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- 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
- In [[mathematics]], a '''Fermat number''', named after [[Pierre de Fermat]] who first studied them, is a positive ...up> + 1).) In other words, every prime of the form {{Kbn|+|n}} is a Fermat number, and such primes are called '''Fermat primes'''. The only known Fermat prim12 KB (1,913 words) - 14:35, 9 August 2021
- The term '''whole number''' does not have a consistent definition. Various authors use it in one of *the positive integers (1, 2, 3, ...) (often called [[natural number]]s)413 bytes (54 words) - 09:51, 8 February 2019
- ...or bang) after a number, it represents multiplying a number by all [[whole number|whole numbers]] smaller than it. *[[Multifactorial number]]729 bytes (93 words) - 13:40, 5 November 2023
- ...he integers <math>a</math> and <math>b</math> are both greater than 1, the number is composite. *[[Wikipedia:Composite number|Wikipedia]]358 bytes (56 words) - 23:30, 26 October 2020
- '''Number theory''' is a branch of pure [[mathematics]] devoted primarily to the stud202 bytes (29 words) - 12:55, 20 January 2019
- ...ber of objects can be placed into exactly 2 groups that have the identical number of objects. *[[Odd number]]425 bytes (61 words) - 11:19, 7 March 2019
- An '''odd number''' is any [[integer]] that is not divisible by 2. *[[Even number]]316 bytes (42 words) - 11:21, 7 March 2019
- A '''real number''' is either a [[rational number]] or an [[irrational number]]. The set of real numbers is denoted by <math>\mathbb{R}</math>. *[[Wikipedia:Real_number|Real number]]390 bytes (57 words) - 15:00, 26 March 2023
- 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
- ...an '''irrational number''' is any [[real number]] that is not a [[rational number]], i.e., one that cannot be written as a ratio of two integers, i.e., it is *[[Wikipedia:Irrational_number|Irrational number]]763 bytes (124 words) - 15:14, 26 March 2023
- *[[Whole number]] *[[Wikipedia:Natural_number|Natural number]]316 bytes (43 words) - 15:00, 26 March 2023
- ...l number {{Vk}} such that all {{Kbn|+|k|n}} for all {{Vn}} are [[Composite number|composite]]. *[[Wikipedia:Sierpiński_number|Sierpiński number]]324 bytes (48 words) - 13:37, 8 April 2023
- 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
- ...value of ''k'' such that {{Kbn|k|n}} is always composite for all [[natural number]]s. In order to demonstrate whether 509203 is the smallest Riesel number or not (the '''[[Riesel problem 1]]'''), a [[distributed computing project]827 bytes (112 words) - 08:21, 25 March 2024
- A '''complex number''' is defined as a pair of [[real number]]s <math>z = (x, y)</math> where the following operations are defined: ...mbers behaves as real numbers. That's why the first element of the complex number is known as the ''real part'' and the second element as the ''imaginary par2 KB (280 words) - 14:59, 26 March 2023
- ...ble Mersenne number''' is a number where the exponent is also a [[Mersenne number]] and usually a [[Mersenne prime]]. These are generally denoted as '''MM<su ...igit]]s long. [[Tony Forbes]] lead an effort to find a [[factor]] for this number. The search has included all '''''[[Value k|k]]''''' values up to {{Num|1164 KB (655 words) - 14:50, 19 September 2021
- {{Shortcut|SNFS|Special number field sieve: special-purpose [[factorization]] algorithm.}} ...(SNFS)''' is a special-purpose [[factorization]] algorithm. The [[general number field sieve]] (GNFS) was derived from it.1 KB (186 words) - 12:07, 19 February 2019
- There are different kinds of '''generalized [[Fermat number]]s'''. :<math>F_{0,r}</math> generates the [[Mersenne number]]s.5 KB (726 words) - 09:57, 12 September 2021
- An '''abundant number''' is any number, '''''n''''', which has a [[sigma|sigma value]] greater than '''''2n'''''. ...bers increase the size of an [[aliquot sequence]] because when an abundant number occurs in a sequence, the next step is larger than the current step. Also,671 bytes (92 words) - 00:34, 30 January 2019
- A '''smooth number''' is an [[integer]] whose [[prime]] [[factor]]s are less or equal to a pre If this bound is B, we can say that the number is B-smooth.436 bytes (63 words) - 21:36, 3 February 2019
