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• Edson Smith
  .... In August 2008, one of these computers found a [[M47| World record prime number.]] Since the first [[Mersenne prime]] found by a computer ([[M13]]) was found at UCLA (as were 6 others in the
  4 KB (564 words) - 00:11, 15 January 2024
• Mathematics
  '''Mathematics''' is the science of space, number and quantity. ...theorem: If you subtract an odd number from an even number you get an odd number.
  1 KB (186 words) - 17:00, 5 February 2019
• Factorial number
  ...or bang) after a number, it represents multiplying a number by all [[whole number|whole numbers]] smaller than it. *[[Factorial prime]]
  729 bytes (93 words) - 13:40, 5 November 2023
• Factor
  A '''factor''' is one of the numbers or expressions that make up another number by [[multiplication]]. Let a and b be integers. Then a divides b (which may ...a number that has factors other than itself and 1 is called a [[composite number]].
  576 bytes (107 words) - 19:03, 5 February 2019
• Composite number
  A positive [[integer]] is '''composite''' if it is neither [[prime]] nor equal to 1. The smallest composite is 4. ...he integers <math>a</math> and <math>b</math> are both greater than 1, the number is composite.
  358 bytes (56 words) - 23:30, 26 October 2020
• Factoring Database
  **[[Home prime]]s of various bases **Greatest prime factor ^2+1, ^2+2, ^2-1, ^2-2, ^3+1, ^3-1
  1 KB (144 words) - 13:44, 24 January 2019
• Factorization
  '''Factorization''' is the process of finding [[prime]] [[factor]]s. This article will only cover integer factorization. ...t can be seen that we have to proceed recursively in order to find all the prime factors of ''c''.
  4 KB (642 words) - 12:57, 5 March 2019
• EFF prizes
  ...substantial award for the person that discovers a ten million digit prime number. If you find such a prime with the software provided, GIMPS will claim the award and distribute the a
  2 KB (321 words) - 18:50, 14 December 2023
• Mlucas
  ...st]]s of prime-exponent [[Mersenne number]]s, and Pépin tests of [[Fermat number]]s. It is written by [[Ernst Mayer]] using C programming language and [[ARM ...es not impose prize-sharing rules, should a user be lucky as to find a new prime eligible for the monetary prize offered by the [[Electronic Frontier Founda
  1 KB (198 words) - 07:28, 22 August 2019
• M48
  | number=581887266232...071724285951 '''M48''' normally refers to the 48th [[Mersenne prime]], in order of size from the smallest to greatest. This is the primary usag
  2 KB (235 words) - 11:49, 18 February 2019
• M47
  | number=316470269330...166697152511 ...] article. The number now refered to as M47 was actually the 45th Mersenne prime found. [[M45]], [[M46]], and M47 were discovered in the order of M47, M45 (
  5 KB (694 words) - 13:17, 21 August 2019
• Prime95
  ...], a [[distributed computing]] project dedicated to finding new [[Mersenne prime]] numbers. More specifically, Prime95 refers to the Windows and Mac OS X ve ...Awards]). As such, a user who uses Prime95 to discover a qualifying prime number would not be able to claim the prize directly. A free software package woul
  11 KB (1,586 words) - 12:24, 7 August 2021
• Odd number
  An '''odd number''' is any [[integer]] that is not divisible by 2. ...expressed in decimal notation, the odd numbers end in 1, 3, 5, 7 or 9. All prime numbers except 2 are odd.
  316 bytes (42 words) - 11:21, 7 March 2019
• M41
  | number=299410429404...882733969407 '''M41''' is the short hand used to refer to the 41st [[Mersenne prime]] 2^{{{Num|24036583}}}-1.
  1 KB (203 words) - 11:26, 18 February 2019
• M43
  | number=315416475618...411652943871 '''M43''' is the short hand used to refer to the 43rd [[Mersenne prime]] 2^{{{Num|30402457}}}-1.
  1 KB (191 words) - 11:31, 18 February 2019
• M46
  | number=169873516452...765562314751 '''M46''' is the short hand used to refer to the 46th [[Mersenne prime]] 2^{{{Num|42643801}}}-1.
