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• List of known Mersenne primes
  *'''#''': number count of the Mersenne primes linked to that prime page *[https://www.mersenne.org/primes/ List of known Mersenne prime numbers] at Mersenne.org
  2 KB (360 words) - 09:44, 6 March 2019
• Seventeen or Bust/Primes
  *[https://primes.utm.edu/primes/search.php All SoB primes]
  2 KB (163 words) - 14:20, 7 March 2019

Page text matches

• 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
• Carol-Kynea table
  ...y generated table from available [[:Category:Carol-Kynea prime|Carol-Kynea primes]]. ==Primes table==
  936 bytes (125 words) - 11:11, 11 June 2019
• Examples
  The <b>[[:Category:Carol-Kynea_prime|category]]</b> for Carol/Kynea primes holds example pages for some bases. * field: rieselk_id = 4 (-> "1" = Mersenne primes)
  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 *[https://www.mersenne.org/primes/ List of known Mersenne prime numbers] at Mersenne.org
  2 KB (360 words) - 09:44, 6 March 2019
• Mersenne prime
  ...enerally, [[Mersenne number]]s (not necessarily primes, but candidates for primes) are numbers that are one less than a power of two; hence, ...l to the sum of their proper divisors. Historically, the study of Mersenne primes was motivated by this connection; in the 4th century BC [[Euclid]] demonstr
  5 KB (857 words) - 14:53, 19 September 2021
• 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
  ==Mersenne primes== In 1644 he conjectured that the only [[Mersenne prime|Mersenne primes]] less than or equal to M(257) were:<br>M(2), M(3), M(5), M(7), M(13), M(17
  11 KB (1,582 words) - 01:17, 15 January 2024
• Chris Caldwell
  733 bytes (107 words) - 11:27, 14 January 2024
• Landon Curt Noll
  *[http://primes.utm.edu/bios/includes/nollnote.php Entry at] [[The Prime Pages]]
  2 KB (333 words) - 12:40, 9 February 2022
• David Slowinski
  ...that he wrote]]) and has been involved in the discovery of seven Mersenne primes, namely: *[http://primes.utm.edu/bios/page.php?lastname=Slowinski The Prime Pages - David Slowinski]
  1 KB (213 words) - 23:53, 14 January 2024
• Fermat number
  ...ber, and such primes are called '''Fermat primes'''. The only known Fermat primes are {{V|F}}₀,...,{{V|F}}₄. ...he sequence {{{V|p}}_{{Vn}}} is an infinite sequence of distinct primes.
  12 KB (1,913 words) - 14:35, 9 August 2021
• Aaron Blosser
  He is listed as co-discoverer of [[M49]], [[M50]] and [[M51]] Mersenne primes.
  192 bytes (26 words) - 12:04, 21 August 2019
• Derrick Henry Lehmer
  ...'' and the superposition of the corresponding stencils to reveal those few primes having these residues ''R''. ...Lehmer presented data to contradict this conjecture, especially for small primes, and [[Christopher Hooley]] later showed that this follows from the [[Gener
  6 KB (1,033 words) - 01:13, 15 January 2024
• Megaprime
  ...y many natural numbers with less than {{Num|1000000}} digits, "nearly all" primes are megaprimes. ...e [[Mersenne prime]]s. The current list is avalable [http://primes.utm.edu/primes/search.php?MinDigits=1000000&&Number=10000&Style=HTML here].
  806 bytes (111 words) - 07:59, 14 July 2021
• Gigaprime
  ...any natural numbers with less than {{Num|1000000000}} digits, "nearly all" primes are gigaprimes.
  871 bytes (119 words) - 07:54, 14 July 2021
• 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
  ...rich prime, satisfying <math>2^{n-1} = 1\ (mod\ n^2)</math>. Only two such primes are known 1093 and 3511, out of a very deep search, and neither of these sq
  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]] ( *[http://primes.utm.edu/bios/includes/nollnote.php Noll at the Prime Pages]
  2 KB (303 words) - 11:01, 26 February 2019
• Lucas-Lehmer test
  ...ent has order N-1 we must show that it does not have order (N-1)/q for all primes q dividing N-1. Thus, if we know all the factors of N-1, we can prove N pri ...1}\over 2}\omega^{{Q+1}\over 2}</math>. Again, 2 is a quadratic residue of primes congruent to <math>\pm 1</math> mod 8, and <math>Q</math> is of this form,
  20 KB (3,572 words) - 14:30, 17 February 2019
• Factoring Database
  **Inverse home primes of various bases
  1 KB (144 words) - 13:44, 24 January 2019
• Electronic Frontier Foundation
  ...to a special donation, EFF confers [[EFF prizes|prizes]] for finding huge primes. It is expected that these prizes will encourage collaborative computing.
