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• Williams prime
  Lists of primes for bases ''b'' and ''n''-values can be found here: ...e included as a separate page.</ref> !! Smallest <ref>The list of smallest primes of any base is an ASCII file for 2 ≤ ''b'' ≤ 1024. For unknown values o
  5 KB (744 words) - 07:30, 5 August 2019
• Carol-Kynea prime 2
  ==History for Carol primes== ==History for Kynea primes==
  5 KB (537 words) - 08:17, 9 October 2020
• Examples
  The <b>[[:Category:Carol-Kynea_prime|category]]</b> for Carol/Kynea primes holds example pages for some bases. The data are collected from the internal SQL database by [https://www.mediawiki.org/wiki/Extension:External_Data Extension:External
  11 KB (1,236 words) - 14:41, 3 September 2020
• Great Internet Mersenne Prime Search
  Mersenne primes are named after [[Marin Mersenne]], a French monk and mathematician, who wa ...ring the largest Mersenne Primes to date. See the [[list of known Mersenne primes]] for more details.
  3 KB (450 words) - 14:37, 21 August 2019
• List of known Mersenne primes
  *'''#''': number count of the Mersenne primes linked to that prime page *'''Date''': year/date of discovery, if available a link to the press release by [[GIMPS]]
  2 KB (360 words) - 09:44, 6 March 2019
• Mersenne prime
  ...minus; 1 = {{Kbn|4}}, for example, is not a prime, because 15 is divisible by 3 and 5. ...enerally, [[Mersenne number]]s (not necessarily primes, but candidates for primes) are numbers that are one less than a power of two; hence,
  5 KB (857 words) - 14:53, 19 September 2021
• Leonhard Euler
  | Name=Leonhard Euler ...ant role in opening up new windows onto our understanding, not just of the primes, but in many other areas of mathematics as well.
  16 KB (2,614 words) - 11:48, 14 January 2024
• Marin Mersenne
  | Name=Marin Mersenne .... It is sometimes incorrectly stated that he was a Jesuit. He was educated by Jesuits, but he never joined the Society of Jesus. He taught theology and p
  11 KB (1,582 words) - 01:17, 15 January 2024
• Landon Curt Noll
  | Name=Landon Curt Noll ...8. This brought them quite a bit of attention. Their discovery was covered by national television news and reported in the New York times on 1978-11-21.
  2 KB (333 words) - 12:40, 9 February 2022
• Fermat number
  ...ber, and such primes are called '''Fermat primes'''. The only known Fermat primes are {{V|F}}₀,...,{{V|F}}₄. for {{Vn}} &ge; 2. Each of these relations can be proved by [[Proof by induction|mathematical induction]]. From the last equation, we can deduce '
  12 KB (1,913 words) - 14:35, 9 August 2021
• Derrick Henry Lehmer
  | Name=Derrick Henry Lehmer ...om his father, [[Derrick Norman Lehmer]] who was also a mathematician, and by his friends as Dick. In this article Derrick or Lehmer means the son, DNL m
  6 KB (1,033 words) - 01:13, 15 January 2024
• Base 2 Home Prime Results
  ==Search for Home Primes base 2== ===Table of open Home Primes up to {{Vn}} = {{Num|12000}}===
  2 KB (175 words) - 18:45, 14 December 2023
• Cunningham project
  ...d for one value by Aurifeuille and the general form was subsequently given by Lucas. Here are the Aurifeuillian factorizations for the other bases. ...<math>x-1</math>. In such cases, <math>b^n-1 \over b-1</math> is divisible by <math>n</math> itself.
  7 KB (1,150 words) - 23:48, 19 April 2023
• 2 Minus Tables
  .... Given here links to [[Factoring Database]] in html and text formats. The primes are the [[Mersenne prime]]s. ==Primes for ''n''==
  2 KB (176 words) - 12:01, 13 February 2019
• M25
  ...dates (31 of 75). There was a theory that there was an 'Island of Mersenne Primes'. They were testing this theory and that Tuckerman's discovery of [[M24]] ( ...s result was verified by Tuckerman of [[IBM]]'s Watson Research Center and by Lehmer at UC Berkeley.
  2 KB (303 words) - 11:01, 26 February 2019
• Lucas-Lehmer test
  ...either composite or prime. It is the last stage in the procedure employed by [[GIMPS]] for finding [[Mersenne prime]]s. Previous stages try to find fact ...= 1 (mod 4), but for all odd prime exponents. The test therefore takes its name from the two mathematicians who invented and developed it, even though they
  20 KB (3,572 words) - 14:30, 17 February 2019
• Factoring Database
  ...atabase''' is a database of [[factor]]s of numbers of any kind, programmed by Markus Tervooren. **Inverse home primes of various bases
  1 KB (144 words) - 13:44, 24 January 2019
• Mlucas
  ...[Mersenne number]]s, and Pépin tests of [[Fermat number]]s. It is written by [[Ernst Mayer]] using C programming language and [[ARM]] assembly. It also ...er be lucky as to find a new prime eligible for the monetary prize offered by the [[Electronic Frontier Foundation]].