- ..." (because it is triangular) after a number) represents the summing of a number with all whole numbers smaller than it. *[[Wikipedia:Triangular_number|Triangular number]]655 bytes (81 words) - 12:49, 25 March 2019
- In [[number theory]], a '''Proth number''' is a number of the form A [[Proth prime]] is a Proth number, which is prime.670 bytes (104 words) - 10:59, 9 July 2021
- ...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
- In [[number theory]], a '''Woodall number''' W<sub>n</sub> is any [[natural number]] of the form for some natural number ''n''.374 bytes (59 words) - 16:41, 31 August 2021
- {{Shortcut|GNFS|General number field sieve: most efficient classical [[Factorization|factoring method]] fo ...r field sieve (GNFS)''' is the most efficient classical [[algorithm]] in [[number theory]] for [[Factorization|factoring]] [[integer]]s with 100+ [[digit]]s.478 bytes (59 words) - 12:04, 19 February 2019
- ...mbers are included, then the ratio of two square integers is also a square number (e.g. 2/3 × 2/3 = 4/9). The number ''m'' is a square number if and only if one can arrange ''m'' points in a square.3 KB (408 words) - 13:56, 19 February 2019
- ...5''' is a value of {{Vk}} such that {{Kbn|+|k|5|n}} is always [[composite number|composite]]. In order to demonstrate whether {{Num|159986}} is the smallest Sierpiński number base 5 or not, a [[distributed computing project]] was created named [[Sier556 bytes (83 words) - 10:57, 14 October 2020
- ...5''' is a value of ''k'' such that {{Kbn|-|k|5|n}} is always a [[composite number]]. In order to demonstrate whether {{Num|346802}} is the smallest Riesel number base 5 or not, a [[distributed computing project]] was created named [[Sier589 bytes (90 words) - 10:30, 26 March 2024
- A '''Cullen number''' {{V|C<sub>n</sub>}} is a number of the form {{Kbn|+|n|2|n}}, a '''generalized Cullen number''' base {{Vb}} is a number of the form {{Kbn|+|n|b|n}}. '''(perhaps own page?)'''2 KB (252 words) - 17:39, 31 August 2021
- [[Category:Number| ]]49 bytes (7 words) - 13:26, 6 March 2019
- A [[Factorial number]] is defined by the product A '''Multifactorial number''' is denoted by560 bytes (81 words) - 14:36, 20 July 2021
- {{Generalized Fermat number128 bytes (12 words) - 09:57, 30 July 2021
- {{Generalized Fermat number125 bytes (12 words) - 15:10, 17 August 2021
- {{Generalized Fermat number133 bytes (12 words) - 07:54, 18 September 2021
- A '''Leyland number''' is a number that can be expressed in the form <math>x^y+y^x</math>, where x and y are p A '''Leyland prime''' is a Leyland number which is also a [[prime]] (see {{OEIS|l|A094133}}).8 KB (906 words) - 09:59, 5 January 2023
- A '''Saouter number''' is a type of [[Generalized Fermat number]]. Numbers of this type have the form ...to this, these numbers share similar properties to those held by [[Fermat number]]s. These numbers were named by [[Tony Reix]]<ref>[https://www.mersenneforu869 bytes (128 words) - 07:02, 15 August 2019
- {{Generalized Fermat number133 bytes (12 words) - 07:49, 18 September 2021
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Page text matches
- 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
- Splitting a sieve file in [[PRP-LLR format]] into a number of separate files using <code>[[wikipedia:AWK|awk]]</code>.1 KB (203 words) - 18:52, 2 October 2022
- ...primes are much rarer than ordinary primes, of which there are an infinite number. The GIMPS effort, exhaustively searching for possible candidates since 1993 KB (450 words) - 14:37, 21 August 2019
- *'''#''': number count of the Mersenne primes linked to that prime page *'''Digits in P<sub>n</sub>''': denotes the [[Perfect number]] 2<sup>n-1</sup> • (2<sup>n</sup>-1) and a downloadable decimal repre2 KB (360 words) - 09:44, 6 March 2019
- More generally, [[Mersenne number]]s (not necessarily primes, but candidates for primes) are numbers that are ...ved that all [[even number|even]] perfect numbers have this form. No [[odd number|odd]] perfect numbers are known, and it is suspected that none exists.5 KB (857 words) - 14:53, 19 September 2021
- 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