  2 KB (248 words) - 11:45, 18 February 2019
• Distributed computing
  There are a number of individuals or groups in the fields of science, mathematics, cryptograph ...ernet, to look for extra-terrestrial radio signals, to look for [[Mersenne prime]]s so large that they have more than [[ten million digits]], to find more e
  4 KB (674 words) - 12:11, 19 February 2019
• M42
  | number=122164630061...280577077247 '''M42''' refers to the 42nd [[Mersenne prime]] 2^{{{Num|25964951}}}-1.
  934 bytes (118 words) - 11:26, 18 February 2019
• M1
  | number= 3 [[Category:Mersenne prime|M01]]
  193 bytes (19 words) - 13:43, 17 February 2019
• Conjectures 'R Us
  ...project]] in search for lowest [[Sierpiński number|Sierpiński]]/[[Riesel number|Riesel]] values.}} ...mbination of algebraic and trivial factor(s), or make [[Generalized Fermat number]]'s.
  3 KB (503 words) - 02:20, 1 May 2024
• Fast Fourier transform
  Let ''x''₀, ...., ''x''_''n''-1 be [[complex number]]s. The DFT is defined by the formula ...lar misconception) there are O(''n'' log ''n'') FFTs for all ''n'', even [[prime]] ''n''.
  17 KB (2,684 words) - 18:50, 28 September 2023
• GpuLucas
  ...[[CUDA]]-based program written by [[Andrew Thall]] for testing [[Mersenne number]]s for primality. ...l, A. [http://andrewthall.org/papers/gpuMersenne2011MKII.pdf Fast Mersenne Prime Testing on the GPU] (2011)
  2 KB (239 words) - 11:12, 13 February 2019
• GpuOwL
  {{InfoboxProgram|workload=[[Lucas-Lehmer test|LL]], [[Probable prime|PRP]]|title=gpuOwL|release=2017|latest=7.2<br>2020-11-01}} ...s a [[OpenCL]]-based program written by Mihai Preda for testing [[Mersenne number]]s for primality.
  1 KB (216 words) - 05:22, 1 December 2020
• MersenneForum
  ...upport [[GIMPS]], the broader community of [[Mersenne number]]s, [[prime]] number, and factoring projects. In addition to being the de facto help and support ==Prime number software discussion and development==
  2 KB (293 words) - 17:33, 5 July 2019
• Primo
  '''Primo''' is a computer program which tests numbers for [[prime|primality]] using the [[Elliptic Curve Primality Proving]] (ECPP) [[algorit ...ot require a number to be of any specific form. If a number is found to be prime, a [[primality certificate]] is produced, which can be quickly verified.
  1 KB (191 words) - 20:33, 12 May 2020
• M32
  | number=174135906820...328544677887 The '''32nd [[Mersenne prime]]''', both in size (smallest to largest) and in order of discover.
  2 KB (279 words) - 08:35, 18 February 2019
• M33
  | number=129498125604...243500142591 '''M33''' refers to 33rd [[Mersenne prime]] number 2^{{{Num|859433}}}-1.
  814 bytes (97 words) - 08:38, 18 February 2019
• M34
  | number=412245773621...976089366527 ...ber {{Num|378632}} [[decimal]] [[digit]]s long. The number was found to be prime in 1996.
  3 KB (513 words) - 08:42, 18 February 2019
• Rational number
  A '''rational number''' is a [[real number]] which can be written as <math>\frac{a}{b}</math> or <math>a/b</math> wher ...r [[greatest common divisor]]. This operation does not change the rational number represented by the fraction.
  3 KB (541 words) - 15:01, 26 March 2023
• Binary
  ...iness' of Mersenne numbers makes calculations in the search for [[Mersenne prime]]s a bit easier.
  1 KB (210 words) - 11:16, 22 January 2019
• Repunit
  ...[[Mersenne number]]s are repunit ('''rep'''eated '''unit''', "1" being the number referred to as "unity") numbers. 111 is a repunit, in base 2 it is equal to A '''Repunit prime''' is a repunit which is also [[prime]].
