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Page title matches
- |CKBase=2 25 KB (537 words) - 08:17, 9 October 2020
- ==Search for Home Primes base 2== {{HP|2|2295|281|189|2013-07-23|}}2 KB (175 words) - 18:45, 14 December 2023
- ==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
- |Rb=2403 bytes (26 words) - 18:40, 2 January 2023
- |Rb=2935 bytes (70 words) - 18:56, 10 December 2022
- |Rb=2255 bytes (24 words) - 22:20, 10 December 2022
- |Pb=2432 bytes (32 words) - 13:38, 2 January 2023
- |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
- ==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
- |Pb=2 |PCount=2581 bytes (64 words) - 19:18, 5 April 2023
- |Rb=2 2;T:ST;C:'''[[M1]]''', {{NWo|+|1}}, {{NWo|-|2}}, {{NWo|4|1}}2 KB (288 words) - 11:41, 3 April 2023
- |Rb=2 2;T:ST;C:{{NWo|+|2}}, {{NWi|MM|4|1}}5 KB (523 words) - 09:47, 5 October 2023
- |Rb=2 22 KB (196 words) - 18:36, 9 October 2021
- |Rb=23 KB (264 words) - 22:08, 5 July 2023
- category=Riesel 2 Low-weight [[Category:Riesel 2 Low-weight| ]]948 bytes (121 words) - 13:08, 21 July 2021
- |Rb=2 2;T:T2 KB (252 words) - 13:29, 5 May 2024
- |Rb=23 KB (329 words) - 07:59, 17 August 2021
- |Rb=22 KB (185 words) - 04:16, 5 May 2024
- |Rb=2 |RCount=2236 bytes (24 words) - 00:24, 17 July 2021
- |WiBase=2 |WiMaxn={{GP|Riesel prime 2 3|RMaxn}}246 bytes (35 words) - 14:04, 1 August 2021
- |WiBase=2 |WiMaxn={{GP|Proth prime 2 1|PMaxn}}243 bytes (35 words) - 08:06, 1 August 2021
- |WiBase=2 |WiMaxn={{GP|Proth prime 2 3|PMaxn}}259 bytes (36 words) - 10:52, 13 July 2021
- |WiBase=2 |WiMaxn={{GP|Riesel prime 2 1|RMaxn}}244 bytes (35 words) - 20:47, 31 July 2021
- |Rb=22 KB (228 words) - 19:30, 19 July 2023
- |Pb=2 2;T:GT212 bytes (30 words) - 15:35, 2 October 2022
- |Pb=2 2;T:GT3 KB (336 words) - 16:58, 15 April 2024
- |Pb=21 KB (144 words) - 11:12, 24 August 2021
- |Pb=2 2;T:G2 KB (267 words) - 21:47, 5 July 2023
- |Pb=2 2;T:G3 KB (432 words) - 18:48, 9 April 2023
- |Pb=22 KB (240 words) - 08:58, 11 January 2023
- |Pb=2 2;T:G1 KB (175 words) - 07:07, 25 August 2021
- |Pb=2 2;T:T3 KB (390 words) - 10:00, 25 August 2021
- |Pb=21 KB (141 words) - 13:50, 25 August 2021
- |Pb=21 KB (145 words) - 09:32, 26 August 2021
- |Pb=2371 bytes (31 words) - 08:06, 18 September 2021
- |WoBase=2 2;C:{{NRi|3}}2 KB (230 words) - 10:36, 27 March 2023
- |CuBase=2 {{DISPLAYTITLE:Cullen primes {{Kbn|+|n|2|n}}|noerror}}2 KB (175 words) - 14:54, 19 September 2021
- |Pb=21 KB (103 words) - 12:07, 7 September 2021
- |Rb=22 KB (184 words) - 22:47, 18 April 2024
- |Rb=2 2;T:S2 KB (224 words) - 06:12, 9 May 2024
- |Rb=24 KB (357 words) - 23:04, 19 April 2024
- |Pb=2826 bytes (91 words) - 09:28, 31 August 2021
- |Pb=2328 bytes (32 words) - 13:00, 12 August 2021
- |Rb=2 22 KB (174 words) - 18:41, 5 May 2024
- |Rb=2 2;T:S3 KB (295 words) - 22:47, 5 July 2023
- |Pb=22 KB (202 words) - 11:31, 31 August 2021
- |Rb=2 {{HistC|2007-03-05|989600|65*2^n-1 thread|99924}}, released2 KB (222 words) - 06:13, 9 May 2024
Page text matches
- ...a [[natural number]] of the form {{Kbn|(b-1)|b|n}} for integers ''b'' ≥ 2 and ''n'' ≥ 1. ...Smallest <ref>The list of smallest primes of any base is an ASCII file for 2 ≤ ''b'' ≤ 1024. For unknown values only the base is given.</ref> !! Rem5 KB (744 words) - 07:30, 5 August 2019