- ...his approach to mathematical research becomes apparent. He saw studies of number theory as being vital to the foundations of calculus, and that special func ...to denote the circumference of a circle. Johann Bernoulli represented the number by c. Euler in 1734 denoted it by p, and in a letter of 1736 (in which he f16 KB (2,614 words) - 11:48, 14 January 2024
- ...ctures that were later proven or refuted by other mathematicians. [[Fermat number]]s are named after him.429 bytes (63 words) - 11:44, 14 January 2024
- ...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
- ...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 languag2 KB (254 words) - 01:23, 15 January 2024
- Entropia grew to collaborate with a number of major technology companies including IBM and British Aerospace in the fi985 bytes (141 words) - 01:30, 15 January 2024
- In [[mathematics]], a '''Fermat number''', named after [[Pierre de Fermat]] who first studied them, is a positive ...up> + 1).) In other words, every prime of the form {{Kbn|+|n}} is a Fermat number, and such primes are called '''Fermat primes'''. The only known Fermat prim12 KB (1,913 words) - 14:35, 9 August 2021
- | number=467333183359...069762179071 ...mputer network administrator. [https://www.popsci.com/worlds-largest-prime-number-discovered] The primality proof took 6 days of non-stop computing.2 KB (333 words) - 13:16, 17 February 2019
- | number=300376418084...391086436351 To confirm that there were no errors in the [[hardware]] or [[software]], the number had to be independently verified by running tests on various machines with2 KB (283 words) - 11:50, 18 February 2019
- ...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 spro6 KB (1,033 words) - 01:13, 15 January 2024
- A '''Titanic prime''' is a [[prime]] number whose decimal representation has {{Num|1000}} or more digits.394 bytes (48 words) - 11:40, 2 July 2020
- A '''gigantic prime''' is a [[prime]] number whose decimal representation has at least {{Num|10000}} [[digit]]s.515 bytes (67 words) - 13:38, 6 March 2019
- 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
- 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
- [[Category:Number]]980 bytes (143 words) - 13:22, 6 March 2019
- ...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 of7 KB (1,150 words) - 23:48, 19 April 2023
- | number=448679166119...353511882751 M25 is 2<sup>{{Num|21701}}</sup>-1, a number of {{Num|6533}} [[digit]]s.2 KB (303 words) - 11:01, 26 February 2019
- ...cas-Lehmer test''' is a deterministic algorithm used to prove a [[Mersenne number]] either composite or prime. It is the last stage in the procedure employed ...<sup>p</sup>-1 would divide into another number, now called a Lucas-Lehmer number denoted S<sub>n</sub> where S<sub>0</sub>=4 and S<sub>n</sub> = (S<sub>n-1<20 KB (3,572 words) - 14:30, 17 February 2019
- ...[[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
- .... In August 2008, one of these computers found a [[M47| World record prime number.]] ...a.edu) discovered a new prime [[M47]]. It remained the largest known prime number for almost four and a half years.4 KB (564 words) - 00:11, 15 January 2024
- ...g fingers) of the hands correspond to the 10 symbols of the common base 10 number system, i.e. the [[decimal]] (ancient Latin adjective ''dec.'' meaning ten) In a given number system, if the [[base]] is an integer, the number of digits required is always equal to the absolute value of the base.1 KB (171 words) - 10:17, 18 January 2019
- ...base 2. The length of a number (how many [[digit]]s it takes to write the number) depends upon the base.1 KB (190 words) - 10:23, 18 January 2019
- In [[Mathematics]], a '''base''' or '''radix''' is the number of different [[digit]]s that a system of counting uses to represent numbers Bases must be a [[whole number]] bigger than 0. If it was 0, then there would be no digits.2 KB (399 words) - 10:37, 18 January 2019
- The term '''whole number''' does not have a consistent definition. Various authors use it in one of *the positive integers (1, 2, 3, ...) (often called [[natural number]]s)413 bytes (54 words) - 09:51, 8 February 2019
