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- |Pb=23 KB (303 words) - 13:57, 26 May 2024
- |Rb=2 {{HistC|2022-04-10|2300000|RPS Megabit Drive 2|603655}}2 KB (202 words) - 08:31, 16 May 2024
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- |LeY=2 |LeProgram=Titanix 2.1.0 (ECPP)176 bytes (19 words) - 13:05, 27 July 2019
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- |Pb=2440 bytes (36 words) - 07:56, 17 May 2024
- |Pb=2498 bytes (31 words) - 13:34, 2 January 2023
- |Rb=2 2;T:S490 bytes (35 words) - 12:22, 11 December 2022
- |Rb=2 2557 bytes (25 words) - 12:35, 11 December 2022
- |Pb=2334 bytes (32 words) - 15:12, 27 January 2023
- ...Programming, Volume 2, 3rd Edition, 1997, Addison-Wesley, ISBN 0-201-89684-22 KB (263 words) - 11:53, 7 February 2019
- | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 2.4 GHz Pentium 4 [[Personal computer|PC]] '''M42''' refers to the 42nd [[Mersenne prime]] 2<sup>{{Num|25964951}}</sup>-1.934 bytes (118 words) - 11:26, 18 February 2019
- | nvalue= 2193 bytes (19 words) - 13:43, 17 February 2019
- ...t in proving the [[Liskovets-Gallot conjectures]] for the forms {{Kbn|±|k|2|n}} where {{Vn}} is always odd '''and''' where {{Vn}} is always even. ==Sub-project #2==3 KB (507 words) - 08:29, 29 May 2024
- :<math>\large f_j = \sum_{k=0}^{n-1} x_k e^{-{2\pi i \over n} jk } \qquad j = 0, ... ,n-1.</math> Evaluating these sums directly would take O(''n''<sup>2</sup>) arithmetical operations . An FFT is an algorithm to compute the same17 KB (2,684 words) - 18:50, 28 September 2023
- ...rform nearly two times faster than [[CUDALucas]] due to using non-power-of-2 [[Fast Fourier transform|FFT]] lengths. [http://www.mersenneforum.org/showt2 KB (239 words) - 11:12, 13 February 2019
- ...ehmer test|LL]], [[Probable prime|PRP]]|title=gpuOwL|release=2017|latest=7.2<br>2020-11-01}} ...nch] at GitHub (version 1 uses 4M FFT and is about 50% faster than version 2) [http://www.mersenneforum.org/showpost.php?p=479585&postcount=320]1 KB (216 words) - 05:22, 1 December 2020
- | foundwith=[[Lucas-Lehmer test]] / Maple on Harwell Lab [[Cray-2]] :2<sup>756 839</sup>-1, a number {{Num|227832}} [[decimal]] [[digit]] long was2 KB (279 words) - 08:35, 18 February 2019
- '''M33''' refers to 33rd [[Mersenne prime]] number 2<sup>{{Num|859433}}</sup>-1. ...percomputer]]. Computation of [[Lucas-Lehmer test]] for this number took 7.2 hours.814 bytes (97 words) - 08:38, 18 February 2019
- ...size (smallest to largest) and in order of discovery. Specifically M34 is 2<sup>{{Num|1257787}}</sup>-1, which is a number {{Num|378632}} [[decimal]] [3 KB (513 words) - 08:42, 18 February 2019
- ...2008-01-10. The project searches for [[Riesel prime]]s of the form {{Kbn|k|2|n}} with odd {{Vk}} and 300 < {{Vk}} < 1001 and {{Vn}} > 260000 not reserve745 bytes (111 words) - 02:17, 1 May 2024
- ==Factorizations Of Cunningham Numbers C<sup>+</sup>(2,n) = 2<sup>n</sup> + 1== * 001 - 100 : {{FDBCunningham|2|+|1|100}}2 KB (127 words) - 15:28, 17 August 2019
- <math>|z| = \sqrt{x^2+y^2}</math>556 bytes (89 words) - 16:58, 29 August 2022
- ...power of 2 multiplied by a perfect power of 5, i.e. it has the form <math>2^n \times 5^m</math>.3 KB (541 words) - 15:01, 26 March 2023