- |CKBase=2 25 KB (537 words) - 08:17, 9 October 2020
- 2 21 KB (85 words) - 10:45, 16 April 2023
- '''srsieve''' (and '''sr1/2/5sieve''') is used to create sieve files for one or more sequences. Those s2 KB (265 words) - 07:36, 28 May 2021
- <pre><math>\sideset{_1^2}{_3^4}\prod_a^b</math></pre> :<math>\sideset{_1^2}{_3^4}\prod_a^b</math>11 KB (1,236 words) - 14:41, 3 September 2020
- ...as born in 1588. Mersenne investigated a particular type of prime numbers: 2<sup>p</sup> - 1, in which ''p'' is an ordinary [[prime]].3 KB (450 words) - 14:37, 21 August 2019
- *'''Digits in M<sub>n</sub>''': denotes the [[Mersenne prime]] 2<sup>n</sup>-1 and a downloadable decimal representation ...n P<sub>n</sub>''': denotes the [[Perfect number]] 2<sup>n-1</sup> • (2<sup>n</sup>-1) and a downloadable decimal representation2 KB (360 words) - 09:44, 6 March 2019
- ...is one less than a [[power of two]]. For example, 3 = 4 − 1 = {{Kbn|2}} is a Mersenne prime; so is 7 = 8 − 1 = {{Kbn|3}}. On the other hand :<math>M_n=2^n{-}1</math> .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 [[integer]]. ...senne number <math>2^n{-}1</math> can be calculated by <math>\lfloor{n*log(2)}\rfloor+1</math> (see [[floor function]]).2 KB (351 words) - 11:28, 7 March 2019
- ...for finite differences <math>\large\delta y</math> and <math>\large\delta^2 y</math> and many more.16 KB (2,614 words) - 11:48, 14 January 2024
- : <math>\sqrt[4]{\frac{2}{3-\sqrt{2}}}</math> ...ined if the ratio of the air oscillation frequencies is also 1 : 2, which in turn is consistent with the source-air-motion-frequency-equivalen11 KB (1,582 words) - 01:17, 15 January 2024
- ...c and fundamental parts of geometry; 1. A point is that which has no part. 2. A line is breadthless length. From these definitions of the point and the2 KB (341 words) - 11:43, 14 January 2024
- ...l candidates with prime [[exponent]]s up to and including M26. During that 2 hour period, it duplicated what had previously occurred over a 520 year per2 KB (333 words) - 12:40, 9 February 2022
- ...aura A. Nickel''') with [[Landon Curt Noll]] discovered on 1978-10-30 that 2<sup>21701</sup>-1 was the [[M25|25th Mersenne prime]]. This made internatio2 KB (254 words) - 01:23, 15 January 2024
- | [[M27]] || 2<sup>{{Num|44497}}</sup>-1 || 1979-04-08 | [[M28]] || 2<sup>{{Num|86243}}</sup>-1 || 1982-09-251 KB (213 words) - 23:53, 14 January 2024
- :{{V|F}}<sub>{{Vn}}</sub> = {{Kbn|+|1|2|2<sup>n</sup>}} :{{V|F}}<sub>1</sub> = {{Kbn|+|2}} = 512 KB (1,913 words) - 14:35, 9 August 2021
- The official discovery date for prime 2<sup>77 232 917</sup>-1 was 2017-12-26. See the [https://www.mersenne.org/pr ...glund also confirmed using Mlucas running on an [[Amazon EC2]] instance in 2.7 days2 KB (333 words) - 13:16, 17 February 2019
- The official discovery date for 2<sup>{{Num|74207281}}</sup>-1 was 2016-01-07. See the [http://www.mersenne.o ...ill, who each ran the [[CUDALucas]] software on NVidia Titan Black GPUs in 2.3 days2 KB (283 words) - 11:50, 18 February 2019