- ...r ''Zahlen'' (German for "numbers"). They are also known as the '''[[whole number]]s''', although that term is also used to refer only to the positive intege [[Category:Number systems]]3 KB (404 words) - 14:58, 26 March 2023
- '''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
- '''Multiplication''' is the process of calculating the result when a number a is [[Addition|added]] to itself b times. The result of a multiplication i ...es are in [[exponent|exponentiation]] (<math>a^0=1</math>) and [[factorial number]]s (0!=1).2 KB (271 words) - 17:00, 29 August 2022
- ...wer a base number is raised to, the exponent is the superscript value of a number written as <math>a^p</math>. ...duct]] a × a × a × a is written as <math>a^4</math>, the number 4 is the index, or exponent.1 KB (273 words) - 16:56, 29 August 2022
- ...or bang) after a number, it represents multiplying a number by all [[whole number|whole numbers]] smaller than it. *[[Multifactorial number]]729 bytes (93 words) - 13:40, 5 November 2023
- 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
- ...he integers <math>a</math> and <math>b</math> are both greater than 1, the number is composite. *[[Wikipedia:Composite number|Wikipedia]]358 bytes (56 words) - 23:30, 26 October 2020
- If the minuend is less than the subtrahend, the difference will be a negative number. For example, 17 − 25 = ( −8 ). We can say this as, "Seventeen893 bytes (128 words) - 16:58, 29 August 2022
- **Near Cunningham number **Near-repdigit1 KB (144 words) - 13:44, 24 January 2019
- ...ality tests|primality test]], we have to attempt the factorization of this number. The same can be said of the other factor ''b''. So it can be seen that we ..."special purpose" methods whose execution time depends on the size (i.e., number of digits), or on other particular properties of the factors.4 KB (642 words) - 12:57, 5 March 2019
- ...substantial award for the person that discovers a ten million digit prime number. ...00}}''' to the first individual or group who discovers a [[Megaprime|prime number with at least '''{{Num|1000000}} decimal digits''']] (awarded 2000-04-06)2 KB (321 words) - 18:50, 14 December 2023
- '''Number theory''' is a branch of pure [[mathematics]] devoted primarily to the stud202 bytes (29 words) - 12:55, 20 January 2019
- ...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 [[ARM1 KB (198 words) - 07:28, 22 August 2019
- | number=581887266232...071724285951 To confirm that there were no errors in the [[hardware]] or [[software]], the number had to be independently verified by running tests on various machines with2 KB (235 words) - 11:49, 18 February 2019
- | number=316470269330...166697152511 ...er possible usages refer to the [[Nomenclature and notation]] article. The number now refered to as M47 was actually the 45th Mersenne prime found. [[M45]],5 KB (694 words) - 13:17, 21 August 2019
- ...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 ...page4.html Web Archive]). This is slightly shorter than a 24 million digit number. Newer versions of Prime95 (version 25, 26 and 27) can handle Mersenne numb11 KB (1,586 words) - 12:24, 7 August 2021
- ...ber of objects can be placed into exactly 2 groups that have the identical number of objects. *[[Odd number]]425 bytes (61 words) - 11:19, 7 March 2019
- An '''odd number''' is any [[integer]] that is not divisible by 2. *[[Even number]]316 bytes (42 words) - 11:21, 7 March 2019
- ...UDA]]-based program written by [[Shoichiro Yamada]] for testing [[Mersenne number]]s for primality with [[Lucas-Lehmer test]].2 KB (275 words) - 11:11, 21 August 2019
- ...a program to perform the [[Lucas-Lehmer test]] for primality on [[Mersenne number]]s. It is related to [[GIMPS]] effort to search the largest primes ever fou3 KB (426 words) - 14:21, 14 February 2019
- | number=299410429404...882733969407 ...senneforum.org/txt/41.txt {{Num|7816230}} decimal digits] long. This prime number was the seventh record prime found by the [[GIMPS]] project.1 KB (203 words) - 11:26, 18 February 2019
- | number=315416475618...411652943871 The number is [http://www.mersenneforum.org/txt/43.txt {{Num|9152052}} decimal digits]1 KB (191 words) - 11:31, 18 February 2019