  1 KB (198 words) - 07:28, 22 August 2019
• M47
  On 2018-04-08 all tests below 2^{{{Num|43112609}}}-1 were verified by [[GIMPS]], officially making it the 47th Mersenne prime. ...Bug]] or a random bit error or [[software]], the number had to be verified by running the Lucas-Lehmer test on at least one different machine (not just a
  5 KB (694 words) - 13:17, 21 August 2019
• Prime95
  ...s the freeware computer program written by [[George Woltman]] that is used by [[Great Internet Mersenne Prime Search|GIMPS]], a [[distributed computing]] ...f December 2018, Prime95 was used to discover all 17 Mersenne primes found by GIMPS.
  11 KB (1,586 words) - 12:24, 7 August 2021
• CUDALucas
  '''CUDALucas''' is a [[CUDA]]-based program written by [[Shoichiro Yamada]] for testing [[Mersenne number]]s for primality with [[ ...itself a port to FFTW of a program tracing its roots back to original code by [[Richard Crandall]] et al.[http://www.ece.neu.edu/groups/nucar/GPGPU4/file
  2 KB (275 words) - 11:11, 21 August 2019
• Glucas
  ...IMPS]] effort to search the largest primes ever found. It was written in C by Guillermo Ballester Valor and Klaus Kastents. ...51.pdf "Discrete weighted transforms and large-integer arithmetic"] (1994) by R. Crandall and B. Fagin. The library is coded in C with some assembler mac
  3 KB (426 words) - 14:21, 14 February 2019
• Distributed computing
  ...s a branch of [[computational science]] that tries to solve large problems by giving small parts of the problem to many computers to solve and then combi ...access to massive computing power that would not otherwise be obtainable. By joining one of these distributed computing projects, you can play an import
  4 KB (674 words) - 12:11, 19 February 2019
• MersenneForum
  ...hers, MersenneForum is used by: <!-- discoverers and verifiers of Mersenne primes, as well as software developers -->
  2 KB (293 words) - 17:33, 5 July 2019
• M34
  ...z machine it took about 60 hours to [[double check]] the number. Woltman, by happenstance, was 95% of the way through a check on that ''very'' number, w ...company or before they joined the company, discovered 10 of the 11 record primes between 1978 and 1996, namely Slowinski, Gage, and [[Landon Curt Noll]] (ei
  3 KB (513 words) - 08:42, 18 February 2019
• No Prime Left Behind
  ...} with odd {{Vk}} and 300 < {{Vk}} < 1001 and {{Vn}} > 260000 not reserved by others with highly presieved ranges.
  745 bytes (111 words) - 02:17, 1 May 2024
• 2 Plus Tables
  ...[[Factoring Database]] in html and text formats. The primes are the Fermat primes. ==Primes for ''n''==
  2 KB (127 words) - 15:28, 17 August 2019
• Mersennewiki
  Using the old database many pages were restored for this new Wiki in 2019 by [[:User:Karbon|Karbon]].
  647 bytes (99 words) - 12:09, 25 February 2019
• Trial factoring
  Such a table can be prepared automatically, usually by an adaption of the [[Sieve of Eratosthenes]], itself requiring a small tabl ...s in using larger digit sizes. Verifying that your CPU functions correctly by testing the add, subtract, multiply and divide operations on all possible p
  7 KB (1,221 words) - 13:20, 11 February 2019
• M45
  M45 was found on 2008-09-06, by a computer owned by [[Hans-Michael Elvenich]] of Germany. The computer was running [[Prime95]] ...ww.mersenne.org/primes/m45and46.htm GIMPS Discovers 45th and 46th Mersenne Primes] (press release)
  2 KB (251 words) - 11:40, 18 February 2019
• Coprime
  Two [[integer]] numbers are '''coprime''' or relatively primes when their [[greatest common divisor]] is 1 (<math>\gcd{(x,y)} = 1</math>). ...ath> and thus the [[Modular arithmetic#Modular division|modular division]] by <math>m \pmod{n}</math>.
  738 bytes (112 words) - 09:50, 23 January 2019
• M35
  ...t [[prime]] discovered by [[GIMPS]] and the first [[Mersenne prime]] found by a [[personal computer]]. A little more than a month earlier, [[David Slowin ...mer test]] took 88 hours to run. The primality of the number was confirmed by Slowinski. This showed the effectiveness of [[distributed computing]].
  2 KB (224 words) - 11:00, 18 February 2019
• University of California, Los Angeles
  ...Angeles (UCLA)''' is the largest of the University of California campuses (by enrollment). It is situated in the Westwood area of Los Angeles. It has a l Prior to the Internet, 7 Mersenne primes were discovered at UCLA
  2 KB (347 words) - 14:54, 19 September 2021
• Raphael M. Robinson
  |Name=Raphael Mitchel Robinson ...essentially undecidable theory need not have an infinite number of axioms by coming up with a counterexample: Robinson arithmetic ''Q''. ''Q'' is finite
  4 KB (526 words) - 14:51, 19 September 2021
• M36
  ...be [[prime]] on 1997-08-24 by [[Gordon Spence]], using [[Prime95]] written by [[George Woltman]]. At time of its discovery, it was the largest known prim ...puter|supercomputer]] by [[David Slowinski]], discoverer of seven Mersenne primes between 1979 and 1996.
  2 KB (279 words) - 11:01, 18 February 2019
• Sierpiński problem
  The '''Sierpiński problem''' in [[number theory]] was proposed by [[Wacław Sierpiński]] in 1960. In early 2002, primes had been found for all but seventeen choices of {{Vk}}. At that point, the
  5 KB (650 words) - 10:25, 26 March 2024
• 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
• 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

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