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• Mersenne prime
  ...Mersenne number]]s (not necessarily primes, but candidates for primes) are numbers that are one less than a power of two; hence, ...umber|even]] perfect numbers have this form. No [[odd number|odd]] perfect numbers are known, and it is suspected that none exists.
  5 KB (857 words) - 14:53, 19 September 2021
• MersenneForum
  *[[Riesel Prime Search]] *[[Sierpiński-Riesel Base 5]]
  2 KB (294 words) - 20:11, 11 August 2024
• Sierpiński problem
  Consider numbers of the form {{V|N}} = {{Kbn|+|k|n}}, where {{Vk}} is odd and {{Vn}} > 0. If ...ence {{Kbn|+|78557|n}} can be prime. The same arguments can be said of the numbers 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, 965
  5 KB (650 words) - 10:25, 26 March 2024
• Covering set
  ...'''covering set''' for a sequence of integers refers to a set of [[prime]] numbers such that every term in the sequence is divisible by at least one member of *[[Riesel problem 1|Riesel problem]]
  380 bytes (56 words) - 10:27, 26 March 2024
• Riesel number
  A '''Riesel number''' is a value of ''k'' such that {{Kbn|k|n}} is always composite for ...the [[Sierpiński problem]] article, [[Hans Riesel]] found in 1956 that [[Riesel prime 2 509203|{{Kbn|509203|n}}]] is always composite.
  827 bytes (112 words) - 08:21, 25 March 2024
• Primality test
  ==Primality tests for numbers {{V|N}} with special form== *[[LLR|Lucas–Lehmer–Riesel test]]: Used for [[Riesel prime]]s.
  3 KB (500 words) - 05:03, 11 August 2024
• LLR
  ...Primality testing program|program]] available to perform primality test on numbers of the form {{Vk}}•2^{{Vn}}±{{V|c}}. *the fastest algorithms are for base two numbers (with {{Vk}} < 2^{{Vn}}):
  2 KB (300 words) - 22:00, 16 December 2023
• Generalized Fermat number
  John Cosgrave has studied the following numbers: Numbers of the form: <math>F_{n,r} = \sum_{i=0}^{p-1} \ 2^{i p^{n}} \ = \ 2^{(p-1)p
  5 KB (774 words) - 07:39, 27 May 2024
• PrimeGrid
  ...Grid''' is a [[distributed computing]] project for searching for [[prime]] numbers of world-record size. It makes use of the [[BOINC|Berkeley Open Infrastruct ...ierpiński base 5|Sierpiński base 5]]: helping to solve the [[Sierpiński-Riesel Base 5]] Problem.
  3 KB (458 words) - 10:28, 26 March 2024
• Riesel Sieve
  The '''Riesel sieve project (RSP)''' is a [[distributed computing]] project. It is now a ...nd primes for all the remaining k values to prove that they are not Riesel numbers.
  2 KB (326 words) - 10:29, 26 March 2024
• Proth number
  ...^{{Vn}} > {{Vk}}, all odd integers greater than 1 would be Proth numbers, but most pages lists them, too. ...nd [[Fermat number]]s ({{Kbn|+|2ⁿ}}) are special forms of Proth numbers.
  670 bytes (104 words) - 10:59, 9 July 2021
• Gerbicz error checking
  ...o ensure validity of [[Proth prime|Proth]] tests and PRP tests on base-2 [[Riesel prime]] candidates, and by those programs and [[PRST]] in an extended versi ...um.org/showthread.php?t=22510 Original proposal of the technique for Proth numbers]
  3 KB (528 words) - 14:59, 3 October 2023
• Tutorial LLR
  '''Tutorial to LLR (Lucas Lehmer Riesel) and PRP:''' [[LLR]] is a program used to prove primality of numbers. It can be rather slow (but faster if you support [[SSE2]]), and that's why
  2 KB (337 words) - 13:24, 20 February 2019
• Riesel 2 Low-weight
  {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with Nash weight < 1000}} Riesel numbers {{Kbn|k|n}} where the [[Nash weight]] is smaller than 1000.
  948 bytes (121 words) - 13:08, 21 July 2021
• PrimeGrid Sophie Germain Search
  The most recent iteration of the project searched for prime numbers of the form {{Kbn|k|1290000}}, for ''k'' ≤ 10¹³. The first version of the project searched for prime numbers {{Kbn|k|n}} for 666,666 ≤ ''n'' ≤ 666,691 with varying ranges of ''k''
  3 KB (337 words) - 15:13, 16 December 2023
• Riesel 2 Riesel
  {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}}}} ...are odd numbers {{Vk}} for which {{Kbn|k|n}} is composite for all natural numbers {{Vn}}.
  808 bytes (110 words) - 21:12, 17 December 2023
• Riesel 2 Count-100
  {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with 100 and more primes}} Riesel numbers {{Kbn|k|n}} with 100 or more prime values {{Vn}}.
  911 bytes (120 words) - 21:56, 25 July 2021
• Riesel 2 15k-value
  {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with {{Vk}} mod 15 = 0}} Riesel numbers {{Kbn|k|n}} where {{Vk}}-value is a multiple of 15.
  1 KB (156 words) - 06:59, 16 July 2021
• Riesel 2 2145k-value
  {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with {{Vk}} mod 2145 = 0}} Riesel numbers {{Kbn|k|n}} where {{Vk}}-value is a multiple of 2145.
  1 KB (156 words) - 07:01, 16 July 2021
• Riesel 2 2805k-value
  {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}} with {{Vk}} mod 2805 = 0}} Riesel numbers {{Kbn|k|n}} where {{Vk}}-value is a multiple of 2805.
  1 KB (156 words) - 07:08, 16 July 2021

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