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• 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}} ...'s theorem is known as '''[[Pépin's test]]'''. Although Pépin's test and Proth's theorem have been implemented on computers to prove the compositeness of
  12 KB (1,913 words) - 14:35, 9 August 2021
• 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 ...699]], [[Proth prime 2 24737|24737]], [[Proth prime 2 55459|55459]], and [[Proth prime 2 67607|67607]] (current status [https://www.primegrid.com/stats_sob_
  5 KB (650 words) - 10:25, 26 March 2024
• Riesel number
  A '''Riesel number''' is a value of ''k'' such that {{Kbn|k|n}} is always composite for all [[natural number]]s. *[[Riesel and Proth Prime Database]]
  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
• Pépin's test
  ...: "The test that we today call Pépin's test is actually [[Proth's theorem|Proth's test]] with a proof provided by Lucas". ...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
• 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
• 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
  *Type Proth: ...rime Search|Proth Prime Search]]: searching for primes of the form {{Kbn|+|k|2|n}}.
  3 KB (458 words) - 10:28, 26 March 2024
• 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 *[[FermFact]] (performing sieving of Proth numbers) http://www.fermatsearch.org/FermFact-09b.zip
  2 KB (220 words) - 11:42, 7 March 2019
• Proth's theorem
  This article is about '''Proth's theorem'''. Proth's theorem (1878) states:
  549 bytes (88 words) - 18:15, 28 September 2023
• Proth prime
  ...in the form {{Kbn|+|k|n}} with 2^''n'' > ''k'' are often called Proth primes. *[[Proth's theorem]]
  656 bytes (91 words) - 07:02, 31 August 2020
• Riesel prime
  ...ial definition of a '''Riesel prime''' mostly all primes of the form {{Kbn|k|n}} with 2^{{Vn}} > {{Vk}} are called like this on many pages. ...mersenneforum.org/showthread.php?t=29635 "Team drive #1 for {{Vk}}<300: 26 k's for {{Vn}}>2M"]: [https://www.mersenneforum.org/showpost.php?p=655608 #1
  2 KB (279 words) - 03:48, 24 April 2024
• Proth number
  In [[number theory]], a '''Proth number''' is a number of the form :{{V|N}} = {{Kbn|+|k|2|n}}
  670 bytes (104 words) - 10:59, 9 July 2021
• Gerbicz error checking
  It is also used by [[LLR]] and [[LLR2]] to ensure validity of [[Proth prime|Proth]] tests and PRP tests on base-2 [[Riesel prime]] candidates, and by those p ...the original formulation of the Gerbicz error check for [[Proth's theorem|Proth tests]], as described in [https://www.mersenneforum.org/showthread.php?t=22
  3 KB (528 words) - 14:59, 3 October 2023
• Proth prime 2 301
  {{Proth prime {{HistF|2012-01-29|1455620|Gus Obermeyer,PrimeGrid Proth Prime Search‎}}
  1 KB (103 words) - 12:07, 7 September 2021
• Proth prime small bases least n
  {{DISPLAYTITLE:Proth primes of the form {{Kbn|+|k|b|n}}, least ''n''-values}} ...h prime]] of the form {{Kbn|+|k|b|n}} for 2 ≤ ''b'' ≤ 1030 and 2 ≤ ''k'' ≤ 12.
  7 KB (789 words) - 11:31, 26 October 2023
• Proth.exe
  |title=Proth '''Proth.exe''' is an ancient program that implements [[Proth's theorem]]. It is used to test the primality of the following forms:
  667 bytes (101 words) - 16:44, 31 August 2021
• Proth prime 2 255
  {{Proth prime {{HistF|2015-02-14|2668448|Gerrit Slomma,PrimeGrid Proth Prime Search}}
  2 KB (245 words) - 10:36, 12 September 2021
• Proth prime 2 513
  {{Proth prime {{HistF|2014-04-01|2135642|Joshua Whiteley,PrimeGrid Proth Prime Search}}
  2 KB (177 words) - 09:40, 7 September 2021
• Proth prime 2 801
  {{Proth prime {{HistF|2021-05-16|3036045|Nathaniel Adam,PrimeGrid Proth Prime Search}}
  1 KB (99 words) - 11:13, 17 September 2021

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