  1 KB (207 words) - 08:04, 12 March 2024
• Trial factoring
  ...are found, the number in question is prime; otherwise, it is a [[composite number]]. ..., P(2) = 3, P(3) = 5, etc, then the last prime factor possibility for some number N would be P(m) where P(m + 1) squared exceeds N.
  7 KB (1,221 words) - 13:20, 11 February 2019
• M40
  | number=125976895450...762855682047 ...Num|6320430}} decimal digits] long. This prime number was the sixth record prime found by the [[GIMPS]] project.
  1 KB (189 words) - 11:17, 18 February 2019
• M39
  | number=924947738006...470256259071 ...[[Michael Cameron]], using [[Prime95]] written by [[George Woltman]]. The number is [http://www.mersenneforum.org/txt/39.txt {{Num|4053946}} decimal digits]
  868 bytes (109 words) - 11:14, 18 February 2019
• M44
  | number=124575026015...154053967871 '''M44''' is the short hand used to refer to the 44th [[Mersenne prime]]. Currently that designation belongs to 2^{{{Num|32582657}}}-1.
  997 bytes (129 words) - 11:35, 18 February 2019
• M45
  | number=202254406890...022308220927 ...''' normally refers to 2^{{{Num|37156667}}}-1, the 45th [[Mersenne prime]] in order of size from the smallest to greatest. This is the primary usage
  2 KB (251 words) - 11:40, 18 February 2019
• Richard Crandall
  ...uter]] scientist and physicist who has made contributions to computational number theory. He received a doctorate from [[Massachusetts Institute of Technolog His Erdös number is 2. He was one of the primary verifiers of [[M32]], [[M33]], and [[M34]].
  3 KB (431 words) - 11:36, 14 January 2024
• M38
  | number=437075744127...142924193791 ...[[Nayan Hajratwala]], using [[Prime95]] written by [[George Woltman]]. The number is [http://www.mersenneforum.org/txt/38.txt {{Num|2098960}} decimal digits]
  1 KB (165 words) - 11:10, 18 February 2019
• Nayan Hajratwala
  ...houseCoopers employee from Michigan who discovered the [[M38|38th Mersenne prime]], 2^{{{Num|6972593}}}-1. ...99-06-01, Hajratwala's 350 MHz IBM Aptiva home computer first reported the prime to the [[GIMPS]] server. The computer had taken 111 days to complete the te
  809 bytes (109 words) - 23:55, 14 January 2024
• Irrational base discrete weighted transform
  ...T''') is a variant of the [[Fast Fourier transform]] using an [[Irrational number|irrational]] base. It was proposed by [[Richard Crandall]] and [[Barry Fagi The IBDWT is used to perform FFT multiplication modulo [[Mersenne number]] in such programs as [[Prime95]], [[CUDALucas]], [[Glucas]], [[gpuLucas]].
  1 KB (172 words) - 18:49, 28 September 2023
• PrimeKit
  ...Mathematica implementations of all 112 algorithms discussed in the book ''Prime Numbers: A Computational Perspective'' (2001) by [[Richard Crandall]] and C ...optimized), but there is also an "Extras" folder containing some efficient number-theoretical C sources.
  1 KB (125 words) - 09:38, 23 January 2019
• Coprime
  ...h>\gcd{(x,y)} = 1</math>). This does not mean that any of these numbers is prime. :Two random numbers are coprime with a probability over 60% (the exact number is <math>6/\pi^2</math>).
  738 bytes (112 words) - 09:50, 23 January 2019
• Greatest common divisor
  ...re <math>a</math> and <math>b</math> are positive integers, is the maximum number that divides both <math>a</math> and <math>b</math>. ...] or relatively prime. This does not mean that either of these numbers are prime.
  2 KB (339 words) - 18:38, 27 September 2023
• Elliptic curve method
  ...le of a point on a random elliptic curve [[modular arithmetic|modulo]] the number to be factored. It is currently the best [[algorithm]] known, among those w ...ber]]. This method cannot be used when it is not known in advance that the number is composite, so it cannot be used as a [[primality test]].