  602 bytes (87 words) - 12:44, 29 January 2019
• Mlucas
  The program was used to verify primes [[M38]], [[M45]], [[M46]], [[M47]], [[M48]], [[M49]], [[M50]] and [[M51]] a
  1 KB (198 words) - 07:28, 22 August 2019
• Ernst Mayer
  2 KB (251 words) - 18:53, 14 December 2023
• M47
  ...mainder being used by GIMPS to provide awards to other finders of Mersenne primes and to cover expenses. *[http://www.math.ucla.edu/~edson/prime/ Edson Smith and primes]
  5 KB (694 words) - 13:17, 21 August 2019
• Prime95
  As of December 2018, Prime95 was used to discover all 17 Mersenne primes found by GIMPS. ==Finding Mersenne primes by distributed computing==
  11 KB (1,586 words) - 12:24, 7 August 2021
• CUDALucas
  The program was used to verify primes [[M48]], [[M49]], [[M50]] and [[M51]] at the times of their discovery.
  2 KB (275 words) - 11:11, 21 August 2019
• Glucas
  ...ersenne number]]s. It is related to [[GIMPS]] effort to search the largest primes ever found. It was written in C by Guillermo Ballester Valor and Klaus Kast Glucas was used to verify [[M41]], [[M43]], [[M46]] and [[M47]] primes at the times of their discovery.
  3 KB (426 words) - 14:21, 14 February 2019
• Distributed computing
  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
  ...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 *[http://primes.utm.edu/notes/1257787.html The Prime Pages]
  3 KB (513 words) - 08:42, 18 February 2019
• Paul Gage
  351 bytes (43 words) - 23:51, 14 January 2024
• No Prime Left Behind
  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
• Binary
  1 KB (210 words) - 11:16, 22 January 2019
• Repunit
  1 KB (207 words) - 08:04, 12 March 2024
• Mersennewiki
  647 bytes (99 words) - 12:09, 25 February 2019
• Trial factoring
  ...arly for the case of a 32-bit digit size, though now there are 203,280,220 primes to test, and, each one requires 32 bits of storage rather than 16 bits... B ...e <math>2^{32} - 1</math>, would suffice for a sieving process to generate primes as candidate factors up to <math>2^{64}</math> that would suffice to test N
  7 KB (1,221 words) - 13:20, 11 February 2019
• Steven Boone
  512 bytes (71 words) - 11:26, 14 January 2024
• M45
  ...ww.mersenne.org/primes/m45and46.htm GIMPS Discovers 45th and 46th Mersenne Primes] (press release) *[https://www.mersenne.org/primes/Known Mersenne primes] at [[GIMPS]]
  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>).
  738 bytes (112 words) - 09:50, 23 January 2019
• M35
  ...program]] useful in both in testing PC's and that it could indeed find new primes.
  2 KB (224 words) - 11:00, 18 February 2019
• University of California, Los Angeles
  Prior to the Internet, 7 Mersenne primes were discovered at UCLA ...were the first ever to be found using a [[computer]]. Robinson's Mersenne primes were the first to be found in 75 years (2 in the very first day of the run,
  2 KB (347 words) - 14:54, 19 September 2021
• Raphael M. Robinson
  4 KB (526 words) - 14:51, 19 September 2021
• M36
  ...puter|supercomputer]] by [[David Slowinski]], discoverer of seven Mersenne primes between 1979 and 1996.
  2 KB (279 words) - 11:01, 18 February 2019
• Jonathan Pace
  ...years prior to the discovery. He first became interested in searching for primes in 2003, when he read an article about the discovery of the [[M40|40th know *[https://www.mersenne.org/primes/press/M77232917.html 50th Known Mersenne Prime Discovered] (press release)
  2 KB (242 words) - 00:08, 15 January 2024
• Sierpiński problem
  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
• Paul Seelhoff
  :[https://primes.utm.edu/curios/page.php?curio_id=11327 Prime Curios!] of [[The Prime Pages]
  2 KB (195 words) - 00:13, 15 January 2024
• Seventeen or Bust
  ...are the largest prime that are not a [[Mersenne prime]]. Six of the eleven primes rest in the Top 100. *[http://www.utm.edu/research/primes/index.html Chris Caldwell's Prime Pages and top rank lists]
  3 KB (544 words) - 16:44, 21 July 2019
• Perfect number
  ...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 ...concrete one-to-one association between even perfect numbers and Mersenne primes. This result is often referred to as the "Euclid-Euler Theorem."