- ...at to be a definition. Some examples of irrational numbers are <math>\sqrt{2}</math> or <math>e</math>.763 bytes (124 words) - 15:14, 26 March 2023
- ...umbers using only two [[digit]]s (usually, 0 and 1). Thus it is a [[base]] 2 numbering system. Example: 10110011<sub>2</sub> = 179<sub>10</sub>1 KB (210 words) - 11:16, 22 January 2019
- ...eing the number referred to as "unity") numbers. 111 is a repunit, in base 2 it is equal to 7 (base 10), in base 3 it is equal to 13 (base 10). A '''Generalized repunit''' for any base {{Vb}} ≥ 2 is defined as1 KB (207 words) - 08:04, 12 March 2024
- ...hen a single [[processor]], multiple processors, or multiple cores perform 2 or more operations (similar or different) at once, that is '''parallel comp ! Step !! Input 1 !! Operation !! Input 2 !! Result !! 1440<br>x 3653 KB (416 words) - 06:47, 1 May 2019
- ...0. Computers normally use a very similar 'shift and add' algorithm in base 2. [[Prime95]] does not use this form of multiplication for large numbers, us2 KB (165 words) - 17:01, 29 August 2022
- ...to use as trial divisors. If P(i) is the i'th prime number so P(1) = 2, P(2) = 3, P(3) = 5, etc, then the last prime factor possibility for some number ...< \sqrt{N}</math>) there is no need to try 7 since 2*7 is excluded because 2 will have been tried, 3*7 is excluded because 3 will have been tried, and 57 KB (1,221 words) - 13:20, 11 February 2019
- | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 2 GHz Dell Dimension ...hort hand used to refer to the 40th [[Mersenne prime]]. Specifically it is 2<sup>{{Num|20996011}}</sup>-1. This number was discovered to be [[prime]] on1 KB (189 words) - 11:17, 18 February 2019
- '''Michael Shafer''' discovered the [[M40|40th]] [[Mersenne prime]], 2<sup>{{Num|20996011}}</sup>-1 at [[GIMPS]] project.660 bytes (88 words) - 00:39, 15 January 2024
- ...nt. He is credited with discovery of the [[M41|41st known Mersenne prime]] 2<sup>{{Num|24036583}}</sup>-1.695 bytes (93 words) - 11:46, 14 January 2024
- ...hort hand used to refer to the 39th [[Mersenne prime]]. Specifically it is 2<sup>{{Num|13466917}}</sup>-1. This number was discovered to be [[prime]] on868 bytes (109 words) - 11:14, 18 February 2019
- ...efer to the 44th [[Mersenne prime]]. Currently that designation belongs to 2<sup>{{Num|32582657}}</sup>-1.997 bytes (129 words) - 11:35, 18 February 2019
- | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 2.83 GHz Core 2 Duo [[Personal computer|PC]] '''M45''' normally refers to 2<sup>{{Num|37156667}}</sup>-1, the 45th [[Mersenne prime]] in order of size2 KB (251 words) - 11:40, 18 February 2019
- ...way who discovered the [[M46|46th Mersenne prime]] (chronologically 47th), 2<sup>{{Num|42643801}}</sup>-1. Strindmo goes by the alias '''Stig M. Valstad Strindmo's 3 GHz Core 2 Duo PC first reported the prime to GIMPS on 2009-04-12. However, due to a s991 bytes (141 words) - 00:33, 15 January 2024
- 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
- | top5000id=2 ...hort hand used to refer to the 38th [[Mersenne prime]]. Specifically it is 2<sup>{{Num|6972593}}</sup>-1. This number was discovered to be [[prime]] on1 KB (165 words) - 11:10, 18 February 2019
