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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
• Conjectures 'R Us
  ...]] in search for lowest [[Sierpiński number|Sierpiński]]/[[Riesel number|Riesel]] values.}} ...t '[[Sierpiński number|Sierpiński value]]' (+1 form) or '[[Riesel number|Riesel value]]' (-1 form) that is composite for all values of {{Vn}} &ge; 1. Conje
  3 KB (503 words) - 02:20, 1 May 2024
• 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
  745 bytes (111 words) - 02:17, 1 May 2024
• 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 *[[Riesel problem 1|Riesel problem]]
  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. ...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
  *[[LLR|Lucas–Lehmer–Riesel test]]: Used for [[Riesel prime]]s. *[[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
• LLR
  '''LLR (Lucas Lehmer Riesel)''' is probably the fastest [[Primality testing program|program]] available **[[Lucas-Lehmer-Riesel 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. ==Björn & Riesel==
  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
• 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
  '''Riesel Prime Search''' (RPS) is a prime searching project established in 2005 by [ :The project is searching for [[Riesel prime]]s {{Kbn|k|n}}, {{Vk}} > 1.
  845 bytes (120 words) - 02:21, 1 May 2024
• 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
• Riesel Sieve
  The '''Riesel sieve project (RSP)''' is a [[distributed computing]] project. It is now a ...e to find 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
  :{{V|N}} = {{Kbn|+|k|2|n}} *[[Riesel number]]
  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 Let <math>p</math> be a Proth number, and let <math>k</math>, <math>n</math>, and <math>a</math> be defined as on [[Proth's theor
  3 KB (528 words) - 14:59, 3 October 2023
• Sierpiński number base 5
  A '''Sierpiński number base 5''' is a value of {{Vk}} such that {{Kbn|+|k|5|n}} is always [[composite number|composite]]. ...r not, a [[distributed computing project]] was created named [[Sierpiński-Riesel Base 5]].
  556 bytes (83 words) - 10:57, 14 October 2020
• Riesel number base 5
  A '''Riesel number base 5''' is a value of ''k'' such that {{Kbn|-|k|5|n}} is always a [[composite number]]. Using the same method presented in the [[Riesel problem 1|Riesel problem]] article, it was found that {{Kbn|-|346802|5|n}} is multiple of 3,
  589 bytes (90 words) - 10:30, 26 March 2024
• Riesel problem 1
  {{DISPLAYTITLE:Riesel problem, {{Kbn|-|k|2|n}}, {{Vk}} < {{Num|509203}}}} The '''Riesel problem''' involves determining the smallest [[Riesel number]].
  6 KB (689 words) - 18:14, 4 April 2024
• Tutorial LLR
  '''Tutorial to LLR (Lucas Lehmer Riesel) and PRP:''' The projects [[Prime Sierpiński Project]] and [[Riesel Sieve]] also use [[LLRNET]], which is recommended for people with a perman
  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
• Riesel prime small bases least n
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|b|n}}, least {{Vn}}-values}} ...wn the least {{Vn}} &ge; 1 generating a [[Riesel prime]] of the form {{Kbn|k|b|n}} for 2 &le; {{Vb}} &le; 1030 and 2 &le; {{Vk}} &le; 12.
  6 KB (684 words) - 09:40, 17 March 2024
• Riesel prime 2 10001
  {{Riesel prime {{HistC|2019|3440042|Rüdiger K. Eckhard}}
  775 bytes (85 words) - 00:10, 17 July 2021
• Riesel prime 2 61
  {{Riesel prime {{HistF|2017-01-30|3366033|Rüdiger K. Eckhard}}
  2 KB (208 words) - 02:44, 12 May 2024
• Riesel prime 2 215
  {{Riesel prime {{HistF|1999-06-29|109130|Rüdiger K. Eckhard}}
  1 KB (133 words) - 05:02, 17 April 2024
• RPS Drive 10
  *Name: [[Riesel Prime Search]] Drive 10 *Purpose: The goal of this drive is to search for primes of the form '''{{Kbn|k|n}}''' for '''128 low-weighted {{Vk}}'s with 10000 < {{Vk}} < 35000'''.
  2 KB (290 words) - 22:54, 10 April 2024
• Riesel 2 1-300
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, {{Vk}} < 300}} Automatically generated table from available [[:Category:Riesel 2 1-300|Riesel primes {{Vk}} < 300]].
  855 bytes (117 words) - 07:27, 16 July 2021
• RPS Megabit Drive 1
  The goal of this drive is to search for primes of the form {{Kbn|k|n}} for {{Vk}} &le; 300 and {{Vn}} > 1000000. | [[Riesel prime 2 35|35]] || {{GP|Riesel prime 2 35|RNash}} || 12517 || 2520000 - ||
  4 KB (439 words) - 10:45, 9 May 2024
• RPS Megabit Drive 2
  The goal of this drive is to search for primes of the form {{Kbn|k|n}} for {{Vk}} &le; 300 and {{Vn}} > 1000000. | [[Riesel prime 2 115|115]] || {{GP|Riesel prime 2 115|RNash}} || 43318 || 1000000 - || 1141719, 1524183
  4 KB (376 words) - 21:41, 8 May 2024
• RPS Megabit Drive 3
  The goal of this drive is to search for primes of the form {{Kbn|k|n}} for {{Vk}} &le; 300 and {{Vn}} > 1400000. | [[Riesel prime 2 203|203]] || {{GP|Riesel prime 2 203|RNash}} || 23371 ||
  2 KB (155 words) - 07:18, 7 May 2024
• Riesel 2 10e4-10e5
  __NOTOC__{{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, {{Num|10000}} &le; {{Vk}} &le; {{Num|25000}}}} *For {{Num|25000}} &le; {{Vk}} &le; {{Num|100000}} see [[Riesel 2 10e4-10e5a|here]]
  1 KB (176 words) - 09:20, 22 July 2021
• Riesel 2 4000-6000
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 4000 < {{Vk}} < 6000}} Automatically generated table from available [[:Category:Riesel 2 4000-6000|Riesel primes 4000 < {{Vk}} < 6000]].