  6 KB (885 words) - 11:33, 7 March 2019
• M9
  ...ed so until 1911. Prior to the developement of the Lucas test all Mersenne primes were proved by some form of [[trial factoring]]. Pervushin used the [[Lucas *[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
  8 KB (1,218 words) - 15:37, 13 August 2020
• Mfakto
  ...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) ...far we sieve the factor candidates on the GPU. The first <GPUSievePrimes> primes are sieved. This parameter also influences the shared mem requirements (low
  17 KB (2,524 words) - 12:39, 24 January 2019
• Riesel and Proth Prime Database
  380 bytes (59 words) - 14:14, 24 January 2019
• Primality test
  3 KB (501 words) - 05:20, 3 August 2021
• Mprime (Cray)
  639 bytes (92 words) - 12:02, 7 February 2019
• Probable prime
  ...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
• Pseudoprime
  ...in the RSA encryption system, where each party needs to generate two large primes, possibly with hundreds of decimal digits. Actually testing candidates for
  1 KB (155 words) - 20:32, 25 July 2020
• 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
  6 KB (962 words) - 10:08, 7 March 2019
• Quadratic residue
  823 bytes (117 words) - 20:11, 26 October 2020
• Ten million digits
  979 bytes (146 words) - 14:23, 6 March 2019
• PSearch
  *[http://primes.utm.edu/bios/page.php?id=437 The Prime Pages Titan Biography]
  1 KB (182 words) - 08:17, 12 July 2020
• Brent-Suyama extension
  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< ...that it is a [[primorial]]. A larger primorial increases the proportion of primes that pair up, at the cost of having to consider a larger number of congruen
  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
  362 bytes (48 words) - 09:20, 29 January 2019
• Generalized Fermat prime
  ...&OnList=yes&Number=10&Style=HTML Current Top10] largest generalized Fermat primes at Prime Pages
  372 bytes (49 words) - 13:35, 6 March 2019
• Generalized Fermat number
  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''. ...p.'' 67 (1998), pp. 441-446</ref> for the first time built a list of large primes of the form: a^{2^m}+b^{2^m}, ''b > a &
  5 KB (726 words) - 09:57, 12 September 2021
• PrimeGrid
  :[[PrimeGrid 321 Prime Search|321 Prime Search]] searching for mega primes of the form {{Kbn|±|3|2|n}}. :[[PrimeGrid 27121 Prime Search|27121 Prime Search]] searching for primes of the forms {{Kbn|±|27|2|n}} and {{Kbn|±|121|2|n}}.
  3 KB (458 words) - 10:28, 26 March 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).
  4 KB (603 words) - 02:31, 18 August 2019
• PrimeNet server
  ...re forced into service has had important benefits. Since one of the 2 new primes was 10 million decimal digits long, it qualified for one of the [[EFF prize
  2 KB (381 words) - 14:05, 21 August 2019
• 100 Million Digit Prefactor Project
  ...nne prime]] was discovered, interest in working on '''100''' million digit primes picked up sharply. This coupled with new versions of Prime95 and PrimeNet,
  3 KB (534 words) - 10:06, 7 March 2019
• 321 Search
  These are the simple steps needed to participate in the 321 Search for primes. Test your range for primes by using [[LLR]].
  1 KB (185 words) - 09:34, 3 August 2021
• Sieve of Eratosthenes
  There are approximately <math>\sqrt{N}\over{log\sqrt{N}}</math> primes smaller than <math>\sqrt{N}</math>, and for each one we do <math>N</math> t The sieve of Eratosthenes is generally used to generate a list of primes for computation of some sort. For example, one may use it to rapidly genera
  4 KB (654 words) - 11:10, 6 February 2019
• Amazon EC2
  Amazon EC2 instances were used to verify record-breaking primes [[M49]] and [[M50]] at the time of their discovery.