  19 KB (3,181 words) - 22:27, 6 July 2023
• M35
  | number=814717564412...868451315711 '''M35''' is the 35th [[Mersenne prime]], both in order of size and date of discovery.
  2 KB (224 words) - 11:00, 18 February 2019
• University of California, Los Angeles
  As an institution, UCLA has contributed to the discovery of 8 [[Mersenne prime]]s. This is more than any other university. [[University of Central Missour ...number of digits of the largest known [[prime]] (in general) and Mersenne Prime from 79 and 39 (respectively) to 687.
  2 KB (347 words) - 14:54, 19 September 2021
• Raphael M. Robinson
  ...0) proved that an essentially undecidable theory need not have an infinite number of axioms by coming up with a counterexample: Robinson arithmetic ''Q''. '' ..., [[M16|2203]], [[M17|2281]]. He discovered the last 5 of these [[Mersenne prime]]s, the largest ones known at the time.
  4 KB (526 words) - 14:51, 19 September 2021
• M36
  | number=623340076248...743729201151 ...It took Spence's 100 MHz [[Pentium]] computer 15 days to prove the number prime. Alan White Managing Director at Technology Business Solutions, who provide
  2 KB (279 words) - 11:01, 18 February 2019
• Jonathan Pace
  ...l engineer. He is credited with discovery of the [[M50|50th known Mersenne prime]] {{Kbn|77232917}}. ...en he read an article about the discovery of the [[M40|40th known Mersenne prime]].
  2 KB (242 words) - 00:08, 15 January 2024
• Sierpiński problem
  The '''Sierpiński problem''' in [[number theory]] was proposed by [[Wacław Sierpiński]] in 1960. ...[[composite number]] {{V|N}}, then {{Vk}} is said to be a '''[[Sierpiński number]]'''.
  5 KB (650 words) - 10:25, 26 March 2024
• Seventeen or Bust
  ...(SOB)''' was a [[distributed computing]] project working on a problem in [[number theory]] called the [[Sierpiński problem]]. It is currently a subproject o ...we are running [[primality test]]s called [[Probable prime|PRP]] (Probable Prime), which take a very long time, for every candidate in the queue.
  3 KB (544 words) - 16:44, 21 July 2019
• M2
  | number= 7 [[Category:Mersenne prime|M02]]
  193 bytes (19 words) - 13:43, 17 February 2019
• M3
  | number= 31 [[Category:Mersenne prime|M03]]
  194 bytes (19 words) - 13:43, 17 February 2019
• M4
  | number= 127 [[Category:Mersenne prime|M04]]
  195 bytes (19 words) - 13:44, 17 February 2019
• M5
  | number= 8191 [[Category:Mersenne prime|M05]]
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• Perfect number
  In [[mathematics]], a '''perfect number''' is defined as an integer which is the sum of its proper positive divisor ...and 3 are its proper 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.
  6 KB (885 words) - 11:33, 7 March 2019
• M9
  | number=2305843009213693951 The ninth [[Mersenne prime]], 2⁶¹-1 or {{Num|2305843009213693951}}.
  2 KB (213 words) - 14:30, 17 February 2019
• Double check
  *human error (entering wrong number to test, misreading data, etc.) ...t]] does a verfication on all [[factor]]s reported. (It is easy to check a number for a single factor.)
