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  • M35
    Specifically 2<sup>{{Num|1398269}}</sup>-1, written out in full [http://www.mersenneforum.org/txt/35.txt {{Num|420921}
    2 KB (224 words) - 11:00, 18 February 2019
  • Raphael M. Robinson
    ...t|Lucas-Lehmer]] [[primality test]] to determine whether 2<sup>''n''</sup>-1 was prime for all prime ''n'' < 2304 on a [[SWAC (computer)|SWAC]] at [[Uni ....htm In memoriam : Raphael Mitchel Robinson,]" ''Bull. Symbolic Logic'' '''1''': 340-43.
    4 KB (526 words) - 14:51, 19 September 2021
  • M36
    ...he 36th [[Mersenne prime]], specifically it is 2<sup>{{Num|2976221}}</sup>-1. This number was dicovered to be [[prime]] on 1997-08-24 by [[Gordon Spence ...umber]] is 2<sup>{{Num|2976220}}</sup> &bull; (2<sup>{{Num|2976221}}</sup>-1). This number is {{Num|1791864}} digits long.
    2 KB (279 words) - 11:01, 18 February 2019
  • 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
  • Covering set
    *[[Riesel problem 1|Riesel problem]]
    380 bytes (56 words) - 10:27, 26 March 2024
  • Seventeen or Bust
    |result=11 k's eliminated as a standalone project, 1 k eliminated as a subproject on PrimeGrid The aim of the project is to find [[prime]]s of the form <math>k*2^n+1</math>, where ''k'' is one of the remaining 17 (now 5) candidates for [[Sie
    3 KB (544 words) - 16:44, 21 July 2019
  • M2
    | digits= 1
    193 bytes (19 words) - 13:43, 17 February 2019
  • Perfect number
    ...roper positive divisors and 1 + 2 + 3 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. The next perfect numbers are 496 and 8128. ...numbers are generated by the formula 2<sup>''n''-1</sup>(2<sup>''n''</sup>-1):
    6 KB (885 words) - 11:33, 7 March 2019
  • M9
    The ninth [[Mersenne prime]], 2<sup>61</sup>-1 or {{Num|2305843009213693951}}. ...mber, ([[Édouard Lucas]] having shown earlier that [[M12]], <math>2^{127}-1</math> is also prime), and it remained so until 1911. Prior to the develope
    2 KB (213 words) - 14:30, 17 February 2019
  • Residue
    ...of the L-L test. When the numbers being tested are large: <math>\gt2^{64}-1</math> (i.e. exponents larger than 64) and above, the residue is 16 hexadec Here is the Lucas test for <math>2^7-1</math>, which is 127:
    1 KB (235 words) - 10:24, 6 February 2019
  • GIMPS clients
    ! LL test !! PRP test !! Trial factoring !! ECM factoring !! P-1 factoring ...mount of factoring work using (say) Pollard's [[p-1 factorization method|p-1 method]] or the [[elliptic curve method]], both of which involve manipulati
    8 KB (1,218 words) - 15:37, 13 August 2020
  • Mfaktc
    ...CPU resources. However GPU sieving is not supported on compute capability 1.x GPUs in 0.20. Mfaktc 0.21 can do GPU sieving for those old GPUs. *A [[CUDA]] capable GPU with compute capability 1.1 (or newer), any Geforce 8000, 9000, 200, 400, 500 series ''except'' those w
    5 KB (765 words) - 14:54, 25 February 2019
  • Mfakto
    -v <n> verbosity level: 0=terse, 1=normal, 2=verbose, 3=debug -st run built-in selftest (about 1,500 testcases) and exit
    17 KB (2,524 words) - 12:39, 24 January 2019
  • Rho factorization method
    *x<sub>1</sub> = f(x<sub>0</sub>) *x<sub>2</sub> = f(x<sub>1</sub>)
    3 KB (558 words) - 10:28, 6 February 2019
  • Riesel number
    ...ether 509203 is the smallest Riesel number or not (the '''[[Riesel problem 1]]'''), a [[distributed computing project]] was created named [[Riesel Sieve *[[Riesel problem 1]]
    827 bytes (112 words) - 08:21, 25 March 2024
  • M12
    ...t [[University of California, Los Angeles]] found [[M13]], 2<sup>521</sup>-1. .../sup>-1=7) also produces a prime. When this value is tested (2<sup>7</sup>-1=127), another prime is produced. So, Lucas was testing to see if this trend
    2 KB (354 words) - 14:52, 19 September 2021
  • Primality test
    *[[Lucas primality test|Lucas Test]]: Used when the number {{V|N}}-1 is completely factored. ...factors of the input number - 1 are known (the unfactored part of {{V|N}}-1 must be less than the [[square root]] of {{V|N}}).
    3 KB (501 words) - 05:20, 3 August 2021
  • Lucas primality test
    ...whether a number N is prime or not, using the complete factorization of N-1. ...>(N-1)/q</sup> is not congruent to 1 modulo N for any prime divisor q of N-1, then N is a prime.
    1 KB (177 words) - 14:31, 17 February 2019
  • Square root
    ...gth of the [[diagonal]] of a [[square (geometry)|square]] with side length 1. ...s to the equation <math>x = \sqrt{x}</math> The solution set is <math>\{0, 1\}</math>.
    13 KB (1,873 words) - 16:52, 24 October 2020

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