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  • Legendre symbol
    *1 if <math>a</math> is a square [[modular arithmetic|modulo]] <math>p</math> *&minus;1 if <math>a</math> is not a square modulo <math>p</math>, or in other words
    2 KB (348 words) - 18:57, 28 September 2023
  • Law of quadratic reciprocity
    *If at least one of <math>p</math> or <math>q</math> are congruent to 1 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and o This does not cover the cases where we want to know whether -1 or 2 are quadratic residues or non-residues modulo <math>p</math>.
    1 KB (208 words) - 18:19, 2 October 2022
  • Ten million digits
    ...overy of [[M38]] (the first [[megaprime]] or [[prime]] number greater than 1 million [[decimal]] [[digit]]s) in June of 1999, the next [[EFF prizes]] fo
    979 bytes (146 words) - 14:23, 6 March 2019
  • LLR
    **{{V|N}}-1 [[Pocklington algorithm]] for {{Kbn|+|k|b|n}} numbers. **{{V|N}}+1 [[Morrison algorithm]] for {{Kbn|k|b|n}} numbers.
    2 KB (300 words) - 22:00, 16 December 2023
  • Double Mersenne number
    ...'MM<sub>p</sub>''', '''MMp''', or '''MM(p)''' and refer to <math>2^{2^p-1}-1</math>. Early on it was thought that if M(p) was prime so too was MM(p). *MM(2) = <math>2^3-1</math> = 7, known prime since antiquity
    4 KB (655 words) - 14:50, 19 September 2021
  • CUDAPm1
    ...ram, based on [[CUDALucas]] code, for testing [[P-1 factorization method|P-1]] testing on [[GPU]]s.
    419 bytes (53 words) - 15:51, 28 January 2019
  • P-1 factorization method
    '''P-1''' is a [[:Category:Factorization|factorization method]] invented by John P ...a prime which does not divide the integer ''a'', then <math>a^{p-1}\equiv 1 \mbox{( mod } p)</math>.
    5 KB (814 words) - 01:35, 12 March 2019
  • Brent-Suyama extension
    ...ossibility of finding factors outside the normal range expected from the P-1 bounds. ...than B1. Then by [[Fermat's Little Theorem]], a prime number p | S-1 if p-1 | E.
    2 KB (421 words) - 11:51, 28 January 2019
  • Self-initializing quadratic sieve
    :<math>45^2\,\equiv \,2^4*7^0*13^1</math> :<math>123^2\,\equiv \,2^{10}*7^0*13^1</math>
    10 KB (1,763 words) - 02:56, 12 March 2019
  • Special number field sieve
    :<math>\Theta\left(\exp\left( \left(\frac{32}{9}n\right)^{\frac{1}{3}} (\log n)^{\frac{2}{3}} \right)\right).</math>
    1 KB (186 words) - 12:07, 19 February 2019
  • Fermat pseudoprimality test
    :<math>a^{p-1}\equiv 1\,\pmod{p}</math> ...', we perform <math>a^{N-1}\equiv 1\,\pmod{N}</math>. If the result is not 1, the number must be composite. Otherwise the number is either a prime or a
    1 KB (164 words) - 10:56, 6 February 2019
  • Miller-Rabin pseudoprimality test
    *The Fermat Little Theorem that states: <math>a^{p-1}\equiv 1\,\pmod p</math>. ...v 1\,\pmod p</math> then <math>m\equiv 1\,\pmod p</math> or <math>m\equiv -1\,\pmod p</math>.
    3 KB (432 words) - 15:33, 28 January 2019
  • Andrew Thall
    ...[Lucas-Lehmer test]] for a [https://en.wikipedia.org/wiki/MasPar Maspar MP-1] (a [[Single instruction, multiple data|SIMD]] supercomputer released in 19
    2 KB (225 words) - 00:22, 15 January 2024
  • Generalized Fermat number
    ...+1}}-1)/(2^{p^n}-1)</math> where p is the prime of apparition rank r (r(2)=1, r(3)=2, r(5)=3, ...) and n is greater or equal to 0. :<math>F_{n,1}</math> generates the [[Fermat number]]s.
    5 KB (774 words) - 07:39, 27 May 2024
  • Patrick Laroche
    ...very of the [[M51|51th known Mersenne prime]] 2<sup>{{Num|82589933}}</sup>-1.
    987 bytes (147 words) - 01:27, 15 January 2024
  • PrimeGrid
    ...ipants (on about 16,000 host computers) from 89 countries, reporting about 1,860 [[Computing power#FLOPS|teraflops]].<ref>[https://www.boincstats.com/st ...Riesel Problem|The Riesel Problem]]: helping to solve the [[Riesel problem 1|Riesel problem]].
    3 KB (458 words) - 10:28, 26 March 2024
  • Worktype
    *[[P-1_factorization_method|P-1]]: A second method that finds factors. *P-1 factoring: See P-1 above.
    4 KB (603 words) - 02:31, 18 August 2019
  • 321 Search
    ...d computing project]] to search for [[prime]]s of the form 3*2<sup>n</sup>-1.
    1 KB (185 words) - 09:34, 3 August 2021
  • Sieve of Eratosthenes
    *First, list out all the integers <math>1 \leq k \leq N</math>. *<math>1</math> is not considered prime; it is ignored.
    4 KB (654 words) - 11:10, 6 February 2019
  • Top GIMPS teams
    | 1 || [[PrimeNet]] || 32679708 *[https://www.mersenne.org/report_top_500_custom/?team_flag=1&type=0&rank_lo=1&rank_hi=50&start_date=1994&end_date= Lifetime team stats] at [[PrimeNet]]
    2 KB (206 words) - 09:56, 7 March 2019

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