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  • Montgomery multiplication
    The Montgomery representation of a number <math>a</math> is the value ...presentation to normal, just perform a Montgomery multiplication using the number 1 as the second factor.
    4 KB (582 words) - 17:01, 29 August 2022
  • Elliptic curve method
    ...le of a point on a random elliptic curve [[modular arithmetic|modulo]] the number to be factored. It is currently the best [[algorithm]] known, among those w ...ber]]. This method cannot be used when it is not known in advance that the number is composite, so it cannot be used as a [[primality test]].
    19 KB (3,181 words) - 22:27, 6 July 2023
  • M35
    | number=814717564412...868451315711 ...er]]. The [[Lucas-Lehmer test]] took 88 hours to run. The primality of the number was confirmed by Slowinski. This showed the effectiveness of [[distributed
    2 KB (224 words) - 11:00, 18 February 2019
  • University of California, Los Angeles
    ...75 years (2 in the very first day of the run, no less). And he raised the number of digits of the largest known [[prime]] (in general) and Mersenne Prime fr
    2 KB (347 words) - 14:54, 19 September 2021
  • Raphael M. Robinson
    ...0) proved that an essentially undecidable theory need not have an infinite number of axioms by coming up with a counterexample: Robinson arithmetic ''Q''. '' ...ity of California, Los Angeles]]. In 1952, he showed that these [[Mersenne number]]s were all composite except for 17 values of ''n'' = 2, 3, 5, 7, 13, 17,
    4 KB (526 words) - 14:51, 19 September 2021
  • M36
    | number=623340076248...743729201151 ...k book. It took Spence's 100 MHz [[Pentium]] computer 15 days to prove the number prime. Alan White Managing Director at Technology Business Solutions, who p
    2 KB (279 words) - 11:01, 18 February 2019
  • Jonathan Pace
    ...umber-discovered How a FedEx employee discovered the world's largest prime number]. ''Popular Science''. 11 Jan 2018. ...-employee.html FedEx employee from Tennessee discovers largest known prime number]. ''CNBC''. 5 Jan 2018.
    2 KB (242 words) - 00:08, 15 January 2024
  • Wacław Sierpiński
    ...h|1882-03-14|1969-10-21}} was a Polish [[mathematician]] contributing in [[number theory]] and others. ...proved there are infinitely many odd integers {{Vk}} (named [[Sierpiński number]]s after him) such that {{Kbn|+|k|n}} is composite for all {{Vn}}.
    592 bytes (86 words) - 00:38, 15 January 2024
  • Sierpiński number
    ...l number {{Vk}} such that all {{Kbn|+|k|n}} for all {{Vn}} are [[Composite number|composite]]. *[[Wikipedia:Sierpiński_number|Sierpiński number]]
    324 bytes (48 words) - 13:37, 8 April 2023
  • Sierpiński problem
    The '''Sierpiński problem''' in [[number theory]] was proposed by [[Wacław Sierpiński]] in 1960. ...[[composite number]] {{V|N}}, then {{Vk}} is said to be a '''[[Sierpiński number]]'''.
    5 KB (650 words) - 10:25, 26 March 2024
  • 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 ...here ''k'' is one of the remaining 17 (now 5) candidates for [[Sierpiński number]]s smaller than 78557, and ''n'' a positive integer. In order to find such
    3 KB (544 words) - 16:44, 21 July 2019
  • M2
    | number= 7
    193 bytes (19 words) - 13:43, 17 February 2019
  • M3
    | number= 31
    194 bytes (19 words) - 13:43, 17 February 2019
  • M4
    | number= 127
    195 bytes (19 words) - 13:44, 17 February 2019
  • M5
    | number= 8191
    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 ...l factoring]]. Pervushin used the [[Lucas-Lehmer test]] to prove that this number is prime.
    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
    ...umber is exactly divisible. For the L-L test a zero residue means that the number is [[prime]].
    1 KB (235 words) - 10:24, 6 February 2019
  • GIMPS clients
    So, to test a number efficiently, one must apply the theory to get the tests down to the "weeks" ...came popular among PC enthusiasts and [[Overclocking|overclockers]] as its number-crunching algorithms exercise the computer's processor and memory to their
    8 KB (1,218 words) - 15:37, 13 August 2020

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