- | number=169873516452...765562314751 The number is [http://www.mersenneforum.org/txt/46.txt {{Num|12837064}} decimal digits2 KB (248 words) - 11:45, 18 February 2019
- There are a number of individuals or groups in the fields of science, mathematics, cryptograph ...ng comes into the picture. Using the [[unused computing power]] of a large number of computers some of these problems can actually be solved within a reasona4 KB (674 words) - 12:11, 19 February 2019
- *Test to see if one number is larger than another *Move a number from one place to another2 KB (366 words) - 09:57, 13 February 2019
- | number=122164630061...280577077247 ...senneforum.org/txt/42.txt {{Num|7816230}} decimal digits] long. This prime number was the eighth record prime found by the [[GIMPS]] project.934 bytes (118 words) - 11:26, 18 February 2019
- | number= 3193 bytes (19 words) - 13:43, 17 February 2019
- ...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
- Let ''x''<sub>0</sub>, ...., ''x''<sub>''n''-1</sub> be [[complex number]]s. The DFT is defined by the formula ...nd conquer algorithm that recursively breaks down a DFT of any [[Composite number|composite]] size ''n'' = ''n''<sub>1</sub>''n''<sub>2</sub> into many small17 KB (2,684 words) - 18:50, 28 September 2023
- ...penCL-based program written by [[Shoichiro Yamada]] for testing [[Mersenne number]]s for primality with [[Lucas-Lehmer test]]. It is an OpenCL counterpart of1 KB (137 words) - 18:48, 14 December 2023
- ...[[CUDA]]-based program written by [[Andrew Thall]] for testing [[Mersenne number]]s for primality.2 KB (239 words) - 11:12, 13 February 2019
- ...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
- ...The architecture of modern supercomputers tend to be built around a large number of "off the shelf" [[CPU]]'s or [[GPU]]'s, rather than those of the past th4 KB (558 words) - 22:55, 3 February 2019
- ...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
- The program does not 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 ...index.php?id=1100000001443762221 40,000 digits]. The certification of this number was done by [[Paul Underwood]] with Primo 4.3.0. The certification process1 KB (191 words) - 20:33, 12 May 2020
- | number=174135906820...328544677887 :2<sup>756 839</sup>-1, a number {{Num|227832}} [[decimal]] [[digit]] long was found to be [[prime]] on 19922 KB (279 words) - 08:35, 18 February 2019
- | number=129498125604...243500142591 '''M33''' refers to 33rd [[Mersenne prime]] number 2<sup>{{Num|859433}}</sup>-1.814 bytes (97 words) - 08:38, 18 February 2019
- | number=412245773621...976089366527 .../sup>-1, which is a number {{Num|378632}} [[decimal]] [[digit]]s long. The number was found to be prime in 1996.3 KB (513 words) - 08:42, 18 February 2019
- A '''real number''' is either a [[rational number]] or an [[irrational number]]. The set of real numbers is denoted by <math>\mathbb{R}</math>. *[[Wikipedia:Real_number|Real number]]390 bytes (57 words) - 15:00, 26 March 2023
- The '''absolute value''' of a [[real number]] is defined as: The absolute value of a [[complex number]] z = x + iy is defined as:556 bytes (89 words) - 16:58, 29 August 2022
- 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
- ...an '''irrational number''' is any [[real number]] that is not a [[rational number]], i.e., one that cannot be written as a ratio of two integers, i.e., it is *[[Wikipedia:Irrational_number|Irrational number]]763 bytes (124 words) - 15:14, 26 March 2023
- [[Mersenne number]]s when written in binary are all 1's. This makes them [[repunit]] numbers.1 KB (210 words) - 11:16, 22 January 2019
- ...[[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 | align="center"|[[Mersenne number]]<br>(Base 2 repunit)1 KB (207 words) - 08:04, 12 March 2024
- ...e is no need to exchange data on each step, it is feasible to process each number on a physically separate machine.3 KB (416 words) - 06:47, 1 May 2019
- ...in a single chip package. A '''many-core''' processor is one in which the number of cores is large enough that traditional multi-processor techniques are no2 KB (269 words) - 14:56, 22 January 2019
- ...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