  2 KB (373 words) - 15:08, 5 June 2019
• Residue
  ...ctly divisible. For the L-L test a zero residue means that the number is [[prime]]. ...test to produced matching erroneaous residues (meaning they both missed a prime) out of a pool of ~ 18.4 pentillion numbers, this is considered to be impos
  1 KB (235 words) - 10:24, 6 February 2019
• GIMPS clients
  The [[Great Internet Mersenne Prime Search]] (GIMPS) as a project is based on two related items: theory and pra ...very large Mersenne prime candidates to be tested for primality ("is it a prime?") faster than other sorts of would-be primes of the same magnitude. "Faste
  8 KB (1,218 words) - 15:37, 13 August 2020
• Mfaktc
  ...ics cards, this is a very fast program. The name mfaktc is "'''M'''ersenne number '''fakt'''oring with '''C'''UDA", it is a mixture of English with the Germa *Prime exponents between 100000 and <math>2^{32}-1</math>
  5 KB (765 words) - 14:54, 25 February 2019
• Rho factorization method
  The idea is to create a sequence iterating a polynomial modulo the number to be factored. When N = pq where p and q are [[coprime]] but not necessarily [[prime]], we will see that after about <math>\sqrt p</math> elements the sequence
  3 KB (558 words) - 10:28, 6 February 2019
• Riesel number
  ...value of ''k'' such that {{Kbn|k|n}} is always composite for all [[natural number]]s. ...Sierpiński problem]] article, [[Hans Riesel]] found in 1956 that [[Riesel prime 2 509203|{{Kbn|509203|n}}]] is always composite.
  827 bytes (112 words) - 08:21, 25 March 2024
• M12
  | number=170141183460...715884105727 ...n a "smart phone" in under one second. This was the largest known Mersenne prime until 1952, when [[Raphael M. Robinson|Robinson]] at [[University of Califo
  2 KB (354 words) - 14:52, 19 September 2021
• Primality test
  .... When the number is declared composite, the algorithm does not reveal the prime [[factor]]s. That is the job of the [[Factorization|factorization methods]] ...(which is far slower than a probable primality test except when the input number has a special form) is run on it.
  3 KB (501 words) - 05:20, 3 August 2021
• Lucas primality test
  ...' invented in 1891 by [[Édouard Lucas]], determines whether a number N is prime or not, using the complete factorization of N-1. ...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
• Primality testing program
  ...ne number]]s<br/>a &times; bⁿ±c (only factoring and [[probable prime|PRP]]-testing) | [[generalized Fermat number]]s
  2 KB (314 words) - 21:23, 29 August 2019
• Pépin's test
  '''Pépin's test''' is mainly used for proving the primality of [[Fermat number]]s, but it is of no help for finding the factors of such numbers. ...for proving the primality of other numbers, like the [[Generalized Fermat number]]s <math>F_{n,2} = 4^{3^n}+2^{3^n}+1</math> with k = 5 instead of k = 3.
  2 KB (401 words) - 14:40, 6 March 2019
• Mprime (Cray)
  ...later versions with [[Paul Gage]]), for testing [[Mersenne number]]s for [[Prime|primality]] on [[Cray Research|Cray]] [[Classes of computers#Supercomputer| This software is responsible for the discovery of 7 [[Mersenne prime]]s. It used [[Fast Fourier transform]]s for the [[multiplication]] of very
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• Probable prime
  ...an [[integer]] that satisfies a specific condition also satisfied by all [[prime]] numbers.}} ...ecific conditions. While there may be probable primes that are [[Composite number|composite]] (called [[pseudoprime]]s), the condition is generally chosen in
  2 KB (232 words) - 07:28, 12 March 2024
• Pseudoprime
  A '''pseudoprime''' is a [[composite number]] which passes some probabilistic [[primality test]]s. For example, a ''strong pseudoprime'' is a composite number that passes one iteration the [[Miller-Rabin pseudoprimality test]].
  1 KB (155 words) - 20:32, 25 July 2020
• Operation Billion Digits
  ...ibuted computing project]] that is searching for a "Billion Digit Mersenne prime". ...e also unfeasible because they require operations modulo the billion digit number. The only part of this project that can be undertaken today is [[trial fact
  6 KB (918 words) - 16:28, 24 July 2020
• M37
  | number=127411683030...973024694271 ...[[Roland Clarkson]], using [[Prime95]] written by [[George Woltman]]. The number is [http://www.mersenneforum.org/txt/37.txt {{Num|909526}} decimal digits]
  877 bytes (111 words) - 11:04, 18 February 2019
• GIMPS factoring and sieving
  ...o do the Lucas-Lehmer Test; in fact, over 60% of [[Mersenne number]]s with prime exponents are eliminated from consideration as possible primes this way, so ...given Mersenne number up to some predetermined size, usually a prescribed number of bits.
