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• Patrick Laroche
  ...less than 4 months and on just his fourth try, he discovered the new prime number. By way of comparison, some GIMPS participants have searched for more than He is credited with discovery of the [[M51|51th known Mersenne prime]] 2^{{{Num|82589933}}}-1.
  987 bytes (147 words) - 01:27, 15 January 2024
• PrimeGrid
  '''PrimeGrid''' is a [[distributed computing]] project for searching for [[prime]] numbers of world-record size. It makes use of the [[BOINC|Berkeley Open I :[[PrimeGrid 321 Prime Search|321 Prime Search]] searching for mega primes of the form {{Kbn|±|3|2|n}}.
  3 KB (458 words) - 10:28, 26 March 2024
• Worktype
  ...nne primes have been missed, and lastly finding [[factor]]s for [[Mersenne number]]s). ...ber. A found factor will conclusively prove that the number is [[Composite number|composite]], which eliminates the need to run a [[primality test]].
  4 KB (603 words) - 02:31, 18 August 2019
• Sieve of Eratosthenes
  The '''sieve of Eratosthenes''' is a method to find all [[prime]] numbers smaller than a given integer <math>N</math>. It's invention is cr ...h>, then <math>N</math> is [[composite number|composite]]; otherwise it is prime.
  4 KB (654 words) - 11:10, 6 February 2019
• Aliquot sequence
  An '''aliquot sequence''' is a sequence of numbers generated from an initial number using the sigma <math>\sigma(n)</math> function. ...visors''' of the number, <math>n</math>, which are all the divisors of the number, excluding itself. Therefore, sequences are generated thusly:
  6 KB (914 words) - 19:49, 21 February 2023
• Prime
  ...ger]] greater than 1 that is only divisible by itself and 1. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19. ...that the idea of a 'largest prime' is fiction. And, if there is no largest prime the primes must be infinite.
  2 KB (447 words) - 00:22, 10 July 2023
• Twin prime
  ...mber]] that differs from another prime number by two, for example the twin prime pair (41, 43). ==Count of twin prime pairs==
  2 KB (255 words) - 06:08, 21 February 2023
• Riesel Prime Search
  '''Riesel Prime Search''' (RPS) is a prime searching project established in 2005 by [[Predrag Minovic]] (Kosmaj). :The project is searching for [[Riesel prime]]s {{Kbn|k|n}}, {{Vk}} > 1.
  845 bytes (120 words) - 02:21, 1 May 2024
• Nomenclature and notation
  ==[[Mersenne number]]== ...{p}-1</math> is generally used when discussing the search for a [[Mersenne prime]].
  3 KB (467 words) - 08:48, 15 May 2024
• Why participate in GIMPS?
  ...s of the form 2^p-1, for some prime ''p'' (now called [[Mersenne prime|Mersennes]]). So the quest for these jewels began near 300 BC. ...umbers, how to characterize their [[factor]]s and discover those which are prime. In short, the tradition of seeking large primes (especially the Mersennes)
  7 KB (1,252 words) - 09:47, 7 March 2019
• Sieving
  '''Sieving''' is an algorithm to discover [[smooth number]]s and [[prime]] numbers from a sequence of [[integer]]s much faster than [[trial factorin The next step depends on whether we need to find prime number or smooth numbers.
  3 KB (521 words) - 11:14, 6 February 2019
• Smooth number
  A '''smooth number''' is an [[integer]] whose [[prime]] [[factor]]s are less or equal to a prescribed bound ('''smoothness bound' If this bound is B, we can say that the number is B-smooth.
  436 bytes (63 words) - 21:36, 3 February 2019
• Sieving program
  *[[MultiSieve]] (performing sieving of different kinds of number) http://home.roadrunner.com/~mrodenkirch/home/MultiSieve.html ...ng [[twin prime]]s of the same form) http://sites.google.com/site/kenscode/prime-programs
  2 KB (220 words) - 11:42, 7 March 2019
• NewPGen
  *k&times;bⁿ±1 ([[twin prime]]s) *k&times;bⁿ-1, 2k&times;bⁿ-1 ([[Sophie Germain prime|Sophie Germain]])
  3 KB (529 words) - 09:32, 7 March 2019
• Sophie Germain prime
  ..., 23 is a Sophie Germain prime because it is a prime and 2*23+1 = 47, also prime. ...e: Possible to give the No. (if available) in the comments of the [[Riesel prime]] page (see [[:Template:NVal|Template NVal]])?
  1 KB (171 words) - 04:26, 3 November 2020
• M13
  | number=686479766013...291115057151 '''M13''' is the 13th known [[Mersenne prime]] 2⁵²¹-1 found on 1952-01-30 by [[Raphael M. Robinson]].
  419 bytes (48 words) - 14:50, 19 September 2021
• M14
  | number=531137992816...219031728127 '''M14''' is the 14th known [[Mersenne prime]] 2⁶⁰⁷-1 found on 1952-01-30 by [[Raphael M. Robinson]].
  420 bytes (48 words) - 14:49, 19 September 2021
• M15
  | number=104079321946...703168729087 '''M15''' is the 15th known [[Mersenne prime]] 2^{{Num|1279}}-1 found on 1952-06-25 by [[Raphael M. Robinson]]
  430 bytes (49 words) - 14:49, 19 September 2021
• M16
  | number=147597991521...686697771007 '''M16''' is the 16th known [[Mersenne prime]] 2^{{Num|2203}}-1 found on 1952-10-07 by [[Raphael M. Robinson]]
  431 bytes (49 words) - 14:49, 19 September 2021
• M17
  | number=446087557183...418132836351 '''M17''' is the 17th known [[Mersenne prime]] 2^{{Num|2281}}-1 found on 1952-11-09 by [[Raphael M. Robinson]]
  431 bytes (49 words) - 14:49, 19 September 2021

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