and Glucas (for non-x86 systems), do not have this restriction.

Also, GIMPS "reserves the right to change this EULA without notice and with reasonable retroactive effect."

Primes found

All Mersenne primes are in the form M_q, where q is the (prime) exponent. The prime number itself is 2^q − 1, so the smallest prime number in this table is 2^1398269 − 1.

M_n is the rank of the Mersenne prime based on its exponent.

Name Mn	Discovery date	Prime Mq	Digits count	Processor
M35	November 13, 1996	M1398269	420,921	Pentium (90 MHz)
M36	August 24, 1997	M2976221	895,932	Pentium (100 MHz)
M37	January 27, 1998	M3021377	909,526	Pentium (200 MHz)
M38	June 1, 1999	M6972593	2,098,960	Pentium (350 MHz)
M39	November 14, 2001	M13466917	4,053,946	AMD T-Bird (800 MHz)
M40	November 17, 2003	M20996011	6,320,430	Pentium (2 GHz)
M41	May 15, 2004	M24036583	7,235,733	Pentium 4 (2.4 GHz)
M42	February 18, 2005	M25964951	7,816,230	Pentium 4 (2.4 GHz)
M43	December 15, 2005	M30402457	9,152,052	Pentium 4 (2 GHz overclocked to 3 GHz)
M44	September 4, 2006	M32582657	9,808,358	Pentium 4 (3 GHz)
M45	September 6, 2008	M37156667	11,185,272
M46	April 12, 2009	M42643801	12,837,064	Intel Core 2 Duo (3 GHz)
M47	August 23, 2008	M43112609	12,978,189	Intel Core 2 Duo E6600 CPU (2.4 GHz)
M48	January 25, 2013	M57885161	17,425,170	Intel Core2 Duo E8400 @ 3.00GHz

^{^ *} As of January 13, 2016, 34,954,163 is the smallest exponent below which all other exponents have been checked twice, so it is not verified whether any undiscovered Mersenne primes exist between the 44th (M_32582657) and the 48th (M_57885161) on this chart; the ranking is therefore provisional. Furthermore, 60,356,927 is the smallest exponent below which all other exponents have been tested at least once, so all Mersenne numbers below the 48th (M_57885161) have been tested.

^{^ **} The number M_57885161 has 17,425,170 decimal digits. To help visualize the size of this number, a standard word processor layout (50 lines per page, 75 digits per line) would require 4,647 pages to display it. If one were to print it out using standard printer paper, single-sided, it would require approximately 10 reams of paper.

Whenever a possible prime is reported to the server, it is verified first before it is announced. The importance of this was illustrated in 2003, when a false positive was reported to possibly be the 40th Mersenne prime but verification failed.

See also

• List of distributed computing projects
• Distributed computing
• PrimeGrid
• Berkeley Open Infrastructure for Network Computing

External links

• GIMPS Home Page
• PrimeNet server
• Mersenne Wiki
• GIMPS Forum