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• Mersenne prime
  ...2}</math>, where <math>S_0=4</math> and for <math>k>0</math>, <math>S_k=S_{k-1}^2-2</math>. * [[Riesel prime 2 1|Riesel primes for k=1]]
  5 KB (857 words) - 14:53, 19 September 2021
• Fermat number
  *'''[[Proth's theorem]]''' -- (1878) Let {{V|N}} = {{Kbn|+|k|2|m}} with odd {{Vk}} < 2^{{V|m}}. If there is an integer {{V|a}} ...des <math>S_{2^n-2}</math> where <math>S_0=5</math> and <math>S_{k+1}=S^2_{k}-2</math> ([http://www.robertgerbicz.tar.hu/Fermatnumbers.pdf Proof] by Rob
  12 KB (1,913 words) - 14:35, 9 August 2021
• Cunningham project
  :<math>(b^{kn}-1) = (b^n-1) \sum _{r=0}^{k-1} b^{rn}</math> for any value of <math>k</math> and
  7 KB (1,150 words) - 23:48, 19 April 2023
• Lucas-Lehmer test
  ...ath>\omega</math> to get that <math>\omega^{k-j}=1</math>, with <math>1\le k-j\le F^2-1</math>. We have proven that <math>\omega</math> satisfies <math Any number of the form <math>I_k=\omega^k + \bar\omega^k</math>, where <math>k</math> is positive odd integer, can be used as an initial value <math>S_0</
  20 KB (3,572 words) - 14:30, 17 February 2019
• Conjectures 'R Us
  For every base ({{Vb}} &le; 1030) for the forms {{Kbn|±|k|b|n}} there is a {{Vk}}-value for each form that has been conjectured to be Assist in proving the [[Liskovets-Gallot conjectures]] for the forms {{Kbn|±|k|2|n}} where {{Vn}} is always odd '''and''' where {{Vn}} is always even.
  3 KB (503 words) - 04:44, 27 March 2024
• Fast Fourier transform
  :<math>\large f_j = \sum_{k=0}^{n-1} x_k e^{-{2\pi i \over n} jk } \qquad j = 0, ... ,n-1.</math> ...Tukey FFTs, for example), via the identity <math>jk = -(j-k)^2/2 + j^2/2 + k^2/2</math>.
  17 KB (2,684 words) - 18:50, 28 September 2023
• No Prime Left Behind
  ...n 2008-01-10. The project searches for [[Riesel prime]]s of the form {{Kbn|k|2|n}} with odd {{Vk}} and 300 < {{Vk}} < 1001 and {{Vn}} > 260000 not reser
  752 bytes (111 words) - 11:31, 5 October 2020
• Rational number
  :<math>\large a + \frac{k(b-a)}{n+1}</math> by varying the number <math>k</math> from 1 to <math>n</math>. Then we can make the value <math>n</math>
  3 KB (541 words) - 15:01, 26 March 2023
• Modular arithmetic
  ...>2^m</math>, let the number to be inverted be <math>N</math> and let <math>k = \log_2 m</math> rounded to the next integer. Then the method is: # Perform k times: Set x = x(2-Nx) mod 2^m
  4 KB (625 words) - 10:25, 23 January 2019
• Montgomery multiplication
  ...] \,+\, a'[1] * 2^k \,+\, a'[2] * 2^{2k} \,+\, ... \,+\, a'[s-1] * 2^{(s-1)k}</math>. and similarly for b' and c'. The number <math>k</math> is the number of bits of the integer, and <math>n = ks</math>.
  4 KB (582 words) - 17:01, 29 August 2022
• Elliptic curve method
  ...ion does not change by multiplying all coordinates by the same value <math>k\neq 0</math>. ...y using another point. When we compute k'''P''' we will be also computing (k+1)'''P'''.
  19 KB (3,181 words) - 22:27, 6 July 2023
• Wacław Sierpiński
  ...ntegers {{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
  ...ierpiński number''' is an odd natural number {{Vk}} such that all {{Kbn|+|k|n}} for all {{Vn}} are [[Composite number|composite]].
  324 bytes (48 words) - 13:37, 8 April 2023
• Sierpiński problem
  Consider numbers of the form {{V|N}} = {{Kbn|+|k|n}}, where {{Vk}} is odd and {{Vn}} > 0. If, for some fixed {{Vk}}, every i
  5 KB (650 words) - 10:25, 26 March 2024
• Seventeen or Bust
  |result=11 k's eliminated as a standalone project, 1 k eliminated as a subproject on PrimeGrid ...he project is to find [[prime]]s of the form <math>k*2^n+1</math>, where ''k'' is one of the remaining 17 (now 5) candidates for [[Sierpiński number]]s
  3 KB (544 words) - 16:44, 21 July 2019
• Perfect number
  :where ''q'', ''p''₁, &hellip;, ''p''_''k'' are distinct primes and ''q'' &equiv; &alpha; &equiv; 1 (mod 4) (Eu
  6 KB (885 words) - 11:33, 7 March 2019
• Mfaktc
  *[[Factor]] sizes <math><2^{95}</math> and '''[[value k]]''' <math><2^{63.9}</math>
  5 KB (765 words) - 14:54, 25 February 2019
• Mfakto
  ...ssSize: defines how far many bits of the sieve each TF block processes (in K bits). Larger values may lead to less wasted cycles by reducing the number
  17 KB (2,524 words) - 12:39, 24 January 2019
• Riesel number
  A '''Riesel number''' is a value of ''k'' such that {{Kbn|k|n}} is always composite for all [[natural number]]s.
  827 bytes (112 words) - 08:21, 25 March 2024
• Primality test
  *[[Proth's theorem]]: Used to test numbers of the form {{Kbn|+|k|n}} with 2^{{Vn}} > {{Vk}}, making it useful in several [[distrib
  3 KB (501 words) - 05:20, 3 August 2021

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