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  • M28
    | foundwith=[[Lucas-Lehmer test]] / [[Cray 1]]
    278 bytes (23 words) - 08:22, 18 February 2019
  • System requirements and compatible hardware
    ...4-bit SP 1 / 64-bit SP 2 / AMD 64-bit / Itanium 64-bit / Itanium 64-bit SP 1 / Itanium 64-bit SP 2) :Windows NT (3 / 4 / 4 SP 1 / 4 SP 2 / 4 SP 3 / 4 SP 4 / 4 SP 5 / 4 SP 6)
    766 bytes (95 words) - 12:25, 19 February 2019
  • Mersenne composite
    A '''Mersenne composite''' is any number of the form 2<sup>n</sup>-1 which is a [[composite number]]. ...is multiple of both [[Mersenne number]]s 2<sup>p</sup>-1 and 2<sup>q</sup>-1.
    347 bytes (62 words) - 13:07, 19 February 2019
  • PrimeNet summary report
    *'''P-1''': [[P-1 factorization method]] assignments. These exponents have had a reasonable a ...lows TF. (Currently the sequence is TF to final [[bit level]] minus one, P-1, then final bit level TF).
    7 KB (1,073 words) - 08:46, 15 May 2024
  • Square number
    :1<sup>2</sup> = 1 ...>2</sup> equals to the sum of the first ''n'' odd numbers (<math>n^2 = 2(n-1)^2-(n-2)^2+2</math>). A square number is also the sum of two consecutive [[
    3 KB (408 words) - 13:56, 19 February 2019
  • Riesel number base 5
    Using the same method presented in the [[Riesel problem 1|Riesel problem]] article, it was found that {{Kbn|-|346802|5|n}} is multipl
    589 bytes (90 words) - 10:30, 26 March 2024
  • Riesel problem 1
    Currently, there are '''{{#expr:{{PAGESINCATEGORY:Riesel problem 1|pages|R}}-2}}''' {{Vk}}-values smaller than {{Num|509203}} that have no kno ...with {{Vn}} in the interval 2<sup>{{V|m}}</sup> ≤ {{Vn}} < 2<sup>{{V|m}}+1</sup>. <ref>[http://www.prothsearch.com/rieselprob.html Riesel problem] by
    6 KB (689 words) - 18:14, 4 April 2024
  • Tutorial LLR
    ...umbers are of the same form (normally k*2<sup>n</sup>+1 or k*2<sup>n</sup>-1).
    2 KB (337 words) - 13:24, 20 February 2019
  • Peano postulates
    ...n 1889; it characterises the set (class, condition) of [[natural number]]s 1, 2, 3, etc., and consists of the following '''Peano postulates''' (also cal #''1'' is a natural number
    2 KB (269 words) - 17:04, 24 October 2020
  • LL test distribution
    ...senne number successfully double checked was 2<sup>{{Num|666666667}}</sup>-1, with {{Num|200686664}} digits. It was tested and double checked by LaurV.
    2 KB (415 words) - 21:32, 12 February 2020
  • ElevenSmooth
    ...actors of the [[Mersenne number]] M(3326400) = 2<sup>{{Num|3326400}}</sup>-1.
    366 bytes (42 words) - 12:49, 21 February 2019
  • Factoring report
    ...ports, it lists the current [[bit level]] and [[P-1 factorization method|P-1]] [[bounds]] for a given list of exponents, that have no known factors.
    524 bytes (78 words) - 13:12, 21 February 2019
  • Mersenne.ca
    ...of finding a [[Mersenne prime]], many GIMPS users purposely skipped the P-1 stage to spend more time doing L-L first-time tests. ...sts are graphed, with known factors overlaid to show how close any known P-1 test(s) were to finding the factor(s). A similar graph shows known factors
    9 KB (1,396 words) - 15:42, 25 February 2019
  • Value k
    :<math>2kp+1</math> where <math>p</math> is the [[exponent]] in <math>2^p-1</math>. <math>\begin{align}2^{23}-1 &= 8388607\\&= 47 * 178481\\
    702 bytes (99 words) - 10:43, 25 October 2020
  • Aurifeuillian factor
    *Numbers of the form <math>2^{4k+2}+1</math> have the following '''Aurifeuillian factorization''': [http://mathwo ::<math>2^{4k+2}+1 = (2^{2k+1}-2^{k+1}+1)\cdot (2^{2k+1}+2^{k+1}+1)</math>
    10 KB (1,257 words) - 08:04, 24 June 2019
  • Cullen number
    {{V|C<sub>n</sub>}} is [[prime]] for {{Vn}} = 1, 141, {{PP|40087|4713}}, {{PP|38112|5795}}, {{PP|37374|6611}}, {{PP|23436|1
    2 KB (252 words) - 17:39, 31 August 2021
  • Factoring program
    *[[GMP-ECM]] (performing ECM, P-1, and P+1) http://gforge.inria.fr/projects/ecm/ ...ime|MPrime]] (for Linux , FreeBSD, and MacOSX) (performing ECM, P-1, and P+1 to search for factors of a &times; b<sup>n</sup> ± c) ftp://mersenne.org/g
    2 KB (273 words) - 21:53, 8 July 2023
  • Mtsieve
    *dmdsieve: search for factors of numbers of the form 2*k*(2<sup>p</sup>-1)+1 (potential divisors of [[Double Mersenne number]]s)
    2 KB (338 words) - 06:58, 28 March 2023
  • Carol-Kynea prime
    ...numbers''' are numbers of the form <math>(b^n-1)^2-2</math> and <math>(b^n+1)^2-2</math>, respectively, while '''Carol primes''' and '''Kynea primes''' ...h>(b^n-1)^2-2</math> and a Kynea number is a number of the form <math>(b^n+1)^2-2</math>. A Carol/Kynea prime is a [[prime]] which has one of the above
    8 KB (1,172 words) - 00:38, 6 July 2023
  • Multifactorial prime
    ...r]] which is prime and of the form <math>\ n!_2{±}1,\ n!_3{±}1,\ n!_4{±}1</math>, and so on.
    429 bytes (50 words) - 14:29, 25 March 2019

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