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. The 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 February 2014[update], eleven of which were the largest known prime number at their respective times of discovery. The largest known prime as of February 2014[ref] is 257,885,161 − 1 (or M57,885,161 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 less expensive trial division phase, [clarify], used to rapidly eliminate Mersenne numbers with small factors, which make up a large proportion of candidates. John Pollard's p − 1 algorithm is also used to search for larger factors.
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 M1,398,269 on November 13, 1996.
As of March 2013[update], GIMPS has a sustained throughput of approximately 137.023 TFLOP/sec. In November 2012 GIMPS maintained 95 Teraflops, theoretically earned the GIMPS virtual computer a place among the TOP500 most powerful known computer systems in the world. Theoretically, in November 2012, GIMPS held rank 330 of the TOP500, after rank 329, which was held than by a 'HP Cluster Platform 3000 BL460c G7' of Hewlett-Packard.
As of early-2010, this was approximately 50 teraflops. In mid-2008, this was approximately 30 teraflops. In mid-2006, 20 teraflops, and in early 2004, 14.
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.
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."
All Mersenne primes are in the form Mq, where q is the (prime) exponent. The prime number itself is 2q − 1, so the smallest prime number in this table is 21398269 − 1.
Mn 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||Core 2 Duo E6600 CPU (2.4 GHz)|
|M48 [*]||January 25, 2013||M57885161 [**]||17,425,170|
^ * As of February 23, 2014, 30,412,999 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 43nd (M30402457) and the 48th (M57,885,161) on this chart; the ranking is therefore provisional. Moreover, 45,807,607 is the smallest exponent below which all other exponents have been tested at least once, so some Mersenne numbers between the 47th (M43112609) and the 48th (M57,885,161) have yet to be tested.
^ ** The number M57885161 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.
- List of distributed computing projects
- Distributed computing
- Berkeley Open Infrastructure for Network Computing
- "Volunteer computing". BOINC. Retrieved 8 October 2012.
- "GIMPS Project Discovers Largest Known Prime Number, 257,885,161-1". Great Internet Mersenne Prime Search. Retrieved 2013-02-05.
- What are Mersenne primes? How are they useful? - GIMPS Home Page
- The Mersenne Newsletter, Issue #9. Retrieved 2011-10-02.
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- The Mersenne Newsletter, Issue #9. Retrieved 2009-08-25.
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- "GIMPS Milestones". Mersenne Research, Inc. Retrieved 2014-02-22.