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• GIMPS chances of finding a prime number
  ...are used to calculate the probability of something happening based on the number of possible outcomes, not on what the last three or three hundred outcomes ...your next throw are 1:6. What has happened in the past does not affect the number of faces on the dice, which is all that is used to calculate the odds.
  3 KB (593 words) - 10:09, 7 March 2019

Page text matches

• Williams prime
  A '''Williams number''' is a [[natural number]] of the form {{Kbn|(b-1)|b|n}} for integers ''b'' ≥ 2 and ''n'' ≥ 1. A '''Williams prime''' is a Williams number which is [[prime]].
  5 KB (744 words) - 07:30, 5 August 2019
• Great Internet Mersenne Prime Search
  ...e Search: A [[distributed computing project]] for the search of [[Mersenne prime]]s.}} ...hat can be downloaded from the Internet, in order to search for [[Mersenne prime]] numbers.
  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 *'''n-value''': value of exponent and if available link to [[The Prime Pages]] entry
  2 KB (360 words) - 09:44, 6 March 2019
• Mersenne prime
  ...}. On the other hand, 15 = 16 − 1 = {{Kbn|4}}, for example, is not a prime, because 15 is divisible by 3 and 5. More generally, [[Mersenne number]]s (not necessarily primes, but candidates for primes) are numbers that are
  5 KB (857 words) - 14:53, 19 September 2021
• Mersenne number
  A '''Mersenne number''' is a number of the form <math>2^n{-}1</math> where <math>n</math> is a non-negative [[i ...[prime]], it is called a [[Mersenne prime]], otherwise it is a [[composite number]].
  2 KB (351 words) - 11:28, 7 March 2019
• Landon Curt Noll
  ...ted in the New York times on 1978-11-21. The 18 year-olds were studying [[number theory]] at the time at CSUH with Dr. [[Derrick Henry Lehmer]] of [[Univers ...e [[multiplication]]s need in [[Lucas-Lehmer test]]ing of large [[Mersenne number]]s.
  2 KB (333 words) - 12:40, 9 February 2022
• Laura A. Nickel
  ...l and Nickel were still high school students. For the verification of this number alone, the pair used almost eight hours of time running an assembly languag
  2 KB (254 words) - 01:23, 15 January 2024
• Fermat number
  In [[mathematics]], a '''Fermat number''', named after [[Pierre de Fermat]] who first studied them, is a positive ...ese factorisations can be found at [http://www.prothsearch.com/fermat.html Prime Factors of Fermat Numbers]
  12 KB (1,913 words) - 14:35, 9 August 2021
• M50
  | number=467333183359...069762179071 '''M50''' normally refers to the 50th [[Mersenne prime]], in order of size from the smallest to greatest. This is the primary usag
  2 KB (333 words) - 13:16, 17 February 2019
• M49
  | number=300376418084...391086436351 '''M49''' normally refers to the 49th [[Mersenne prime]], in order of size from the smallest to greatest. This is the primary usag
  2 KB (283 words) - 11:50, 18 February 2019
• Derrick Henry Lehmer
  ...factoring a number ''N'' is hereby reduced to the discovery of an adequate number of quadratic residues ''R'' of ''N'' and the superposition of the correspon ...ber sieves]] to be run on a computer. He had previously built an automatic number sieve from a small electric motor and some bicycle chains hanging from spro
  6 KB (1,033 words) - 01:13, 15 January 2024
• Titanic prime
  A '''Titanic prime''' is a [[prime]] number whose decimal representation has {{Num|1000}} or more digits. The smallest titanic prime is {{T5000|58901|10⁹⁹⁹+7}}.
  394 bytes (48 words) - 11:40, 2 July 2020
• Gigantic prime
  A '''gigantic prime''' is a [[prime]] number whose decimal representation has at least {{Num|10000}} [[digit]]s. The smallest gigantic prime is 10^{{Num|9999}}+{{Num|33603}}.
  515 bytes (67 words) - 13:38, 6 March 2019
• Megaprime
  A '''Megaprime''' is a [[prime]] number whose decimal representation has {{Num|1000000}} or more digits. There are ...st 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
  A '''Gigaprime''' is a [[prime]] number whose [[decimal]] representation has {{Num|1000000000}} or more [[digit]]s. [[Operation Billion Digits]] is factoring [[Mersenne number]]s in this range.
  871 bytes (119 words) - 07:54, 14 July 2021
• Home prime
  ...me prime depends on the [[base]] (except in the case where ''n'' itself is prime). While it is expected that every ''n'' in every base has a home prime, experimental evidence indicates that these chains can get quite long.
  980 bytes (143 words) - 13:22, 6 March 2019
• Cunningham project
  ...it is considered the oldest continuously ongoing activity in computational number theory. ...exponent. The second type is [[aurifeuillian factor]], in which the whole number can be split into two parts directly, for certain combination of values of
  7 KB (1,150 words) - 23:48, 19 April 2023
• M25
  | number=448679166119...353511882751 The 25th [[Mersenne prime]], in order from smallest to largest and in order of discovery.
  2 KB (303 words) - 11:01, 26 February 2019
• Lucas-Lehmer test
  ...e last stage in the procedure employed by [[GIMPS]] for finding [[Mersenne prime]]s. Previous stages try to find factors, as explained on [[GIMPS factoring ...lete proof that this was not only true when p = 1 (mod 4), but for all odd prime exponents. The test therefore takes its name from the two mathematicians wh
  20 KB (3,572 words) - 14:30, 17 February 2019
• Édouard Lucas
  ...[[Mersenne prime]] for almost 75 years, and is still the highest [[prime]] number discovered without the aid of a computer.
  2 KB (296 words) - 01:09, 15 January 2024
• 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]]
  204 bytes (18 words) - 13:46, 17 February 2019
• 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
  639 bytes (92 words) - 12:02, 7 February 2019
• 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

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