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  • Base 2 Home Prime Results
    ==Search for Home Primes base 2== {{HP|2|2295|281|189|2013-07-23|}}
    2 KB (175 words) - 18:45, 14 December 2023
  • Cunningham tables
    *[[2 Minus Tables]] *[[2 Plus Tables]]
    614 bytes (69 words) - 12:08, 13 February 2019
  • Cunningham project
    ...zation]] of numbers of the form <math>b^n\pm 1</math> for <math>b</math> = 2, 3, 5, 6, 7, 10, 11, 12. The values of the exponent <math>n</math> are sele | 2 || 3 || 5 || 6 || 7 || 10 || 11 || 12
    7 KB (1,150 words) - 23:48, 19 April 2023
  • 2 Minus Tables
    ==Factorizations Of Cunningham Numbers C<sup>-</sup>(2,n) = 2<sup>n</sup> - 1== * 001 - 100 : {{FDBCunningham|2|-|1|100}}
    2 KB (176 words) - 12:01, 13 February 2019
  • M25
    M25 is 2<sup>{{Num|21701}}</sup>-1, a number of {{Num|6533}} [[digit]]s. .... They were testing this theory and that Tuckerman's discovery of [[M24]] (2<sup>{{Num|19937}}</sup>-1) was the start of this island.
    2 KB (303 words) - 11:01, 26 February 2019
  • Lucas-Lehmer test
    ...S<sub>0</sub>=4 and S<sub>n</sub> = (S<sub>n-1</sub>)<sup>2</sup> &minus; 2. In 1930, the American mathematician [[Derrick Henry Lehmer]] (1905 - 1991) ...hat 2<sup>5</sup> - 1 divides S<sub>3</sub> (37634 / 31 = 1214) shows that 2<sup>5</sup> - 1 is prime.
    20 KB (3,572 words) - 14:30, 17 February 2019
  • Édouard Lucas
    ...te the [[Lucas-Lehmer test]]. In 1876, Lucas proved the primality of <math>2^{127}{-}1</math> ([[M12]]) and this remained the highest [[Mersenne prime]]
    2 KB (296 words) - 01:09, 15 January 2024
  • Decimal
    ...at people use in most of the world. [[Computer]]s use '''binary''' or base 2. The length of a number (how many [[digit]]s it takes to write the number) ...us symbols (called [[digit]]s) for no more than ten distinct values (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) to represent any numbers, no matter how large. The
    1 KB (190 words) - 10:23, 18 January 2019
  • Base
    Different bases are often used in [[computer|computers]]. Binary (base 2) is used because at the most simple level, computers can only deal with 0s ! Decimal<br>base=10 !! Binary<br>base=2 !! Hexadecimal<br>base=16
    2 KB (399 words) - 10:37, 18 January 2019
  • Whole number
    *the nonnegative [[integer]]s (0, 1, 2, 3, ...) *the positive integers (1, 2, 3, ...) (often called [[natural number]]s)
    413 bytes (54 words) - 09:51, 8 February 2019
  • Integer
    ...[natural number]]s (1, 2, 3, &hellip;), their negatives (&minus;1, &minus;2, &minus;3, ...) and the number zero. The set of all integers is usually den ...f [[division]], since the quotient of two integers (''e.g.'', 1 divided by 2), need not be an integer.
    3 KB (404 words) - 14:58, 26 March 2023
  • Mathematics
    ...s <math>a</math> and <math>b</math>, <math>(a + b) * (a - b)\,=\,a^2\,-\,b^2</math>.
    1 KB (186 words) - 17:00, 5 February 2019
  • Addition
    In [[mathematics]]: to sum 2 numbers. It is normally symbolized by the plus sign '+'. :2 + 2 = 4
    333 bytes (43 words) - 16:55, 29 August 2022
  • Multiplication
    ...largest available register is ''n'' bits wide the factors can only be ''n/2'' bits wide each.
    2 KB (271 words) - 17:00, 29 August 2022
  • Factorial number
    :<math>n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n</math> :5! = 5 * 4 * 3 * 2 * 1 = 120
    729 bytes (93 words) - 13:40, 5 November 2023
  • Division
    :<math>\frac 63 = 2</math> :<math>2 \times 3 = 6</math>.
    2 KB (368 words) - 16:58, 29 August 2022
  • Remainder
    ...ft over after dividing something. Dividing 13 into groups of 5 would yield 2 groups, with a remainder of 3.
