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• Primality testing program
  | k × bⁿ±c general numbers | k × bⁿ±c
  2 KB (314 words) - 21:23, 29 August 2019
• Pépin's test
  ...t 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
• Proof by induction
  :<math>\sum_{k=1}^{n}\,(2k-1)\,=\,n^{2}</math> ::<math>\sum_{k=1}^{1}\,(2k-1)\,=\,2-1\,=\,1^{2}</math>
  4 KB (679 words) - 13:57, 20 February 2019
• GIMPS factoring and sieving
  ...e of the algebraic form <math>2kp+1</math> for some positive integer <math>k</math> and furthermore must also leave a remainder of either 1 or 7 upon di
  6 KB (962 words) - 10:08, 7 March 2019
• LLR
  **[[Lucas-Lehmer-Riesel algorithm]] for {{Kbn|k|n}} numbers. **[[Proth's theorem|Proth algorithm]] for {{Kbn|+|k|n}} numbers.
  2 KB (300 words) - 22:00, 16 December 2023
• P-1 factorization method
  ...1</math>, where ''k'' is a non-negative integer. This means that <math>a^{k(p-1)} - 1</math>
  5 KB (814 words) - 01:35, 12 March 2019
• Self-initializing quadratic sieve
  ...operatorname{tlog}[p]</math> to all locations <math>\operatorname{soln1} + k*p</math> of the sieve array. ...operatorname{tlog}[p]</math> to all locations <math>\operatorname{soln2} + k*p</math> of the sieve array.
  10 KB (1,763 words) - 02:56, 12 March 2019
• Miller-Rabin pseudoprimality test
  ...er being tested for primality, and <math>N = 2^n\,k + 1</math> where <math>k</math> is an odd number. Then consider the sequence <math>a^k</math>, <math>a^{2k}</math>, <math>a^{4k}</math>..., <math>a^{N-1}</math> m
  3 KB (432 words) - 15:33, 28 January 2019
• Generalized Fermat number
  ...F_{n,2}</math> numbers can be proven prime by using [[Pépin's test]] with k=5. ...[[Generalized Fermat number]]s for any [[Proth prime|Proth primes {{Kbn|+|k|n}}]] are listed as ''GF Divisor'' on their own page. They are listed as ''
  5 KB (726 words) - 09:57, 12 September 2021
• PrimeGrid
  ...rime Search|Proth Prime Search]]: searching for primes of the form {{Kbn|+|k|2|n}}. ...ed|Proth Prime Search Extended]]: searching for primes of the form {{Kbn|+|k|2|n}}.
  3 KB (458 words) - 10:28, 26 March 2024
• Sieve of Eratosthenes
  *First, list out all the integers <math>1 \leq k \leq N</math>. ...ssary because all composite numbers <math>11 \geq \sqrt{N} = 10 \geq \sqrt{k}</math> have already been crossed out.
  4 KB (654 words) - 11:10, 6 February 2019
• Twin Prime Search
  ...t that looks for large [[twin prime]]s ([[Riesel prime|Riesel type]] {{Kbn|k|n}}) of world record size.
  826 bytes (100 words) - 11:04, 21 March 2024
• Riesel Prime Search
  :The project is searching for [[Riesel prime]]s {{Kbn|k|n}}, {{Vk}} > 1.
  845 bytes (120 words) - 02:21, 1 May 2024
• Seventeen or Bust/Factoring
  factor | k*2^n+1
  3 KB (491 words) - 13:39, 1 February 2019
• Seventeen or Bust/PRP
  ==Working on the k,n pair==
  888 bytes (145 words) - 13:40, 1 February 2019
• Sieving
  ...ts of the array <math>k</math>, <math>k+p</math>, <math>k+2p</math>, <math>k+3p</math>, and so on correspond to multiples of the prime.
  3 KB (521 words) - 11:14, 6 February 2019
• Sieving program
  ...of numbers of the form K &times; 2ⁿ + 1 or - 1. Independent of K's, but good for many N's too) and [[TPSieve]] (similar to PPSieve, but for *[[TwinGen]] (performing sieving of numbers of the form k&times;2ⁿ+/-1) http://www.underbakke.com/primes/
  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
• Proth's theorem
  Let <math>p = k*2^n+1</math> and <math>k < 2^n</math>; then <math>p</math> is prime if there is an integer <math>a</
  549 bytes (88 words) - 18:15, 28 September 2023
• Proth prime
  ...f numbers, but primes in the form {{Kbn|+|k|n}} with 2^''n'' > ''k'' are often called Proth primes. *[[Proth prime table|Table]] with all available ''k''-values
  656 bytes (91 words) - 07:02, 31 August 2020

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