  883 bytes (117 words) - 08:42, 22 July 2021
• Riesel 2 300-2000
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 300 < {{Vk}} < 2000}} Automatically generated table from available [[:Category:Riesel 2 300-2000|Riesel primes 300 < {{Vk}} < 2000]].
  878 bytes (117 words) - 08:27, 22 July 2021
• RPS Drive 7
  *Name: [[Riesel Prime Search]] Drive 7 *Purpose: The goal of this drive is to search for primes of the form {{Kbn|k|n}} for 21 high-weighted 2200 < {{Vk}} < 3000.
  1 KB (123 words) - 03:03, 17 April 2024
• Riesel 2 10e5-10e6
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 10⁵ < {{Vk}} < 10⁶}} Automatically generated table from available [[:Category:Riesel 2 10e5-10e6|Riesel primes 10⁵ < {{Vk}} < 10⁶]].
  1 KB (153 words) - 09:34, 22 July 2021
• Riesel 2 10e6-10e7
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 10⁶ < {{Vk}} < 10⁷}} Automatically generated table from available [[:Category:Riesel 2 10e6-10e7|Riesel primes 10⁶ < {{Vk}} < 10⁷]].
  1 KB (153 words) - 09:46, 22 July 2021
• Riesel 2 10e7-10e8
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 10⁷ < {{Vk}} < 10⁸}} Automatically generated table from available [[:Category:Riesel 2 10e7-10e8|Riesel primes 10⁷ < {{Vk}} < 10⁸]].
  1 KB (153 words) - 09:58, 22 July 2021
• Riesel 2 10e8-10e9
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 10⁸ < {{Vk}} < 10⁹}} Automatically generated table from available [[:Category:Riesel 2 10e8-10e9|Riesel primes 10⁸ < {{Vk}} < 10⁹]].
  1 KB (153 words) - 10:00, 22 July 2021
• Riesel 2 10e9-10e10
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 10⁹ < {{Vk}} < 10¹⁰}} Automatically generated table from available [[:Category:Riesel 2 10e9-10e10|Riesel primes 10⁹ < {{Vk}} < 10¹⁰]].
  1 KB (153 words) - 10:05, 22 July 2021
• PrimeGrid Sierpiński base 5
  ==k-values left== *[[PrimeGrid Riesel base 5]]
  2 KB (245 words) - 11:43, 5 September 2021
• Riesel prime 2 10003
  {{Riesel prime {{HistC|2019|1999911|Rüdiger K. Eckhard}}
  267 bytes (22 words) - 06:58, 19 July 2021
• Riesel prime 2 10005
  {{Riesel prime {{HistF|2020-06-12|1573410|Rüdiger K. Eckhard}}
  979 bytes (92 words) - 06:59, 19 July 2021
• Riesel prime 2 10007
  {{Riesel prime {{HistC|2018|2256224|Rüdiger K. Eckhard}}
  359 bytes (29 words) - 07:00, 19 July 2021
• Riesel prime 2 10009
  {{Riesel prime {{HistF|2020-06-12|1580131|Rüdiger K. Eckhard}}
  401 bytes (31 words) - 07:00, 19 July 2021
• PrimeGrid Sophie Germain Search
  ...he project searched for prime numbers of the form {{Kbn|k|1290000}}, for ''k'' ≤ 10¹³. ...Kbn|k|1290001}} or {{Kbn|k|1289999}}, and Twin pairs take the form {{Kbn|+|k|1290000}}.<ref>[https://www.primegrid.com/forum_thread.php?id=1450&nowrap=t
  3 KB (337 words) - 15:13, 16 December 2023
• Riesel 2 2000-4000
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 2000 < {{Vk}} < 4000}} Automatically generated table from available [[:Category:Riesel 2 2000-4000|Riesel primes 2000 < {{Vk}} < 4000]].
  883 bytes (117 words) - 08:39, 22 July 2021
• Riesel 2 6000-8000
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 6000 < {{Vk}} < 8000}} Automatically generated table from available [[:Category:Riesel 2 6000-8000|Riesel primes 6000 < {{Vk}} < 8000]].
  883 bytes (117 words) - 08:56, 22 July 2021
• Riesel 2 8000-10000
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, 8000 < {{Vk}} < 10000}} Automatically generated table from available [[:Category:Riesel 2 8000-10000|Riesel primes 8000 < {{Vk}} < 10000]].
  888 bytes (117 words) - 09:00, 22 July 2021
• Riesel 2 10e10-infinity
  {{DISPLAYTITLE:Riesel primes of the form {{Kbn|k|n}}, {{Vk}} > 10¹⁰}} ...tically generated table from available [[:Category:Riesel 2 10e10-infinity|Riesel primes {{Vk}} > 10¹⁰]].
  1 KB (146 words) - 10:08, 22 July 2021
• RPS Drive 9
  *Name: [[Riesel Prime Search]] Drive 9 *Purpose: The goal of this drive is to search for primes of the form {{Kbn|k|n}} for 40 high-weighted 10000 < {{Vk}} < 30000.
  2 KB (151 words) - 10:56, 11 January 2023
• Riesel 2 Riesel
  {{DISPLAYTITLE:Riesel numbers of the form {{Kbn|k|n}}}} '''Riesel numbers''' 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

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