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• PrimeKit
  ...Mathematica implementations of all 112 algorithms discussed in the book ''Prime Numbers: A Computational Perspective'' (2001) by [[Richard Crandall]] and C ...optimized), but there is also an "Extras" folder containing some efficient number-theoretical C sources.
  1 KB (125 words) - 09:38, 23 January 2019
• Coprime
  ...h>\gcd{(x,y)} = 1</math>). This does not mean that any of these numbers is prime. :Two random numbers are coprime with a probability over 60% (the exact number is <math>6/\pi^2</math>).
  738 bytes (112 words) - 09:50, 23 January 2019
• Greatest common divisor
  ...re <math>a</math> and <math>b</math> are positive integers, is the maximum number that divides both <math>a</math> and <math>b</math>. ...] or relatively prime. This does not mean that either of these numbers are prime.
  2 KB (339 words) - 18:38, 27 September 2023
• Elliptic curve method
  ...le of a point on a random elliptic curve [[modular arithmetic|modulo]] the number to be factored. It is currently the best [[algorithm]] known, among those w ...ber]]. This method cannot be used when it is not known in advance that the number is composite, so it cannot be used as a [[primality test]].
  19 KB (3,181 words) - 22:27, 6 July 2023
• M35
  | number=814717564412...868451315711 '''M35''' is the 35th [[Mersenne prime]], both in order of size and date of discovery.
  2 KB (224 words) - 11:00, 18 February 2019
• University of California, Los Angeles
  As an institution, UCLA has contributed to the discovery of 8 [[Mersenne prime]]s. This is more than any other university. [[University of Central Missour ...number of digits of the largest known [[prime]] (in general) and Mersenne Prime from 79 and 39 (respectively) to 687.
  2 KB (347 words) - 14:54, 19 September 2021
• Raphael M. Robinson
  ...0) proved that an essentially undecidable theory need not have an infinite number of axioms by coming up with a counterexample: Robinson arithmetic ''Q''. '' ..., [[M16|2203]], [[M17|2281]]. He discovered the last 5 of these [[Mersenne prime]]s, the largest ones known at the time.
  4 KB (526 words) - 14:51, 19 September 2021
• M36
  | number=623340076248...743729201151 ...It took Spence's 100 MHz [[Pentium]] computer 15 days to prove the number prime. Alan White Managing Director at Technology Business Solutions, who provide
  2 KB (279 words) - 11:01, 18 February 2019
• Jonathan Pace
  ...l engineer. He is credited with discovery of the [[M50|50th known Mersenne prime]] {{Kbn|77232917}}. ...en he read an article about the discovery of the [[M40|40th known Mersenne prime]].
  2 KB (242 words) - 00:08, 15 January 2024
• Sierpiński problem
  The '''Sierpiński problem''' in [[number theory]] was proposed by [[Wacław Sierpiński]] in 1960. ...[[composite number]] {{V|N}}, then {{Vk}} is said to be a '''[[Sierpiński number]]'''.
  5 KB (650 words) - 10:25, 26 March 2024
• Seventeen or Bust
  ...(SOB)''' was a [[distributed computing]] project working on a problem in [[number theory]] called the [[Sierpiński problem]]. It is currently a subproject o ...we are running [[primality test]]s called [[Probable prime|PRP]] (Probable Prime), which take a very long time, for every candidate in the queue.
  3 KB (544 words) - 16:44, 21 July 2019
• M2
  | number= 7 [[Category:Mersenne prime|M02]]
  193 bytes (19 words) - 13:43, 17 February 2019
• M3
  | number= 31 [[Category:Mersenne prime|M03]]
  194 bytes (19 words) - 13:43, 17 February 2019
• M4
  | number= 127 [[Category:Mersenne prime|M04]]
  195 bytes (19 words) - 13:44, 17 February 2019
• M5
  | number= 8191 [[Category:Mersenne prime|M05]]
  204 bytes (18 words) - 13:46, 17 February 2019
• Perfect number
  In [[mathematics]], a '''perfect number''' is defined as an integer which is the sum of its proper positive divisor ...and 3 are its proper positive divisors and 1 + 2 + 3 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. The next perfect numbers are 496 and 8128.
  6 KB (885 words) - 11:33, 7 March 2019
• M9
  | number=2305843009213693951 The ninth [[Mersenne prime]], 2⁶¹-1 or {{Num|2305843009213693951}}.
  2 KB (213 words) - 14:30, 17 February 2019
• Double check
  *human error (entering wrong number to test, misreading data, etc.) ...t]] does a verfication on all [[factor]]s reported. (It is easy to check a number for a single factor.)
  2 KB (373 words) - 15:08, 5 June 2019
• Residue
  ...ctly divisible. For the L-L test a zero residue means that the number is [[prime]]. ...test to produced matching erroneaous residues (meaning they both missed a prime) out of a pool of ~ 18.4 pentillion numbers, this is considered to be impos
  1 KB (235 words) - 10:24, 6 February 2019
• GIMPS clients
  The [[Great Internet Mersenne Prime Search]] (GIMPS) as a project is based on two related items: theory and pra ...very large Mersenne prime candidates to be tested for primality ("is it a prime?") faster than other sorts of would-be primes of the same magnitude. "Faste
  8 KB (1,218 words) - 15:37, 13 August 2020

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