  6 KB (962 words) - 10:08, 7 March 2019
• Quadratic residue
  In [[mathematics]], a number {{V|q}} is called a '''quadratic residue''' [[modular arithmetic|modulo]] { ...w of quadratic reciprocity]] says something about quadratic residues and [[prime]]s.
  823 bytes (117 words) - 20:11, 26 October 2020
• Modular square root
  A '''modular square root''' <math>r</math> of an [[integer]] number <math>a</math> modulo an integer <math>m</math> greater than 1 is an intege ...modulus is [[prime]]. Otherwise we can compute the square roots modulo the prime factors of <math>m</math> and then generate a solution using the Chinese Re
  5 KB (726 words) - 10:38, 6 February 2019
• Legendre symbol
  If <math>p</math> is an odd [[prime]] number and <math>a</math> is an [[integer]], then the Legendre symbol There are a number of useful properties of the Legendre symbol which can be used to speed up c
  2 KB (348 words) - 18:57, 28 September 2023
• Law of quadratic reciprocity
  ...</math> is a [[quadratic residue]] or non-residue modulo another odd prime number <math>q</math> if we know whether <math>q</math> is a quadratic residue or
  1 KB (208 words) - 18:19, 2 October 2022
• Ten million digits
  ...llion [[decimal]] [[digit]]s) in June of 1999, the next [[EFF prizes]] for prime numbers was '''ten million decimal digits'''. ...was found, [[M46]]. By the end of 2010, all exponents that would produce a number less than {{Num|10000000}} digits had been [[primality test|tested]] at lea
  979 bytes (146 words) - 14:23, 6 March 2019
• Double Mersenne number
  ...efer to <math>2^{2^p-1}-1</math>. Early on it was thought that if M(p) was prime so too was MM(p). *MM(2) = <math>2^3-1</math> = 7, known prime since antiquity
  4 KB (655 words) - 14:50, 19 September 2021
• PSearch
  ...g project|distributed computing project]] in search of the largest [[Proth prime]]s. ! scope="col" | Number
  1 KB (182 words) - 08:17, 12 July 2020
• P-1 factorization method
  Let ''p'' be a prime which does not divide the integer ''a'', then <math>a^{p-1}\equiv 1 \mbox{( ...tiple of ''N'', so a [[greatest common divisor]] operation will reveal the prime divisor.
  5 KB (814 words) - 01:35, 12 March 2019
• Brent-Suyama extension
  ...of prime powers less than B1. Then by [[Fermat's Little Theorem]], a prime number p | S-1 if p-1 | E. ...tage 2 would then compute T=S^q = 3^E*q for successive prime q in the range (B1,B2]. Then p | T-1 if p-1 | q*E.
  2 KB (421 words) - 11:51, 28 January 2019
• Self-initializing quadratic sieve
  Let N be the number to be factored. This number must not be a perfect power. If somehow we find two integers X and Y such t ...form <math>t^2 \equiv u\,\pmod N</math> where u is the product of small [[prime]] numbers. The set of these primes is the ''factor base''. These relations
  10 KB (1,763 words) - 02:56, 12 March 2019
• Lone Mersenne Hunters
  ...imeNet]] in order to eliminate [[Mersenne number]]s as possible [[Mersenne prime]] candidates. This work is suited to older and slower processors, often wit
  1 KB (213 words) - 09:58, 7 March 2019
• Fermat pseudoprimality test
  where ''p'' is a [[prime]] number and ''a'' is not multiple of <math>p</math>. ...t is not 1, the number must be composite. Otherwise the number is either a prime or a Fermat [[pseudoprime]] with respect to base <math>a</math>.
  1 KB (164 words) - 10:56, 6 February 2019
• Miller-Rabin pseudoprimality test
  The '''Miller-Rabin pseudoprimality test''' is based in two facts for prime numbers: ...primality, and <math>N = 2^n\,k + 1</math> where <math>k</math> is an odd number.
