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• Proth prime 2 1
  {{Proth prime |Pk=1
  333 bytes (46 words) - 21:20, 16 October 2024

Page text matches

• Fermat number
  :{{V|F}}_{{Vn}} = {{Kbn|+|1|2|2ⁿ}} :{{V|F}}₀ = {{Kbn|+|1}} = 3
  12 KB (1,913 words) - 14:35, 9 August 2021
• Sierpiński problem
  *{{Kbn|+|78557|4n+1}} is multiple of 5. *{{Kbn|+|78557|3n+1}} is multiple of 7.
  5 KB (650 words) - 10:25, 26 March 2024
• Paul Seelhoff
  ...50?tify={%22pages%22:%5B306%5D,%22view%22:%22%22} "Generalregister zu Band 1-50 der Zeitschrift für Mathematik und Physik"], p.292) ...fy={%22pages%22:%5B412%5D,%22view%22:%22%22} "Die Zahlen von der Form k.2n+1"], Zeitschrift fur Mathematik und Physik, '''Vol. 31''' (1886) p380
  2 KB (195 words) - 00:13, 15 January 2024
• Riesel number
  ...Sierpiński problem]] article, [[Hans Riesel]] found in 1956 that [[Riesel prime 2 509203|{{Kbn|509203|n}}]] is always composite. ...ether 509203 is the smallest Riesel number or not (the '''[[Riesel problem 1]]'''), a [[distributed computing project]] was created named [[Riesel Sieve
  827 bytes (112 words) - 08:21, 25 March 2024
• Primality test
  .... When the number is declared composite, the algorithm does not reveal the prime [[factor]]s. That is the job of the [[Factorization|factorization methods]] ...the confidence grows, but we cannot be completely sure that the number is prime until a primality test (which is far slower than a probable primality test
  3 KB (500 words) - 05:03, 11 August 2024
• 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". ...s, like the [[Generalized Fermat number]]s <math>F_{n,2} = 4^{3^n}+2^{3^n}+1</math> with k = 5 instead of k = 3.
  2 KB (402 words) - 01:16, 11 August 2024
• LLR
  **[[Proth's theorem|Proth algorithm]] for {{Kbn|+|k|n}} numbers. **{{V|N}}-1 [[Pocklington algorithm]] for {{Kbn|+|k|b|n}} numbers.
  2 KB (300 words) - 22:00, 16 December 2023
• Generalized Fermat number
  ...+1}}-1)/(2^{p^n}-1)</math> where p is the prime of apparition rank r (r(2)=1, r(3)=2, r(5)=3, ...) and n is greater or equal to 0. :<math>F_{n,1}</math> generates the [[Fermat number]]s.
  5 KB (774 words) - 07:39, 27 May 2024
• PrimeGrid
  ...ipants (on about 16,000 host computers) from 89 countries, reporting about 1,860 [[Computing power#FLOPS|teraflops]].<ref>[https://www.boincstats.com/st *Type Proth:
  3 KB (458 words) - 10:28, 26 March 2024
• Sieving program
  ...ing sieving of generalized Cullen/Woodall numbers n &times; bⁿ+-1) http://sites.google.com/site/geoffreywalterreynolds/programs/gcwsieve ...ng [[twin prime]]s of the same form) http://sites.google.com/site/kenscode/prime-programs
  2 KB (220 words) - 11:42, 7 March 2019
• Proth's theorem
  Proth's theorem (1878) states: ...<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</math> such that
  517 bytes (83 words) - 01:16, 11 August 2024
• Proth prime
  ...in the form {{Kbn|+|k|n}} with 2^''n'' > ''k'' are often called Proth primes. Different from this definition all values ''n'' ≥ 1 are listed in {{SITENAME}}.
  656 bytes (91 words) - 07:02, 31 August 2020
• Riesel prime
  Although there's no official definition of a '''Riesel prime''' mostly all primes of the form {{Kbn|k|n}} with 2^{{Vn}} > {{Vk Different from this definition all values {{Vn}} ≥ 1 are listed in {{SITENAME}}.
  2 KB (274 words) - 16:44, 25 October 2024
• Proth number
  In [[number theory]], a '''Proth number''' is a number of the form ...that 2^{{Vn}} > {{Vk}}, all odd integers greater than 1 would be Proth numbers, but most pages lists them, too.
  670 bytes (104 words) - 10:59, 9 July 2021
• Gerbicz error checking
  ...e validity of [[Proth prime|Proth]] tests and PRP tests on base-2 [[Riesel prime]] candidates, and by those programs and [[PRST]] in an extended version for ...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
• Williams prime MP 2
  {{Williams prime |WiMaxn={{GP|Proth prime 2 1|PMaxn}}
  288 bytes (40 words) - 18:59, 1 September 2024
• Williams prime PP 2
  {{Williams prime |WiMaxn={{GP|Proth prime 2 3|PMaxn}}
  290 bytes (40 words) - 12:47, 5 September 2024
• Proth prime 2 1
  {{Proth prime |Pk=1
  333 bytes (46 words) - 21:20, 16 October 2024
• Proth prime 2 3
  {{Proth prime 1;T:GT
  3 KB (441 words) - 20:27, 26 September 2024
• Proth prime 2 5
  {{Proth prime 1
  1 KB (165 words) - 20:36, 26 September 2024

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