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  • Double check
    ...volved 2 independent double checks. [[Mlucas]] and [[Glucas]] are used and 2 different processor types are used. [[Landon Curt Noll]]'s [[Mprime (Cray)|
    2 KB (373 words) - 15:08, 5 June 2019
  • Residue
    Here is the Lucas test for <math>2^7-1</math>, which is 127: :S1 = (4 * 4 - 2) mod 127 = 14
    1 KB (235 words) - 10:24, 6 February 2019
  • GIMPS clients
    ! rowspan="2" | Hardware ...one, and the average GIMPS participant has completed less than three (mean 2.67).
    8 KB (1,218 words) - 15:37, 13 August 2020
  • Mfaktc
    ...variants) should work. (The [[Mfaktc#Future|next version]] will require CC 2.0 or newer.) **executables: CUDA >= 4.2 capable driver (295 series or newer)
    5 KB (765 words) - 14:54, 25 February 2019
  • Mfakto
    -v <n> verbosity level: 0=terse, 1=normal, 2=verbose, 3=debug -tf <exp> <min> <max> trial factor M<exp> from 2^<min> to 2^<max> and exit instead of parsing the worktodo file
    17 KB (2,524 words) - 12:39, 24 January 2019
  • Rho factorization method
    *x<sub>2</sub> = f(x<sub>1</sub>) ...<sub>n+1</sub> = x<sub>n</sub><sup>2</sup> + a, where a <math>\neq </math>-2.
    3 KB (558 words) - 10:28, 6 February 2019
  • Riesel number
    ...ński problem]] article, [[Hans Riesel]] found in 1956 that [[Riesel prime 2 509203|{{Kbn|509203|n}}]] is always composite. *[[Riesel 2 Riesel|Riesel numbers]]
    827 bytes (112 words) - 08:21, 25 March 2024
  • M12
    ...son|Robinson]] at [[University of California, Los Angeles]] found [[M13]], 2<sup>521</sup>-1. ...mula (2<sup>2</sup>-1=7) also produces a prime. When this value is tested (2<sup>7</sup>-1=127), another prime is produced. So, Lucas was testing to see
    2 KB (354 words) - 14:52, 19 September 2021
  • Primality test
    *[[Proth's theorem]]: Used to test numbers of the form {{Kbn|+|k|n}} with 2<sup>{{Vn}}</sup> > {{Vk}}, making it useful in several [[distributed comput
    3 KB (501 words) - 05:20, 3 August 2021
  • Lucas primality test
    Prove that N = 811 is prime knowing that N-1 = 2 &times; 3<sup>4</sup> &times; 5 :<math>3^{810/2}\,= \,3^{405}\,\equiv \, 810\,\pmod{811}</math>
    1 KB (177 words) - 14:31, 17 February 2019
  • Square root
    For example, <math>\sqrt 9 = 3</math> since <math>3^2 = 3 \times 3 = 9</math>. ...uadratic equations such as <math>x^2=9</math> or, more generally, <math>ax^2+bx+c=0</math>.
    13 KB (1,873 words) - 16:52, 24 October 2020
  • Pépin's test
    ...r 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. ...<math>F_n = 2^{2^n}+1</math> is a prime if and only if <math>\ 3^{(F_n-1)/2} \ \equiv -1 \ \pmod{F_n}</math>.
    2 KB (401 words) - 14:40, 6 March 2019
  • Proof by induction
    *'''Step 2''' :<math>\sum_{k=1}^{n}\,(2k-1)\,=\,n^{2}</math>
    4 KB (679 words) - 13:57, 20 February 2019
  • Floating-point
    ...and scaled using an [[exponent]]. The [[base]] for the scaling is normally 2, 10 or 16. The typical number that can be represented exactly is of the for
    2 KB (294 words) - 22:56, 3 February 2019
  • Complex number
    ...on is <math>z = x + iy</math>. From the previous paragraph we get: <math>i^2 = -1</math>. ..._1 y_1 + x_2 y_2}{x_2^2 + y_2^2}\,+\,\frac {x_2 y_1 - x_1 y_2}{x_2^2 + y_2^2} \,i</math>
    2 KB (280 words) - 14:59, 26 March 2023
  • Operation Billion Digits
    *'''M(''exponent'') no factor from 2^(''startdepth'') to 2^(''end depth'')'''. ...system. They're currently at Level 21.07 (around twenty one candidates to 2^87). Their greatest factor was found at bit depth 85 by Åke Tilander, a fa
    6 KB (918 words) - 16:28, 24 July 2020
  • M37
    ...hort hand used to refer to the 37th [[Mersenne prime]]. Specifically it is 2<sup>{{Num|3021377}}</sup>-1. This number was discovered to be [[prime]] on
    877 bytes (111 words) - 11:04, 18 February 2019
  • Team Prime Rib
    ...ting power#P90 years|P90 CPU years]] of [[Lucas-Lehmer test|LL testing]] (#2 in [[PrimeNet]]) and over 7200 P90 CPU years of [[GIMPS factoring and sievi
    620 bytes (88 words) - 11:46, 12 February 2019
  • GIMPS factoring and sieving
    It is known that any factor of the Mersenne number <math>2^p-1</math> must be of the algebraic form <math>2kp+1</math> for some positi ...t an efficient way to do this, however! It is much easier to compute <math>2^p\,\bmod n</math>, i.e., the remainder after division by <math>n</math> by
    6 KB (962 words) - 10:08, 7 March 2019
  • Quadratic residue
    :<math>{x^2}\equiv{q}\ (mod\ p)</math>
    823 bytes (117 words) - 20:11, 26 October 2020

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