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• Generalized Fermat number
  ...e built a list of large primes of the form: b^{2^m}+1, ''b ≥ 2'' and ''m ≥ 1''. ...primes of the form: a^{2^m}+b^{2^m}, ''b > a ≥ 2'' and ''m ≥ 1''.
  5 KB (726 words) - 09:57, 12 September 2021
• PrimeGrid
  ...eralized Fermat Prime Search]]: searching for primes of the form {{Kbn|+|1|b|2^{{Vn}}}}. ...eralized Cullen Prime Search]]: searching for primes of the form {{Kbn|+|n|b|n}}.
  3 KB (458 words) - 10:28, 26 March 2024
• Aliquot sequence
  :<math>s_n = \sigma(s_{n-1}) - s_{n-1}</math> :<math>N=p^{a}*q^{b}*r^{c}</math>. . .
  6 KB (914 words) - 19:49, 21 February 2023
• Math rendering
  | <code>\exp_a b = a^b, \exp b = e^b, 10^m</code> | <math>\exp_a b = a^b, \exp b = e^b, 10^m</math>
  33 KB (4,920 words) - 10:54, 7 March 2019
• Sieving
  ...nce forms an arithmetic progression, so it has the form <math>m\, =\, an + b</math>, while in the second the sequence has the form <math>m\, =\, an^2 + ...n</math> is the element number of the array. We have to compute <math>k = -b/a \,\pmod p</math>. Then the elements of the array <math>k</math>, <math>k+
  3 KB (521 words) - 11:14, 6 February 2019
• Sieving program
  ...ieve]] (performing sieving of generalized Cullen/Woodall numbers n &times; bⁿ+-1) http://sites.google.com/site/geoffreywalterreynolds/program *[[AthGFNSieve]] (performing sieving of generalized Fermat numbers b^2ⁿ+1) http://www.underbakke.com/AthGFNsv/
  2 KB (220 words) - 11:42, 7 March 2019
• NewPGen
  *k&times;bⁿ+1 *k&times;bⁿ-1
  3 KB (529 words) - 09:32, 7 March 2019
• Multiple polynomial quadratic sieve
  ...t^2\equiv u\,\pmod N</math> where <math>t = ax+b</math> and <math>u = g_{a,b}(x)</math>. ...agraph does not depend on the particular values of <math>a</math> or <math>b</math>, so the factor base can be computed at the beginning of MPQS. The up
  6 KB (1,068 words) - 14:33, 13 February 2019
• GIMPS chances of finding a prime number
  ...ed to the default limits for exponent p, that it has 1 chance in ( p / ( (b-1) x 1.803 )) of being prime.
  3 KB (593 words) - 10:09, 7 March 2019
• Worktodo.txt
  *[[PRP]]=k,b,n,c<nowiki>[</nowiki>,how_far_factored,tests_saved<nowiki>][</nowiki>,known *Pfactor=assignment ID,[[value k|k]],b ([[base]]),n ([[exponent]]),c,how far factored,[[Lucas-Lehmer test|LL]] tes
  2 KB (273 words) - 22:58, 11 May 2019
• P+1 factorization method
  <math>\large U_n = uU_{n-1} - U_{n-2}\,,\, V_n = uV_{n-1} - V_{n-2}</math> for <math>n\geq 2</math> ...iplication explained above can be translated to pseudocode as follows (let B = V_n):
  8 KB (1,536 words) - 11:35, 12 February 2019
• SNFS polynomial selection
  ...resulting polynomial is symmetric: (for the sake of less typing, let <math>b=a^k</math>) ...b^{11}-1)/(b-1) = b^{10} + b^9 + b^8 + b^7 + b^6 + b^5 + b^4 + b^3 + b^2 + b + 1</math>
  7 KB (1,238 words) - 16:14, 12 February 2019
• Aurifeuillian factor
  ...rs of the form <math>b^n - 1</math> or <math>\Phi_n(b)</math>, where <math>b = s^2 \cdot t</math> with [[Square-free integer|square-free]] <math>t</math ...d 4, <math>b^n-1</math> have aurifeuillean factorization, otherwise, <math>b^n+1</math> have aurifeuillean factorization.
  10 KB (1,257 words) - 08:04, 24 June 2019
• Cullen number
  ...generalized Cullen number''' base {{Vb}} is a number of the form {{Kbn|+|n|b|n}}. '''(perhaps own page?)'''
  2 KB (252 words) - 17:39, 31 August 2021
• Factoring program
  ...d MacOSX) (performing ECM, P-1, and P+1 to search for factors of a &times; bⁿ ± c) ftp://mersenne.org/gimps/, also http://mersenneforum.org/
  2 KB (273 words) - 21:53, 8 July 2023
• Mtsieve
  ...factors of numbers in the form {{Kbn|+|k|b|n}} and {{Kbn|k|b|n}} for fixed b and n and variable k *fkbnsieve: search for factors of the form k*bⁿ+c for fixed k, b, and n and variable c
  2 KB (338 words) - 06:58, 28 March 2023
• Carol-Kynea prime
  ...nea numbers''' are numbers of the form <math>(b^n-1)^2-2</math> and <math>(b^n+1)^2-2</math>, respectively, while '''Carol primes''' and '''Kynea primes ...<math>(b^n-1)^2-2</math> and a Kynea number is a number of the form <math>(b^n+1)^2-2</math>. A Carol/Kynea prime is a [[prime]] which has one of the ab
  8 KB (1,172 words) - 00:38, 6 July 2023
• Williams prime MM least
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|(b-1)|b|n}}, least {{Vn}}-values}} ...Vb}} ≤ 2049 which generates a [[Williams prime]] of the form {{Kbn|(b-1)|b|n}}.
  2 KB (211 words) - 07:40, 1 August 2021
• Sieving a range of sequences
  Sieving a range {{Kbn|3|2|n}} to {{Kbn|20|19|n}} (in general {{Kbn|(b+1)|b|n}}) create a batch file named "run.bat" with: srsieve -G -n 1 -N 10000 -P 3000000000 "%b1%*%base%^n-1"
  775 bytes (124 words) - 08:39, 22 April 2019
• LLR testing a range of sequences
  Testing a range {{Kbn|3|2|n}} to {{Kbn|20|19|n}} (in general {{Kbn|(b+1)|b|n}}) create a batch file named "run.bat" with:
  871 bytes (147 words) - 12:29, 23 April 2019

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