- ...ers employee from Michigan who discovered the [[M38|38th Mersenne prime]], 2<sup>{{Num|6972593}}</sup>-1.809 bytes (109 words) - 23:55, 14 January 2024
- ...s 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
- ...s arithmetic modulo 12 and the set of numbers representing the hours 0, 1, 2, 3,..., 11 is known as <b>Z</b>/12<b>Z</b>. ...</b>/n<b>Z</b> of numbers modulo n contains the numbers 0, 1, 2, 3, ..., n-2 and n-1. The following operations are defined:4 KB (625 words) - 10:25, 23 January 2019
- ...math>ab\,\equiv \,c\,\pmod{m}</math>. We will also assume that <math>m\,<\,2^n</math>. :<math>a'=2^n\,a\,\bmod{m}</math>.4 KB (582 words) - 17:01, 29 August 2022
- ...iplication|multiplying]] lots of different prime numbers together. So that 2 x 3 x 5 x 7 x 11 x 13 etc will be a highly composite number. But that is on ...,9</math> is a quadratic expression (because the highest power of ''x'' is 2).19 KB (3,181 words) - 22:27, 6 July 2023
- Specifically 2<sup>{{Num|1398269}}</sup>-1, written out in full [http://www.mersenneforum.2 KB (224 words) - 11:00, 18 February 2019
- ...ter]]. Robinson's Mersenne primes were the first to be found in 75 years (2 in the very first day of the run, no less). And he raised the number of dig ...ugust of 2008, a Dell Optplex 745 (running a Intel Core 2 Duo E6600 CPU at 2.4GHz) in the UCLA Math department computer lab, found [[M47|47th Mersenne p2 KB (347 words) - 14:54, 19 September 2021
- ...e [[Mersenne number]]s were all composite except for 17 values of ''n'' = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, [[M12|127]], [[M13|521]], [[M14|607]4 KB (526 words) - 14:51, 19 September 2021
- ...hort hand used to refer to the 36th [[Mersenne prime]], specifically it is 2<sup>{{Num|2976221}}</sup>-1. This number was dicovered to be [[prime]] on 1 The corresponding [[perfect number]] is 2<sup>{{Num|2976220}}</sup> • (2<sup>{{Num|2976221}}</sup>-1). This number is {{Num|1791864}} digits long.2 KB (279 words) - 11:01, 18 February 2019
- |0||1||2||3||4||5||6||7||8||9||10||11||12||13||14||15||16||17||18||19||20||21||22||2 ...th prime 2 24737|24737]], [[Proth prime 2 55459|55459]], and [[Proth prime 2 67607|67607]] (current status [https://www.primegrid.com/stats_sob_llr.php5 KB (650 words) - 10:25, 26 March 2024
- :Found factor [[Proth prime 2 5|{{Kbn|+|5|2|39}}]] of {{DGF|36}}2 KB (195 words) - 00:13, 15 January 2024
- The aim of the project is to find [[prime]]s of the form <math>k*2^n+1</math>, where ''k'' is one of the remaining 17 (now 5) candidates for [ |format=,*[[%PAGE%|²{#titleparts:%TITLE%¦1¦2}²]]\n,,3 KB (544 words) - 16:44, 21 July 2019
- | rank= 2 | pdigits= 2193 bytes (19 words) - 13:43, 17 February 2019
- | digits= 2194 bytes (19 words) - 13:43, 17 February 2019
- ...r 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. ...irst four perfect numbers are generated by the formula 2<sup>''n''-1</sup>(2<sup>''n''</sup>-1):6 KB (885 words) - 11:33, 7 March 2019
- The ninth [[Mersenne prime]], 2<sup>61</sup>-1 or {{Num|2305843009213693951}}. ...prime number, ([[Édouard Lucas]] having shown earlier that [[M12]], <math>2^{127}-1</math> is also prime), and it remained so until 1911. Prior to the2 KB (213 words) - 14:30, 17 February 2019