- ...-09-04 when the pair discovered the [[M44|44th]] known [[Mersenne prime]], 2<sup>32 582 657</sup>-1. As of 2008-09-15 his account is ranked #1 on [[Prim On 2013-01-25 Cooper discovered his third Mersenne prime, 2<sup>57 885 161</sup>-1, the [[M48|48th]] known.2 KB (237 words) - 11:34, 14 January 2024
- ...k's father enabled them to find factors for all integers up to ''48911<sup>2</sup>'', and these factorisations were published in a book in 1929. That su ...improvement to the [[Lucas primality test]] for [[Mersenne prime]]s <math>2^p{-}1</math>, extending its application to all odd prime exponents ''p'', a6 KB (1,033 words) - 01:13, 15 January 2024
- ==Base 2== HP<sub>2</sub>(10):980 bytes (143 words) - 13:22, 6 March 2019
- ==Search for Home Primes base 2== {{HP|2|2295|281|189|2013-07-23|}}2 KB (175 words) - 18:45, 14 December 2023
- *[[2 Minus Tables]] *[[2 Plus Tables]]614 bytes (69 words) - 12:08, 13 February 2019
- ...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 || 127 KB (1,150 words) - 23:48, 19 April 2023
- ==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 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
- ...S<sub>0</sub>=4 and S<sub>n</sub> = (S<sub>n-1</sub>)<sup>2</sup> − 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
- ...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
- ...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. The1 KB (190 words) - 10:23, 18 January 2019
- 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=162 KB (399 words) - 10:37, 18 January 2019
- *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
- ...[natural number]]s (1, 2, 3, …), their negatives (−1, −2, −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
- ...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
- In [[mathematics]]: to sum 2 numbers. It is normally symbolized by the plus sign '+'. :2 + 2 = 4333 bytes (43 words) - 16:55, 29 August 2022
- ...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
- :<math>n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n</math> :5! = 5 * 4 * 3 * 2 * 1 = 120729 bytes (93 words) - 13:40, 5 November 2023
- :<math>\frac 63 = 2</math> :<math>2 \times 3 = 6</math>.2 KB (368 words) - 16:58, 29 August 2022
- ...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
- **Greatest prime factor ^2+1, ^2+2, ^2-1, ^2-2, ^3+1, ^3-11 KB (144 words) - 13:44, 24 January 2019
- ...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 methods4 KB (642 words) - 12:57, 5 March 2019
- 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 Numberphile2 KB (235 words) - 11:49, 18 February 2019
- ...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 making5 KB (694 words) - 13:17, 21 August 2019
- ...fafaf; background-color: #f9f9f9; border-collapse: collapse;" cellpadding="2" !Comparison of CPU core power!!Frequency!!Cores!!colspan="2" | [[Fast Fourier transform|FFT]]!![[Trial factoring]]!!TDP11 KB (1,586 words) - 12:24, 7 August 2021
- ...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
- 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
- | 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
- | 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
- | 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
- |Rb=2403 bytes (26 words) - 18:40, 2 January 2023
- |Rb=2935 bytes (70 words) - 18:56, 10 December 2022