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  • Mersenneplustwo factorizations
    ...p>-1 being prime). All such numbers are divisible by 3 since 2<sup>p</sup>-1 is not divisible by 3 (it's assumed to be prime) and 2<sup>p</sup> is not d
    2 KB (215 words) - 13:33, 5 March 2019
  • ECMclient
    1. Get it [http://home.earthlink.net/~elevensmooth/ElevenSmooth.zip here] and
    2 KB (383 words) - 11:16, 26 February 2019
  • GMP-ECM
    ...d|ECM]], [[P-1 factorization method|p-1]] and [[P+1 factorization method|p+1]] algorithms. The current version is 7.0.5-dev (svn 3038). 1. First you'll need to get the right environment and stuff to work with:
    4 KB (567 words) - 10:54, 6 December 2019
  • Gerbicz error checking
    # <math>d(t+1) \equiv d(t)*u((t+1)L) \pmod{p}</math> # <math>d(t+1) \equiv u(0)*d(t)^{2^L} \pmod{p}</math>
    3 KB (528 words) - 14:59, 3 October 2023
  • Jacobi error checking
    ...the residue plus 2 <math>\left(\frac{Res+2}{M_p}\right)</math> has to be +1 ...the residue minus 2 <math>\left(\frac{Res-2}{M_p}\right)</math> has to be -1
    1 KB (166 words) - 18:36, 27 September 2023
  • ECPP-DJ
    |latest=1.04<br><small>2014-08-16</small> :BLS75 proof using N-1
    2 KB (237 words) - 18:04, 2 December 2019
  • BLS75
    ...5-0384673-1.pdf "New Primality Criteria and Factorizations of 2^{{V|m}} ± 1"]. ''Mathematics of Computation.'' Volume 29, Number 130: 620-647. ...-1 factorization method|{{V|p}}-1]] and [[P+1 factorization method|{{V|p}}+1]].
    584 bytes (85 words) - 20:12, 26 October 2020
  • GIMPS PrimeNet reports
    ...Lehmer test|LL Tests]], LL [[double check]]s, [[P-1 Factorization methid|P-1]] factoring, and [[Elliptic curve method|ECM Factoring]]. These are also up Lists the current [[bit level]] and [[P-1 factorization method|P-1]] [[bounds]] for a given list of exponents which have no known factors and
    7 KB (1,137 words) - 15:30, 13 August 2020
  • Sierpiński-Riesel Base 5
    ...base 5]]: There are <b>{{#expr:{{PAGESINCATEGORY:PrimeGrid Riesel base 5}}-1}}</b> values to prove. ...5]]: There are <b>{{#expr:{{PAGESINCATEGORY:PrimeGrid Sierpiński base 5}}-1}}</b> values to prove.
    2 KB (231 words) - 11:42, 5 October 2020
  • M27
    | foundwith=[[Lucas-Lehmer test]] / [[Cray 1]]
    302 bytes (26 words) - 08:16, 18 February 2019
  • 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

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