- | number=125976895450...762855682047 ...senneforum.org/txt/40.txt {{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
- | 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
- | number=124575026015...154053967871 ...senneforum.org/txt/44.txt {{Num|9808358}} decimal digits] long. This prime number was the tenth record prime found by the [[GIMPS]] project.997 bytes (129 words) - 11:35, 18 February 2019
- | number=202254406890...022308220927 In an interview Hans-Michael Elvenich, a German electrical engineer and prime number enthusiast, stated: "After four years of searching for a prime on [[GIMPS]]2 KB (251 words) - 11:40, 18 February 2019
- *[[Whole number]] *[[Wikipedia:Natural_number|Natural number]]316 bytes (43 words) - 15:00, 26 March 2023
- ...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
- | 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
- *[http://primes.utm.edu/notes/6972593 And the winning number is...]809 bytes (109 words) - 23:55, 14 January 2024
- ...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
- ...optimized), but there is also an "Extras" folder containing some efficient number-theoretical C sources.1 KB (125 words) - 09:38, 23 January 2019
- :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
- ...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>. There are faster methods, especially when number of thousands or millions of digits are used, as in [[GIMPS]], but they are2 KB (339 words) - 18:38, 27 September 2023
- We can visualize this arithmetic using a clock. Suppose that the number 12 in the clock is replaced by zero. Then when we have to add an hour, we g where B is the number such that <math>A * B = 1</math> (mod <math>n</math>).4 KB (625 words) - 10:25, 23 January 2019
- The Montgomery representation of a number <math>a</math> is the value ...presentation to normal, just perform a Montgomery multiplication using the number 1 as the second factor.4 KB (582 words) - 17:01, 29 August 2022
- ...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
- | number=814717564412...868451315711 ...er]]. The [[Lucas-Lehmer test]] took 88 hours to run. The primality of the number was confirmed by Slowinski. This showed the effectiveness of [[distributed2 KB (224 words) - 11:00, 18 February 2019
- ...75 years (2 in the very first day of the run, no less). And he raised the number of digits of the largest known [[prime]] (in general) and Mersenne Prime fr2 KB (347 words) - 14:54, 19 September 2021
- ...0) proved that an essentially undecidable theory need not have an infinite number of axioms by coming up with a counterexample: Robinson arithmetic ''Q''. '' ...ity of California, Los Angeles]]. In 1952, he showed that these [[Mersenne number]]s were all composite except for 17 values of ''n'' = 2, 3, 5, 7, 13, 17,4 KB (526 words) - 14:51, 19 September 2021
- | number=623340076248...743729201151 ...k book. It took Spence's 100 MHz [[Pentium]] computer 15 days to prove the number prime. Alan White Managing Director at Technology Business Solutions, who p2 KB (279 words) - 11:01, 18 February 2019
- ...umber-discovered How a FedEx employee discovered the world's largest prime number]. ''Popular Science''. 11 Jan 2018. ...-employee.html FedEx employee from Tennessee discovers largest known prime number]. ''CNBC''. 5 Jan 2018.2 KB (242 words) - 00:08, 15 January 2024
- ...h|1882-03-14|1969-10-21}} was a Polish [[mathematician]] contributing in [[number theory]] and others. ...proved there are infinitely many odd integers {{Vk}} (named [[Sierpiński number]]s after him) such that {{Kbn|+|k|n}} is composite for all {{Vn}}.592 bytes (86 words) - 00:38, 15 January 2024
- ...l number {{Vk}} such that all {{Kbn|+|k|n}} for all {{Vn}} are [[Composite number|composite]]. *[[Wikipedia:Sierpiński_number|Sierpiński number]]324 bytes (48 words) - 13:37, 8 April 2023
- 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
- ...(SOB)''' was a [[distributed computing]] project working on a problem in [[number theory]] called the [[Sierpiński problem]]. It is currently a subproject o ...here ''k'' is one of the remaining 17 (now 5) candidates for [[Sierpiński number]]s smaller than 78557, and ''n'' a positive integer. In order to find such3 KB (544 words) - 16:44, 21 July 2019
