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• Modular square root
  A '''modular square root''' <math>r</math> of an [[integer]] number <math>a</math> modulo an integer <math>m</math> greater than 1 is an intege ...modulus is [[prime]]. Otherwise we can compute the square roots modulo the prime factors of <math>m</math> and then generate a solution using the Chinese Re
  5 KB (726 words) - 10:38, 6 February 2019
• Legendre symbol
  If <math>p</math> is an odd [[prime]] number and <math>a</math> is an [[integer]], then the Legendre symbol There are a number of useful properties of the Legendre symbol which can be used to speed up c
  2 KB (348 words) - 18:57, 28 September 2023
• Law of quadratic reciprocity
  ...</math> is a [[quadratic residue]] or non-residue modulo another odd prime number <math>q</math> if we know whether <math>q</math> is a quadratic residue or
  1 KB (208 words) - 18:19, 2 October 2022
• Ten million digits
  ...llion [[decimal]] [[digit]]s) in June of 1999, the next [[EFF prizes]] for prime numbers was '''ten million decimal digits'''. ...was found, [[M46]]. By the end of 2010, all exponents that would produce a number less than {{Num|10000000}} digits had been [[primality test|tested]] at lea
  979 bytes (146 words) - 14:23, 6 March 2019
• Double Mersenne number
  ...efer 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
• PSearch
  ...g project|distributed computing project]] in search of the largest [[Proth prime]]s. ! scope="col" | Number
  1 KB (182 words) - 08:17, 12 July 2020
• P-1 factorization method
  Let ''p'' be a prime which does not divide the integer ''a'', then <math>a^{p-1}\equiv 1 \mbox{( ...tiple of ''N'', so a [[greatest common divisor]] operation will reveal the prime divisor.
  5 KB (814 words) - 01:35, 12 March 2019
• Brent-Suyama extension
  ...of prime powers less than B1. Then by [[Fermat's Little Theorem]], a prime number p | S-1 if p-1 | E. ...tage 2 would then compute T=S^q = 3^E*q for successive prime q in the range (B1,B2]. Then p | T-1 if p-1 | q*E.
  2 KB (421 words) - 11:51, 28 January 2019
• Self-initializing quadratic sieve
  Let N be the number to be factored. This number must not be a perfect power. If somehow we find two integers X and Y such t ...form <math>t^2 \equiv u\,\pmod N</math> where u is the product of small [[prime]] numbers. The set of these primes is the ''factor base''. These relations
  10 KB (1,763 words) - 02:56, 12 March 2019
• Lone Mersenne Hunters
  ...imeNet]] in order to eliminate [[Mersenne number]]s as possible [[Mersenne prime]] candidates. This work is suited to older and slower processors, often wit
  1 KB (213 words) - 09:58, 7 March 2019
• Fermat pseudoprimality test
  where ''p'' is a [[prime]] number and ''a'' is not multiple of <math>p</math>. ...t is not 1, the number must be composite. Otherwise the number is either a prime or a Fermat [[pseudoprime]] with respect to base <math>a</math>.
  1 KB (164 words) - 10:56, 6 February 2019
• Miller-Rabin pseudoprimality test
  The '''Miller-Rabin pseudoprimality test''' is based in two facts for prime numbers: ...primality, and <math>N = 2^n\,k + 1</math> where <math>k</math> is an odd number.
  3 KB (432 words) - 15:33, 28 January 2019
• Template:PP
  This template will create a link to a given ID in the [[The Prime Pages|'''P'''rime '''P'''ages]]. *<display>: how this number will be displayed in here
  790 bytes (111 words) - 13:47, 7 March 2019
• Generalized Fermat prime
  ...'generalized Fermat prime''' is a [[generalized Fermat number]] which is [[prime]]. *[[Wikipedia:Fermat_number#Generalized_Fermat_primes|Generalized Fermat prime]]
  372 bytes (49 words) - 13:35, 6 March 2019
• Generalized Fermat number
  There are different kinds of '''generalized [[Fermat number]]s'''. ...2^{2p^n}+2^{p^n}+1 \ = \ (2^{p^{n+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 equa
  5 KB (774 words) - 07:39, 27 May 2024
• M51
  | number=148894445742...325217902591 '''M51''' normally refers to the 51st [[Mersenne prime]], in order of size from the smallest to greatest. This is the primary usag
  2 KB (255 words) - 05:53, 21 July 2021
• Patrick Laroche
  ...less than 4 months and on just his fourth try, he discovered the new prime number. By way of comparison, some GIMPS participants have searched for more than He is credited with discovery of the [[M51|51th known Mersenne prime]] 2^{{{Num|82589933}}}-1.
  987 bytes (147 words) - 01:27, 15 January 2024
• PrimeGrid
  '''PrimeGrid''' is a [[distributed computing]] project for searching for [[prime]] numbers of world-record size. It makes use of the [[BOINC|Berkeley Open I :[[PrimeGrid 321 Prime Search|321 Prime Search]] searching for mega primes of the form {{Kbn|±|3|2|n}}.
  3 KB (458 words) - 10:28, 26 March 2024
• Worktype
  ...nne primes have been missed, and lastly finding [[factor]]s for [[Mersenne number]]s). ...ber. A found factor will conclusively prove that the number is [[Composite number|composite]], which eliminates the need to run a [[primality test]].
  4 KB (603 words) - 02:31, 18 August 2019
• Sieve of Eratosthenes
  The '''sieve of Eratosthenes''' is a method to find all [[prime]] numbers smaller than a given integer <math>N</math>. It's invention is cr ...h>, then <math>N</math> is [[composite number|composite]]; otherwise it is prime.
  4 KB (654 words) - 11:10, 6 February 2019

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