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• Williams prime
  A '''Williams number''' is a [[natural number]] of the form {{Kbn|(b-1)|b|n}} for integer A '''Williams prime''' is a Williams number which is [[prime]].
  5 KB (744 words) - 07:30, 5 August 2019
• Examples
  {{Box|hide=true|title=Example of prime sequence and reservation|content=[[Williams prime MM 5]]}} The <b>[[:Category:Carol-Kynea_prime|category]]</b> for Carol/Kynea primes holds example pages for some bases.
  11 KB (1,236 words) - 14:41, 3 September 2020
• Lucas-Lehmer test
  ...ent has order N-1 we must show that it does not have order (N-1)/q for all primes q dividing N-1. Thus, if we know all the factors of N-1, we can prove N pri ...all the prime factors of N-1 or N+1 are known. (See Chapter 4.3 and 8.4 of Williams' book). When we test N = 2^p-1, the recursion is particularly sim
  20 KB (3,572 words) - 14:30, 17 February 2019
• Williams prime MM 10
  {{Williams prime |WiRemarks=These primes are [[Near-repdigit]] numbers; see [https://stdkmd.net/nrr/8/89999.htm Fact
  1 KB (143 words) - 02:41, 5 November 2020
• Williams prime MM least
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|(b-1)|b|n}}, least {{Vn}}-values}} ...e ≥ 1 for any base {{Vb}} with 2 ≤ {{Vb}} ≤ 2049 which generates a [[Williams prime]] of the form {{Kbn|(b-1)|b|n}}.
  2 KB (211 words) - 07:40, 1 August 2021
• Williams prime MM table
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|(b-1)|b|n}}}} ==Primes table==
  460 bytes (65 words) - 23:05, 31 July 2021
• Williams prime MP table
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|+|(b-1)|b|n}}}} ==Primes table==
  462 bytes (65 words) - 08:05, 1 August 2021
• Williams prime PM table
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|(b+1)|b|n}}}} ==Primes table==
  458 bytes (65 words) - 14:02, 1 August 2021
• Williams prime PP table
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|+|(b+1)|b|n}}}} ==Primes table==
  447 bytes (65 words) - 08:12, 18 June 2019
• Williams prime MP least
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|+|(b-1)|b|n}}, least {{Vn}}-values}} ...e ≥ 1 for any base {{Vb}} with 2 ≤ {{Vb}} ≤ 1024 which generates a [[Williams prime]] of the form {{Kbn|+|(b-1)|b|n}}.
  3 KB (408 words) - 08:00, 1 August 2021
• Williams prime PM least
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|(b+1)|b|n}}, least {{Vn}}-values}} ...e ≥ 1 for any base {{Vb}} with 2 ≤ {{Vb}} ≤ 1024 which generates a [[Williams prime]] of the form {{Kbn|(b+1)|b|n}}.
  1 KB (161 words) - 13:57, 1 August 2021
• Williams prime PP least
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|+|(b+1)|b|n}}, least {{Vn}}-values}} ...e ≥ 1 for any base {{Vb}} with 2 ≤ {{Vb}} ≤ 1024 which generates a [[Williams prime]] of the form {{Kbn|+|(b+1)|b|n}}.
  2 KB (306 words) - 09:54, 7 September 2020
• Williams prime MM remaining
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|(b-1)|b|n}}, remaining data}} ...e all remaining data given not yet available as separate page for Williams primes of the form {{Kbn|(b-1)|b|n}} for {{Vb}} < 2050.
  962 bytes (137 words) - 07:42, 1 August 2021
• Williams prime PP remaining
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|+|(b+1)|b|n}}, remaining data}} ...e all remaining data given not yet available as separate page for Williams primes of the form {{Kbn|+|(b+1)|b|n}} for ''b'' < 1025.
  962 bytes (135 words) - 07:49, 26 June 2019
• Williams prime PM remaining
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|(b+1)|b|n}}, remaining data}} ...e all remaining data given not yet available as separate page for Williams primes of the form {{Kbn|(b+1)|b|n}} for {{Vb}} < 1025.
  962 bytes (136 words) - 14:00, 1 August 2021
• Williams prime MP remaining
  {{DISPLAYTITLE:Williams primes of the form {{Kbn|+|(b-1)|b|n}}, remaining data}} ...e all remaining data given not yet available as separate page for Williams primes of the form {{Kbn|+|(b-1)|b|n}} for {{Vb}} < 1025.
  966 bytes (138 words) - 08:03, 1 August 2021
• Statistics
  | [[:Category:Mersenne prime|Mersenne primes]] || number || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Me | [[:Category:Riesel 2|Riesel primes {{Kbn|k|2|n}}]] || {{Vk}}-value || style="text-align:right;"|{{Num|{{PAGESI
  11 KB (1,385 words) - 17:23, 5 April 2024