  1 KB (155 words) - 11:48, 12 February 2019
• Prime
  ...dea of a 'largest prime' is fiction. And, if there is no largest prime the primes must be infinite. ...rs must end with either 1 more or 5 more than these digits. Therefore, all primes greater than 2 will end with a 1, 3, 5, 7, or 9, and, since any number endi
  2 KB (447 words) - 00:22, 10 July 2023
• Twin prime
  ...y twin primes. But it is known that the sum of the reciprocals of all twin primes converges to Brun's constant (about 1.902160583104). ==List of twin primes==
  2 KB (255 words) - 06:08, 21 February 2023
• Twin Prime Search
  826 bytes (100 words) - 11:04, 21 March 2024
• Riesel Prime Search
  :# {{Vk}}-values that can produce many primes in the given range of exponent {{Vn}} :# Low-weight {{Vk}}-values that produce a very small number of primes (opposite to (1) above)
  845 bytes (120 words) - 02:21, 1 May 2024
• Nomenclature and notation
  ...h>2^{127}-1</math> or other [[List of known Mersenne primes|known Mersenne primes]] as M61, M127, or such. The reader will generally understand that in case
  3 KB (467 words) - 20:32, 14 February 2019
• Seventeen or Bust/Primes
  *[https://primes.utm.edu/primes/search.php All SoB primes]
  2 KB (163 words) - 14:20, 7 March 2019
• Seventeen or Bust/FAQ
  *[[Seventeen or Bust/Primes|Primes]]: Primes found and open values.
  550 bytes (87 words) - 13:39, 1 February 2019
• Seventeen or Bust/Sieving
  ...still be very pleasing. The drawback of sieving is that you'll never find primes by sieving, like [[Seventeen or Bust/Factoring|factoring]].
  2 KB (363 words) - 13:41, 1 February 2019
• Seventeen or Bust/PRP
  ...his is the part where workers actually find new [[Seventeen or Bust/Primes|primes]]. This is the easiest part of the project.
  888 bytes (145 words) - 13:40, 1 February 2019
• Why participate in GIMPS?
  ...://www.utm.edu/research/primes/notes/faq/why.html Why do people find these primes?] ...numbers (no odd perfect numbers are known) are all closely related to the primes of the form 2^p-1, for some prime ''p'' (now called [[Mersenne pr
  7 KB (1,252 words) - 09:47, 7 March 2019
• Sieving
  If we need to find prime numbers, for all primes between 2 and the square root of the maximum member of the sequence, set to ...s less than the computed square root, this procedure can fail, because all primes less than that value will be marked as composites. But this can be fixed ea
  3 KB (521 words) - 11:14, 6 February 2019
• Sieving program
  ...f numbers of the form k&times;2ⁿ+/-1) http://www.underbakke.com/primes/
  2 KB (220 words) - 11:42, 7 March 2019
• NewPGen
  *k&times;n#±1 (twin primes) ...nds of primes you ought to rapidly sieve out any k or n divisible by small primes. Since it works with a large set of numbers and uses fast implementations,
  3 KB (529 words) - 09:32, 7 March 2019
• Sophie Germain prime
  It is not known whether there are infinitely many Sophie Germain primes. ==List of Sophie Germain primes==
  1 KB (171 words) - 04:26, 3 November 2020
• M13
  *[[List of known Mersenne primes]]
  419 bytes (48 words) - 14:50, 19 September 2021
• M14
  *[[List of known Mersenne primes]]
  420 bytes (48 words) - 14:49, 19 September 2021
• M15
  *[[List of known Mersenne primes]]
  430 bytes (49 words) - 14:49, 19 September 2021
• M16
  *[[List of known Mersenne primes]]
  431 bytes (49 words) - 14:49, 19 September 2021
• M17
  *[[List of known Mersenne primes]]
  431 bytes (49 words) - 14:49, 19 September 2021
• M18
  *[[List of known Mersenne primes]]
  415 bytes (47 words) - 22:26, 17 February 2019
• M11
  *[[List of known Mersenne primes]]
  412 bytes (47 words) - 14:23, 17 February 2019
• M10
  *[[List of known Mersenne primes]]
  403 bytes (44 words) - 13:54, 17 February 2019
• Proth prime
  ...e form {{Kbn|+|k|n}} with 2^''n'' > ''k'' are often called Proth primes. *[http://primes.utm.edu/glossary/page.php?sort=ProthPrime Definition from The Prime Glossar
  656 bytes (91 words) - 07:02, 31 August 2020
• Riesel prime
  Although there's no official definition of a '''Riesel prime''' mostly all primes of the form {{Kbn|k|n}} with 2^{{Vn}} > {{Vk}} are called like th *[https://www.mersenneforum.org/showthread.php?t=13180 "Post Top-5000 Primes Here"]: [https://www.mersenneforum.org/showpost.php?p=208696 #1 (2010-03-17
  2 KB (279 words) - 03:48, 24 April 2024

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