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- 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
- {{Generalized Fermat number127 bytes (12 words) - 19:00, 17 September 2021
- {{Generalized Fermat number133 bytes (12 words) - 18:55, 17 September 2021
- {{Generalized Fermat number141 bytes (12 words) - 08:56, 18 September 2021
- {{Generalized Fermat number124 bytes (12 words) - 12:34, 6 July 2021
- {{Generalized Fermat number124 bytes (12 words) - 14:11, 28 July 2021
- {{Generalized Fermat number130 bytes (12 words) - 12:32, 6 July 2021
- {{Generalized Fermat number122 bytes (12 words) - 11:02, 18 May 2024
- {{Generalized Fermat number120 bytes (12 words) - 08:54, 5 July 2021
- {{Generalized Fermat number120 bytes (12 words) - 18:11, 1 August 2021
- {{Generalized Fermat number122 bytes (12 words) - 08:54, 5 July 2021
- {{Generalized Fermat number124 bytes (12 words) - 08:55, 5 July 2021
- {{Generalized Fermat number128 bytes (12 words) - 08:55, 5 July 2021
- {{Generalized Fermat number140 bytes (12 words) - 00:56, 23 June 2021
- {{Generalized Fermat number159 bytes (12 words) - 10:46, 23 June 2021
- {{Generalized Fermat number130 bytes (12 words) - 19:57, 1 August 2021
- {{Generalized Fermat number129 bytes (12 words) - 14:07, 28 July 2021
- {{Generalized Fermat number178 bytes (12 words) - 08:18, 16 September 2021
- {{Generalized Fermat number122 bytes (12 words) - 16:02, 17 August 2021
- {{Generalized Fermat number120 bytes (12 words) - 15:52, 17 August 2021
- {{Generalized Fermat number134 bytes (12 words) - 16:10, 17 August 2021
- {{Generalized Fermat number149 bytes (12 words) - 16:14, 17 August 2021
- {{Generalized Fermat number169 bytes (12 words) - 16:19, 17 August 2021
- {{Generalized Fermat number177 bytes (13 words) - 10:30, 2 July 2021
- {{Generalized Fermat number124 bytes (12 words) - 16:32, 17 August 2021
- {{Generalized Fermat number120 bytes (12 words) - 16:30, 17 August 2021
- {{Generalized Fermat number204 bytes (12 words) - 14:01, 28 July 2021
- {{Generalized Fermat number196 bytes (13 words) - 10:05, 16 September 2021
- {{Generalized Fermat number134 bytes (12 words) - 14:12, 28 July 2021
- {{Generalized Fermat number192 bytes (14 words) - 12:21, 2 July 2021
- {{Generalized Fermat number206 bytes (14 words) - 11:50, 8 July 2021
- {{Generalized Fermat number233 bytes (21 words) - 13:32, 8 July 2021
- {{Generalized Fermat number267 bytes (25 words) - 13:34, 8 July 2021
Page text matches
- ...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
