البحث الكبير على الإنترنت عن أعداد مرسن الأولية

البحث الكبير على الإنترنت عن أعداد مرسن الأولية Great Internet Mersenne Prime Search (GIMPS)، هو مشروع 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 هو نائب الرئيس التنفيذي 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.[1]

The project has found a total of fourteen Mersenne primes اعتبارا من 5 فبراير 2013 (2013-02-05), eleven of which were the largest known prime number at their respective times of discovery. The largest known prime اعتبارا من يناير 2013 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.[2]

To perform its testing, the project relies primarily on Édouard Lucas and Derrick Henry Lehmer's primality test,[3] 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.

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التاريخ

The project began in early January 1996,[4][5] with a program that ran on i386 computers.[6][7] The name for the project was coined by Luther Welsh one of its earlier searchers and the discoverer of the 29th Mersenne prime.[8] Within a few months, several dozen people had joined, and over a thousand by the end of the first year.[7][9] Joel Armengaud, a participant, discovered the primality of M1,398,269 on November 13, 1996.[10]


الحالة

اعتبارا من نوفمبر 2012, GIMPS has a sustained throughput of approximately 95 teraflops,[11] 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),[12] after rank 329, which is held by a 'HP Cluster Platform 3000 BL460c G7' of Hewlett-Packard.[13]

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,[14] technically it is not free software, since it has a restriction that users must abide by the project's distribution terms[15] 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.[16]


الأعداد المكتشفة

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.


تاريخ الاكتشاف العدد الأولي Mq Digits count Name Mn Electronic machine platform
13 نوفمبر 1996 M1398269 420,921 M35 Pentium (90 MHz)
24 أغسطس 1997 M2976221 895,932 M36 Pentium (100 MHz)
27 يناير 1998 M3021377 909,526 M37 Pentium (200 MHz)
1 يونيو 1999 M6972593 2,098,960 M38 Pentium (350 MHz)
14 نوفمبر 2001 M13466917 4,053,946 M39 AMD T-Bird (800 MHz)
17 نوفمبر 2003 M20996011 6,320,430 M40 Pentium (2 GHz)
15 مايو 2004 M24036583 7,235,733 M41 Pentium 4 (2.4 GHz)
18 فبراير 2005 M25964951 7,816,230 M42 Pentium 4 (2.4 GHz)
15 ديسمبر 2005 M30402457 9,152,052 M43 ? Pentium 4 (2 GHz overclocked to 3 GHz)
4 سبتمبر 2006 M32582657 9,808,358 M44 ? Pentium 4 (3 GHz)
23 أغسطس 2008 M43112609 12,978,189 M47 ? Core 2 Duo E6600 CPU (2.4 GHz)
6 سبتمبر 2008 M37156667 11,185,272 M45 ?
12 أبريل 2009 M42643801 12,837,064 M46 ? Intel Core 2 Duo (3 GHz)
25 يناير 2013 M57885161 17,425,170 M48 ?



انظر أيضاً

المصادر

  1. ^ "Volunteer computing". BOINC. Retrieved 8 October 2012.
  2. ^ "GIMPS Project Discovers Largest Known Prime Number, 257,885,161-1". Great Internet Mersenne Prime Search. Retrieved 2013-02-05. {{cite web}}: Italic or bold markup not allowed in: |publisher= (help)
  3. ^ What are Mersenne primes? How are they useful? - GIMPS Home Page
  4. ^ The Mersenne Newsletter, Issue #9. Retrieved 2011-10-02.
  5. ^ Mersenne forum Retrieved 2011-10-02
  6. ^ Woltman, George (February 24, 1996). "The Mersenne Newsletter, issue #1" (txt). Great Internet Mersenne Prime Search (GIMPS). Retrieved 2009-06-16.
  7. ^ أ ب Woltman, George (January 15, 1997). "The Mersenne Newsletter, issue #9" (txt). GIMPS. Retrieved 2009-06-16.
  8. ^ The Mersenne Newsletter, Issue #9. Retrieved 2009-08-25.
  9. ^ Woltman, George (April 12, 1996). "The Mersenne Newsletter, issue #3" (txt). GIMPS. Retrieved 2009-06-16.
  10. ^ Woltman, George (November 23, 1996). "The Mersenne Newsletter, issue #8" (txt). GIMPS. Retrieved 2009-06-16.
  11. ^ PrimeNet Activity Summary, GIMPS, (updated automatically), http://www.mersenne.org/primenet/, retrieved on 2012-04-05 
  12. ^ "TOP500 - November 2012". Retrieved 22 November 2012.
  13. ^ TOP500 per November 2012; HP BL460c with 95.1 TFLOP/s (R max)."TOP500 - Rank 329". Retrieved 22 November 2012.
  14. ^ http://www.mersenne.org/freesoft/default.php#source
  15. ^ EFF Cooperative Computing Awards, Electronic Frontier Foundation, http://www.eff.org/awards/coop, retrieved on 2011-09-19 

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