    245 bytes (34 words) - 14:07, 18 January 2019
  • Factoring Database
    **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
    ...composite numbers have small factors (half of the numbers are multiples of 2, a third are multiples of 3 and so on) it pays to run factorization methods
    4 KB (642 words) - 12:57, 5 March 2019
  • M48
    The official discovery date for 2<sup>{{Num|57885161}}</sup>-1 was 2013-01-25. See the [http://www.mersenne.o *[https://www.youtube.com/watch?v=QSEKzFGpCQs New Largest Known Prime Number 2<sup>57,885,161</sup>-1] at YouTube channel Numberphile
    2 KB (235 words) - 11:49, 18 February 2019
  • M47
    ...found. [[M45]], [[M46]], and M47 were discovered in the order of M47, M45 (2 weeks later), then M46 (8 months later). On 2018-04-08 all tests below 2<sup>{{Num|43112609}}</sup>-1 were verified by [[GIMPS]], officially making
    5 KB (694 words) - 13:17, 21 August 2019
  • Prime95
    ...fafaf; background-color: #f9f9f9; border-collapse: collapse;" cellpadding="2" !Comparison of CPU core power!!Frequency!!Cores!!colspan="2" | [[Fast Fourier transform|FFT]]!![[Trial factoring]]!!TDP
    11 KB (1,586 words) - 12:24, 7 August 2021
  • Even number
    ...n the physcial world, an even number of objects can be placed into exactly 2 groups that have the identical number of objects. All numbers ending in 0, 2, 4, 6, or 8 are even.
    425 bytes (61 words) - 11:19, 7 March 2019
  • Odd number
    An '''odd number''' is any [[integer]] that is not divisible by 2. ...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
    | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 2.4 GHz Pentium 4 [[Personal computer|PC]] '''M41''' is the short hand used to refer to the 41st [[Mersenne prime]] 2<sup>{{Num|24036583}}</sup>-1.
    1 KB (203 words) - 11:26, 18 February 2019
  • M43
    | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 2 GHz Pentium 4 [[Personal computer|PC]] '''M43''' is the short hand used to refer to the 43rd [[Mersenne prime]] 2<sup>{{Num|30402457}}</sup>-1.
    1 KB (191 words) - 11:31, 18 February 2019
  • M46
    | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 3 GHz Core 2 [[Personal computer|PC]] '''M46''' is the short hand used to refer to the 46th [[Mersenne prime]] 2<sup>{{Num|42643801}}</sup>-1.
    2 KB (248 words) - 11:45, 18 February 2019
  • Riesel prime 2 21143
    |Rb=2
    403 bytes (26 words) - 18:40, 2 January 2023
  • Riesel prime 2 102765
    |Rb=2
    935 bytes (70 words) - 18:56, 10 December 2022
  • Riesel prime 2 182627
    |Rb=2
    255 bytes (24 words) - 22:20, 10 December 2022
  • Proth prime 2 1089927
    |Pb=2
    440 bytes (36 words) - 07:56, 17 May 2024
  • Proth prime 2 12321
    |Pb=2
    498 bytes (31 words) - 13:34, 2 January 2023
  • Riesel prime 2 187605
    |Rb=2 2;T:S
    490 bytes (35 words) - 12:22, 11 December 2022
  • Riesel prime 2 132165
    |Rb=2 2
    557 bytes (25 words) - 12:35, 11 December 2022
  • Proth prime 2 1943873
    |Pb=2
    334 bytes (32 words) - 15:12, 27 January 2023
  • Program
    ...Programming, Volume 2, 3rd Edition, 1997, Addison-Wesley, ISBN 0-201-89684-2
    2 KB (263 words) - 11:53, 7 February 2019
  • M42
    | 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
  • M1
    | nvalue= 2
    193 bytes (19 words) - 13:43, 17 February 2019
  • Conjectures 'R Us
    ...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 (503 words) - 02:20, 1 May 2024
  • Fast Fourier transform
    :<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 same
    17 KB (2,684 words) - 18:50, 28 September 2023
  • GpuLucas
    ...rform nearly two times faster than [[CUDALucas]] due to using non-power-of-2 [[Fast Fourier transform|FFT]] lengths. [http://www.mersenneforum.org/showt
    2 KB (239 words) - 11:12, 13 February 2019
  • GpuOwL
    ...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
  • M32
    | foundwith=[[Lucas-Lehmer test]] / Maple on Harwell Lab [[Cray-2]] :2<sup>756 839</sup>-1, a number {{Num|227832}} [[decimal]] [[digit]] long was
    2 KB (279 words) - 08:35, 18 February 2019
  • M33
    '''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
  • M34
    ...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
  • No Prime Left Behind
    ...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 reserve
    745 bytes (111 words) - 02:17, 1 May 2024
  • 2 Plus Tables
    ==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
  • Absolute value
    <math>|z| = \sqrt{x^2+y^2}</math>
    556 bytes (89 words) - 16:58, 29 August 2022
  • Rational number
    ...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
  • Irrational number
    ...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

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