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• Seventeen or Bust
  ..., we try to eliminate as many non-prime numbers as possible from the queue by [[sieving]], which means to take a (relatively) small integer and check whe ...pair]] in a few hours before running a test which will take several weeks, by [[p-1 factorization method|p-1]] factoring.
  3 KB (544 words) - 16:44, 21 July 2019
• Perfect number
  [[Euclid]] discovered that the first four perfect numbers are generated by the formula 2^''n''-1(2^''n''-1): ...ese assumptions was that since 2, 3, 5, and 7 are precisely the first four primes, the fifth perfect number would be obtained when ''n'' = 11, the fifth prim
  6 KB (885 words) - 11:33, 7 March 2019
• M9
  ...rior to the developement of the Lucas test all Mersenne primes were proved by some form of [[trial factoring]]. Pervushin used the [[Lucas-Lehmer test]] *[http://primes.utm.edu/curios/page.php/2305843009213693951.html Prime curios: 230584300921
  2 KB (213 words) - 14:30, 17 February 2019
• GIMPS clients
  ...ested for primality ("is it a prime?") faster than other sorts of would-be primes of the same magnitude. "Faster" here is still measured in weeks, but that c ...ry to get the tests down to the "weeks" range. The assembler cuts the time by at least another factor of two over straight C.
  8 KB (1,218 words) - 15:37, 13 August 2020
• Mfakto
  *First announced 07-Jun-2011 by Bdot. ...or candidates (FCs) are pre-sieved on the CPU. The first <SievePrimes> odd primes are used to sieve the FCs. (relevant for CPU sieving only)
  17 KB (2,524 words) - 12:39, 24 January 2019
• Riesel and Proth Prime Database
  It was created in 2007 and is maintained by [[:User:Karbon|Karsten Bonath]].
  380 bytes (59 words) - 14:14, 24 January 2019
• Primality test
  ...test for numbers less than 10000 digits, especially with the improvements by Mihailescu. But ECPP is preferred because of the certificates it provides.
  3 KB (501 words) - 05:20, 3 August 2021
• Mprime (Cray)
  '''mprime''' was the [[software]], initially authored by [[David Slowinski]] (later versions with [[Paul Gage]]), for testing [[Mers ...of very large numbers. This represented an advance over the software used by [[Landon Curt Noll]] &amp; [[Laura A. Nickel]]. Noll had suggested the use
  639 bytes (92 words) - 12:02, 7 February 2019
• Probable prime
  ...e prime: an [[integer]] that satisfies a specific condition also satisfied by all [[prime]] numbers.}} ...ble primes have different specific conditions. While there may be probable primes that are [[Composite number|composite]] (called [[pseudoprime]]s), the cond
  2 KB (232 words) - 07:28, 12 March 2024
• GIMPS factoring and sieving
  ...mber]]s with prime exponents are eliminated from consideration as possible primes this way, so factoring is an important component of maximizing the work thr ...and furthermore must also leave a remainder of either 1 or 7 upon division by 8. See below for an explanation.
  6 KB (962 words) - 10:08, 7 March 2019
• Ten million digits
  ...of {{Num|33219281}} and higher). When first made available and handed out by [[PrimeNet]], the [[Lucas-Lehmer test]]s of these [[exponent]]s took over a ...009 a third prime greater that {{Num|10000000}} digits was found, [[M46]]. By the end of 2010, all exponents that would produce a number less than {{Num|
  979 bytes (146 words) - 14:23, 6 March 2019
• Brent-Suyama extension
  ...S=3^E where E is the product of prime powers less than B1. Then by [[Fermat's Little Theorem]], a prime number p | S-1 if p-1 | E. Slicker would be to note that all primes > 3 are of form 6k+/-1. Suppose instead that we compute T=S<sup>(6k)<sup>2<
  2 KB (421 words) - 11:51, 28 January 2019
• Self-initializing quadratic sieve
  .../math> where u is the product of small [[prime]] numbers. The set of these primes is the ''factor base''. These relations will be found using [[sieving]] as ...th> modulo any prime of the factor base. This means that about half of the primes cannot be in the factor base because <math>N</math> cannot be a [[quadratic
  10 KB (1,763 words) - 02:56, 12 March 2019
• Template:PP
  Mostly such links are used in tables only by giving the exponent like </noinclude><includeonly><span class="plainlinks">[https://primes.utm.edu/primes/page.php?id={{{1}}} {{{2}}}]</span></includeonly>
  790 bytes (111 words) - 13:47, 7 March 2019
• GeneferCUDA
  It is a port of [[Genefer]] to [[CUDA]] by [[Shoichiro Yamada]]. It was also ported for AMD video cards.
  362 bytes (48 words) - 09:20, 29 January 2019
• Generalized Fermat number
  Saouter has proven that <math>F_{n,2}</math> numbers can be proven prime by using [[Pépin's test]] with k=5. In 1985, Dubner for the first time built a list of large primes of the form: b^{2^m}+1, ''b &ge; 2'' and ''m &ge; 1''.
  5 KB (774 words) - 07:39, 27 May 2024
• Worktype
  ...ain goals of GIMPS (finding [[Mersenne prime]]s, ensuring that no Mersenne primes have been missed, and lastly finding [[factor]]s for [[Mersenne number]]s). ...chine and with a different [[offset]]. Ensures that a prime was not missed by error.
  4 KB (603 words) - 02:31, 18 August 2019
• PrimeNet server
  ...s taken over by [[Aaron Blosser]], and site maintenance (''Mersenne.org'') by Aaron Blosser and [[James Heinrich]]. ...and both software packages, the range of GIMPS [[exponent]]s being handled by PrimeNet increased from [[79.3 million]] to 999,999,999.
  2 KB (381 words) - 14:05, 21 August 2019
• 100 Million Digit Prefactor Project
  ...and can be used to take exponents to a [[bit level]] higher than practical by using Prime95 alone. Factor5 can be found at: [http://www.moregimps.it/bill The project started with the introduction of 'Factor' by [[Luigi Morelli]]. It was handled using a Geocities website and e-mail. Aft
  3 KB (534 words) - 10:06, 7 March 2019
• 321 Search
  '''''This project is maintained by [[PrimeGrid]] now.''''' These are the simple steps needed to participate in the 321 Search for primes.
  1 KB (185 words) - 09:34, 3 August 2021

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