  3 KB (432 words) - 15:33, 28 January 2019
• Generalized Fermat prime
  ...'generalized Fermat prime''' is a [[generalized Fermat number]] which is [[prime]]. *[[Wikipedia:Fermat_number#Generalized_Fermat_primes|Generalized Fermat prime]]
  372 bytes (49 words) - 13:35, 6 March 2019
• Generalized Fermat number
  There are different kinds of '''generalized [[Fermat number]]s'''. ...2^{2p^n}+2^{p^n}+1 \ = \ (2^{p^{n+1}}-1)/(2^{p^n}-1)</math> where p is the prime of apparition rank r (r(2)=1, r(3)=2, r(5)=3, ...) and n is greater or equa
  5 KB (726 words) - 09:57, 12 September 2021
• M51
  | number=148894445742...325217902591 '''M51''' normally refers to the 51st [[Mersenne prime]], in order of size from the smallest to greatest. This is the primary usag
  2 KB (255 words) - 05:53, 21 July 2021
• Patrick Laroche
  ...less than 4 months and on just his fourth try, he discovered the new prime number. By way of comparison, some GIMPS participants have searched for more than He is credited with discovery of the [[M51|51th known Mersenne prime]] 2^{{{Num|82589933}}}-1.
  987 bytes (147 words) - 01:27, 15 January 2024
• PrimeGrid
  '''PrimeGrid''' is a [[distributed computing]] project for searching for [[prime]] numbers of world-record size. It makes use of the [[BOINC|Berkeley Open I :[[PrimeGrid 321 Prime Search|321 Prime Search]] searching for mega primes of the form {{Kbn|±|3|2|n}}.
  3 KB (458 words) - 10:28, 26 March 2024
• Worktype
  ...nne primes have been missed, and lastly finding [[factor]]s for [[Mersenne number]]s). ...ber. A found factor will conclusively prove that the number is [[Composite number|composite]], which eliminates the need to run a [[primality test]].
  4 KB (603 words) - 02:31, 18 August 2019
• Sieve of Eratosthenes
  The '''sieve of Eratosthenes''' is a method to find all [[prime]] numbers smaller than a given integer <math>N</math>. It's invention is cr ...h>, then <math>N</math> is [[composite number|composite]]; otherwise it is prime.
  4 KB (654 words) - 11:10, 6 February 2019
• Aliquot sequence
  An '''aliquot sequence''' is a sequence of numbers generated from an initial number using the sigma <math>\sigma(n)</math> function. ...visors''' of the number, <math>n</math>, which are all the divisors of the number, excluding itself. Therefore, sequences are generated thusly:
  6 KB (914 words) - 19:49, 21 February 2023
• Prime
  ...ger]] greater than 1 that is only divisible by itself and 1. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19. ...that the idea of a 'largest prime' is fiction. And, if there is no largest prime the primes must be infinite.
  2 KB (447 words) - 00:22, 10 July 2023
• Twin prime
  ...mber]] that differs from another prime number by two, for example the twin prime pair (41, 43). ==Count of twin prime pairs==
  2 KB (255 words) - 06:08, 21 February 2023
• Riesel Prime Search
  '''Riesel Prime Search''' (RPS) is a prime searching project established in 2005 by [[Predrag Minovic]] (Kosmaj). :The project is searching for [[Riesel prime]]s {{Kbn|k|n}}, {{Vk}} > 1.
  845 bytes (120 words) - 02:21, 1 May 2024
• Nomenclature and notation
  ==[[Mersenne number]]== ...{p}-1</math> is generally used when discussing the search for a [[Mersenne prime]].
  3 KB (467 words) - 08:48, 15 May 2024
• Why participate in GIMPS?
  ...s of the form 2^p-1, for some prime ''p'' (now called [[Mersenne prime|Mersennes]]). So the quest for these jewels began near 300 BC. ...umbers, how to characterize their [[factor]]s and discover those which are prime. In short, the tradition of seeking large primes (especially the Mersennes)
  7 KB (1,252 words) - 09:47, 7 March 2019

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