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• Repunit
  ...[[Mersenne number]]s are repunit ('''rep'''eated '''unit''', "1" being the number referred to as "unity") numbers. 111 is a repunit, in base 2 it is equal to A '''Repunit prime''' is a repunit which is also [[prime]].
  1 KB (207 words) - 08:04, 12 March 2024
• Trial factoring
  ...are found, the number in question is prime; otherwise, it is a [[composite number]]. ..., P(2) = 3, P(3) = 5, etc, then the last prime factor possibility for some number N would be P(m) where P(m + 1) squared exceeds N.
  7 KB (1,221 words) - 13:20, 11 February 2019
• M40
  | number=125976895450...762855682047 ...Num|6320430}} decimal digits] long. This prime number was the sixth record prime found by the [[GIMPS]] project.
  1 KB (189 words) - 11:17, 18 February 2019
• M39
  | number=924947738006...470256259071 ...[[Michael Cameron]], using [[Prime95]] written by [[George Woltman]]. The number is [http://www.mersenneforum.org/txt/39.txt {{Num|4053946}} decimal digits]
  868 bytes (109 words) - 11:14, 18 February 2019
• M44
  | number=124575026015...154053967871 '''M44''' is the short hand used to refer to the 44th [[Mersenne prime]]. Currently that designation belongs to 2^{{{Num|32582657}}}-1.
  997 bytes (129 words) - 11:35, 18 February 2019
• M45
  | number=202254406890...022308220927 ...''' normally refers to 2^{{{Num|37156667}}}-1, the 45th [[Mersenne prime]] in order of size from the smallest to greatest. This is the primary usage
  2 KB (251 words) - 11:40, 18 February 2019
• Richard Crandall
  ...uter]] scientist and physicist who has made contributions to computational number theory. He received a doctorate from [[Massachusetts Institute of Technolog His Erdös number is 2. He was one of the primary verifiers of [[M32]], [[M33]], and [[M34]].
  3 KB (431 words) - 11:36, 14 January 2024
• M38
  | number=437075744127...142924193791 ...[[Nayan Hajratwala]], using [[Prime95]] written by [[George Woltman]]. The number is [http://www.mersenneforum.org/txt/38.txt {{Num|2098960}} decimal digits]
  1 KB (165 words) - 11:10, 18 February 2019
• Nayan Hajratwala
  ...houseCoopers employee from Michigan who discovered the [[M38|38th Mersenne prime]], 2^{{{Num|6972593}}}-1. ...99-06-01, Hajratwala's 350 MHz IBM Aptiva home computer first reported the prime to the [[GIMPS]] server. The computer had taken 111 days to complete the te
  809 bytes (109 words) - 23:55, 14 January 2024
• Irrational base discrete weighted transform
  ...T''') is a variant of the [[Fast Fourier transform]] using an [[Irrational number|irrational]] base. It was proposed by [[Richard Crandall]] and [[Barry Fagi The IBDWT is used to perform FFT multiplication modulo [[Mersenne number]] in such programs as [[Prime95]], [[CUDALucas]], [[Glucas]], [[gpuLucas]].
  1 KB (172 words) - 18:49, 28 September 2023
• 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

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