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• Fast Fourier transform
  Let ''x''₀, ...., ''x''_''n''-1 be [[complex number]]s. The DFT is defined by the formula ...lar misconception) there are O(''n'' log ''n'') FFTs for all ''n'', even [[prime]] ''n''.
  17 KB (2,684 words) - 18:50, 28 September 2023
• GpuLucas
  ...[[CUDA]]-based program written by [[Andrew Thall]] for testing [[Mersenne number]]s for primality. ...l, A. [http://andrewthall.org/papers/gpuMersenne2011MKII.pdf Fast Mersenne Prime Testing on the GPU] (2011)
  2 KB (239 words) - 11:12, 13 February 2019
• GpuOwL
  {{InfoboxProgram|workload=[[Lucas-Lehmer test|LL]], [[Probable prime|PRP]]|title=gpuOwL|release=2017|latest=7.2<br>2020-11-01}} ...s a [[OpenCL]]-based program written by Mihai Preda for testing [[Mersenne number]]s for primality.
  1 KB (216 words) - 05:22, 1 December 2020
• MersenneForum
  ...upport [[GIMPS]], the broader community of [[Mersenne number]]s, [[prime]] number, and factoring projects. In addition to being the de facto help and support ==Prime number software discussion and development==
  2 KB (293 words) - 17:33, 5 July 2019
• Primo
  '''Primo''' is a computer program which tests numbers for [[prime|primality]] using the [[Elliptic Curve Primality Proving]] (ECPP) [[algorit ...ot require a number to be of any specific form. If a number is found to be prime, a [[primality certificate]] is produced, which can be quickly verified.
  1 KB (191 words) - 20:33, 12 May 2020
• M32
  | number=174135906820...328544677887 The '''32nd [[Mersenne prime]]''', both in size (smallest to largest) and in order of discover.
  2 KB (279 words) - 08:35, 18 February 2019
• M33
  | number=129498125604...243500142591 '''M33''' refers to 33rd [[Mersenne prime]] number 2^{{{Num|859433}}}-1.
  814 bytes (97 words) - 08:38, 18 February 2019
• M34
  | number=412245773621...976089366527 ...ber {{Num|378632}} [[decimal]] [[digit]]s long. The number was found to be prime in 1996.
  3 KB (513 words) - 08:42, 18 February 2019
• Rational number
  A '''rational number''' is a [[real number]] which can be written as <math>\frac{a}{b}</math> or <math>a/b</math> wher ...r [[greatest common divisor]]. This operation does not change the rational number represented by the fraction.
  3 KB (541 words) - 15:01, 26 March 2023
• Binary
  ...iness' of Mersenne numbers makes calculations in the search for [[Mersenne prime]]s a bit easier.
  1 KB (210 words) - 11:16, 22 January 2019
• 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

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