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• Seventeen or Bust
  ...(SOB)''' was a [[distributed computing]] project working on a problem in [[number theory]] called the [[Sierpiński problem]]. It is currently a subproject o ...we are running [[primality test]]s called [[Probable prime|PRP]] (Probable Prime), which take a very long time, for every candidate in the queue.
  3 KB (544 words) - 16:44, 21 July 2019
• M2
  | number= 7 [[Category:Mersenne prime|M02]]
  193 bytes (19 words) - 13:43, 17 February 2019
• M3
  | number= 31 [[Category:Mersenne prime|M03]]
  194 bytes (19 words) - 13:43, 17 February 2019
• M4
  | number= 127 [[Category:Mersenne prime|M04]]
  195 bytes (19 words) - 13:44, 17 February 2019
• M5
  | number= 8191 [[Category:Mersenne prime|M05]]
  204 bytes (18 words) - 13:46, 17 February 2019
• Perfect number
  In [[mathematics]], a '''perfect number''' is defined as an integer which is the sum of its proper positive divisor ...and 3 are its proper positive divisors and 1 + 2 + 3 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. The next perfect numbers are 496 and 8128.
  6 KB (885 words) - 11:33, 7 March 2019
• M9
  | number=2305843009213693951 The ninth [[Mersenne prime]], 2⁶¹-1 or {{Num|2305843009213693951}}.
  2 KB (213 words) - 14:30, 17 February 2019
• Double check
  *human error (entering wrong number to test, misreading data, etc.) ...t]] does a verfication on all [[factor]]s reported. (It is easy to check a number for a single factor.)
  2 KB (373 words) - 15:08, 5 June 2019
• Residue
  ...ctly divisible. For the L-L test a zero residue means that the number is [[prime]]. ...test to produced matching erroneaous residues (meaning they both missed a prime) out of a pool of ~ 18.4 pentillion numbers, this is considered to be impos
  1 KB (235 words) - 10:24, 6 February 2019
• GIMPS clients
  The [[Great Internet Mersenne Prime Search]] (GIMPS) as a project is based on two related items: theory and pra ...very large Mersenne prime candidates to be tested for primality ("is it a prime?") faster than other sorts of would-be primes of the same magnitude. "Faste
  8 KB (1,218 words) - 15:37, 13 August 2020
• Mfaktc
  ...ics cards, this is a very fast program. The name mfaktc is "'''M'''ersenne number '''fakt'''oring with '''C'''UDA", it is a mixture of English with the Germa *Prime exponents between 100000 and <math>2^{32}-1</math>
  5 KB (765 words) - 14:54, 25 February 2019
• Rho factorization method
  The idea is to create a sequence iterating a polynomial modulo the number to be factored. When N = pq where p and q are [[coprime]] but not necessarily [[prime]], we will see that after about <math>\sqrt p</math> elements the sequence
  3 KB (558 words) - 10:28, 6 February 2019
• Riesel number
  ...value of ''k'' such that {{Kbn|k|n}} is always composite for all [[natural number]]s. ...Sierpiński problem]] article, [[Hans Riesel]] found in 1956 that [[Riesel prime 2 509203|{{Kbn|509203|n}}]] is always composite.
  827 bytes (112 words) - 08:21, 25 March 2024
• M12
  | number=170141183460...715884105727 ...n a "smart phone" in under one second. This was the largest known Mersenne prime until 1952, when [[Raphael M. Robinson|Robinson]] at [[University of Califo
  2 KB (354 words) - 14:52, 19 September 2021
• Primality test
  .... When the number is declared composite, the algorithm does not reveal the prime [[factor]]s. That is the job of the [[Factorization|factorization methods]] ...(which is far slower than a probable primality test except when the input number has a special form) is run on it.
  3 KB (501 words) - 05:20, 3 August 2021
• Lucas primality test
  ...' invented in 1891 by [[Édouard Lucas]], determines whether a number N is prime or not, using the complete factorization of N-1. ...is not congruent to 1 modulo N for any prime divisor q of N-1, then N is a prime.
  1 KB (177 words) - 14:31, 17 February 2019
• Primality testing program
  ...ne number]]s<br/>a &times; bⁿ±c (only factoring and [[probable prime|PRP]]-testing) | [[generalized Fermat number]]s
  2 KB (314 words) - 21:23, 29 August 2019
• Pépin's test
  '''Pépin's test''' is mainly used for proving the primality of [[Fermat number]]s, but it is of no help for finding the factors of such numbers. ...for proving the primality of other numbers, like the [[Generalized Fermat number]]s <math>F_{n,2} = 4^{3^n}+2^{3^n}+1</math> with k = 5 instead of k = 3.
  2 KB (401 words) - 14:40, 6 March 2019
• Mprime (Cray)
  ...later versions with [[Paul Gage]]), for testing [[Mersenne number]]s for [[Prime|primality]] on [[Cray Research|Cray]] [[Classes of computers#Supercomputer| This software is responsible for the discovery of 7 [[Mersenne prime]]s. It used [[Fast Fourier transform]]s for the [[multiplication]] of very
  639 bytes (92 words) - 12:02, 7 February 2019
• Probable prime
  ...an [[integer]] that satisfies a specific condition also satisfied by all [[prime]] numbers.}} ...ecific conditions. While there may be probable primes that are [[Composite number|composite]] (called [[pseudoprime]]s), the condition is generally chosen in
  2 KB (232 words) - 07:28, 12 March 2024

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