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  • 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
  • Aliquot sequence
    :<math>s_n = \sigma(s_{n-1}) - s_{n-1}</math> :<math>s_0\ =\ 10,\ \sigma(10)=1\ +\ 2\ +\ 5\ +\ 10</math>
    6 KB (914 words) - 19:49, 21 February 2023
  • Abundant number
    The divisors of 12 are <math>(1, 2, 3, 4, 6, 12)</math>, so :<math>\sigma(12)\ =\ 1+2+3+4+6+12\ =\ 28</math>
    671 bytes (92 words) - 00:34, 30 January 2019
  • Prime
    ...''') is an [[integer]] 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. ...P divides evenly into Q, because each division would leave a remainder of 1. If Q is not prime, it must be evenly divisible by some prime larger than P
    2 KB (447 words) - 00:22, 10 July 2023
  • Twin prime
    ...of the reciprocals of all twin primes converges to Brun's constant (about 1.902160583104). | align="right" | 10<sup>1</sup> || align="right" | 2
    2 KB (255 words) - 06:08, 21 February 2023
  • Riesel Prime Search
    :The project is searching for [[Riesel prime]]s {{Kbn|k|n}}, {{Vk}} > 1. ...ght {{Vk}}-values that produce a very small number of primes (opposite to (1) above)
    845 bytes (120 words) - 02:21, 1 May 2024
  • Nomenclature and notation
    ...math> (the exponent) must also be prime. Thus, the notation of <math>2^{p}-1</math> is generally used when discussing the search for a [[Mersenne prime] ...mber that is itself prime '''and''' can be written in the form <math>2^{x}-1</math>. These are what [[GIMPS]] is searching for.
    3 KB (467 words) - 08:48, 15 May 2024
  • Computing power
    ...calculating effort one 90 MHz Pentium computer produces over the course of 1 calendar year (365 days). Because of the early adoption of this unit by [[G ...ay. One P90 year equals 5.075 GHz-days. 1 TFLOPS equals 500 GHz-days, thus 1 P90 year is about 10 GFLOPS.
    2 KB (258 words) - 08:40, 15 May 2024
  • Seventeen or Bust/Primes
    | 4847 || {{PP|75994|4847 &times; 2<sup>{{Num|3321063}}</sup>+1}} || 999744 || 2005-10-15 || Richard Hassler | 5359 || {{PP|67719|5359 &times; 2<sup>{{Num|5054502}}</sup>+1}} || 1521561 || 2003-12-06 || Randy Sundquist
    2 KB (163 words) - 14:20, 7 March 2019
  • Seventeen or Bust/FAQ
    *[[Seventeen or Bust/Factoring|Factoring]]: How can I P-1 factor for SoB? It's too complicated!
    550 bytes (87 words) - 13:39, 1 February 2019
  • Seventeen or Bust/Factoring
    ...actoring for Seventeen or Bust is made by the [[P-1 factorization method|P-1 factoring]] method only. The programs commonly used to P-1 factor these numbers are [[Prime95]] and [http://linux.redbird.com/~alien88
    3 KB (491 words) - 13:39, 1 February 2019

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