البحث الكبير على الإنترنت عن أعداد مرسن الأولية

البحث الكبير على الإنترنت عن أعداد مرسن الأولية Great Internet Mersenne Prime Search (GIMPS)، هومشروع تعاوني لمتطوعين باستخدام برنامج مجاني متاح للبحث عن أعداد مرسن الأولية. أسس المشروع جورج وولتمان، الذي صمم أيضاً برنامج پرايم95 وإم‌پرايم]] للمشروع. صمم سكوت كوروسكي خادم إنترنت برايم‌نت الذي يعدم أبحاث برنامج إنتروپيا للحوسبة الموزعة، شركة تأسست عام 1997. المشروع مسجل باسم مرسن رسرش، كوروسكي هونائب الرئيس التطبيقي ورئيس مجلس ادارة مرسن رسرش 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 اعتبارا من 5 فبراير 2013 (2013-02-05)^[تحديث], eleven of which were the largest known prime number at their respective times of discovery. The largest known prime اعتبارا من يناير 2013^[ref] 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 Édouard Lucas and Derrick Henry Lehmer's 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, taking hours instead of weeks, 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.

التاريخ

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.

الحالة

اعتبارا من نوفمبر 2012^[تحديث], GIMPS has a sustained throughput of approximately 95 teraflops, theoretically earning the GIMPS virtual computer a place among the TOP500 most powerful known computer systems in the world. Theoretically, GIMPS holds rank 330 of the TOP500 (November 2012), after rank 329, which is held 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.

ترخيص البرنامج

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.

الأعداد المكتشفة

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.

تاريخ الاكتشاف	العدد الأولي M_q	Digits count	Name Mn	Electronic machine platform
13 نوفمبر 1996	M_1398269	420,921	M35	Pentium (90 MHz)
24 أغسطس 1997	M_2976221	895,932	M36	Pentium (100 MHz)
27 يناير 1998	M_3021377	909,526	M37	Pentium (200 MHz)
1 يونيو1999	M_6972593	2,098,960	M38	Pentium (350 MHz)
14 نوفمبر 2001	M_13466917	4,053,946	M39	AMD T-Bird (800 MHz)
17 نوفمبر 2003	M_20996011	6,320,430	M40	Pentium (2 GHz)
15 مايو2004	M_24036583	7,235,733	M41	Pentium أربعة (2.4 GHz)
18 فبراير 2005	M_25964951	7,816,230	M42	Pentium أربعة (2.4 GHz)
15 ديسمبر 2005	M_30402457	9,152,052	M43 ?	Pentium أربعة (2 GHz overclocked to 3 GHz)
4 سبتمبر 2006	M_32582657	9,808,358	M44 ?	Pentium أربعة (3 GHz)
23 أغسطس 2008	M_43112609	12,978,189	M47 ?	Core 2 Duo E6600 CPU (2.4 GHz)
6 سبتمبر 2008	M_37156667	11,185,272	M45 ?
12 أبريل 2009	M_42643801	12,837,064	M46 ?	Intel Core 2 Duo (3 GHz)
25 يناير 2013	M_57885161	17,425,170	M48 ?

انظر أيضاً

قائمة مشاريع الحوسبة الموزعة
حوسبة موزعة
پرايم‌گريد
Berkeley Open Infrastructure for Network Computing

المصادر

^ "Volunteer computing". BOINC. Retrieved 8 October 2012.
^ -1". Great Internet Mersenne Prime Search. Retrieved 2013-02-05. Italic or bold markup not allowed in: |publisher= (help)
^ - GIMPS Home Page
^ The Mersenne Newsletter, Issue #9. Retrieved 2011-10-02.
^ Mersenne forum Retrieved 2011-10-02
^ Woltman, George (February 24, 1996). "The Mersenne Newsletter, issue #1" (txt). Great Internet Mersenne Prime Search (GIMPS). Retrieved 2009-06-16.
^ Woltman, George (January 15, 1997). "The Mersenne Newsletter, issue #9" (txt). GIMPS. Retrieved 2009-06-16.
^ The Mersenne Newsletter, Issue #9. Retrieved 2009-08-25.
^ Woltman, George (April 12, 1996). "The Mersenne Newsletter, issue #3" (txt). GIMPS. Retrieved 2009-06-16.
^ Woltman, George (November 23, 1996). "The Mersenne Newsletter, issue #8" (txt). GIMPS. Retrieved 2009-06-16.
^ PrimeNet Activity Summary, GIMPS, (updated automatically), http://www.mersenne.org/primenet/, retrieved on 2012-04-05
^ "TOP500 - November 2012". Retrieved 22 November 2012.
^ TOP500 per November 2012; HP BL460c with 95.1 TFLOP/s (R max)."TOP500 - Rank 329". Retrieved 22 November 2012.
^ http://www.mersenne.org/freesoft/default.php#source
^ GIMPS Legalese, GIMPS, http://www.mersenne.org/legal/, retrieved on 2011-09-19
^ EFF Cooperative Computing Awards, Electronic Frontier Foundation, http://www.eff.org/awards/coop, retrieved on 2011-09-19