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  • Williams prime MM 5
    1 {{HistC|2018-12-06|1 - 321000|Karsten Bonath|501959}}
    917 bytes (86 words) - 12:13, 22 May 2019
  • Williams prime
    ...ber]] of the form {{Kbn|(b-1)|b|n}} for integers ''b'' ≥ 2 and ''n'' ≥ 1. | MM: {{Kbn|(b-1)|b|n}} || [[:Category:Williams prime MM|here]] ||[[Williams prime MM table|
    5 KB (744 words) - 07:30, 5 August 2019
  • Carol-Kynea prime 2
    1
    5 KB (537 words) - 08:17, 9 October 2020
  • Carol-Kynea prime 6
    1 1
    1 KB (85 words) - 10:45, 16 April 2023
  • Carol-Kynea prime 10
    1
    1 KB (144 words) - 16:10, 29 March 2024
  • Srsieve
    srsieve -G -n 1 -N 100000 -P 10000000000 "1000*999^n+1" *<code>-n 1</code>: lowest value of ''n'' to search
    2 KB (265 words) - 07:36, 28 May 2021
  • Splitting a sieve file
    BEGIN {getline line; i=1} head[i]=1
    1 KB (203 words) - 18:52, 2 October 2022
  • Examples
    3n+1, & \mbox{if }n\mbox{ is odd} 3n+1, & \mbox{if }n\mbox{ is odd}
    11 KB (1,236 words) - 14:41, 3 September 2020
  • Great Internet Mersenne Prime Search
    ...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
  • List of known Mersenne primes
    *'''Digits in M<sub>n</sub>''': denotes the [[Mersenne prime]] 2<sup>n</sup>-1 and a downloadable decimal representation ...>''': denotes the [[Perfect number]] 2<sup>n-1</sup> &bull; (2<sup>n</sup>-1) and a downloadable decimal representation
    2 KB (360 words) - 09:44, 6 March 2019
  • Mersenne prime
    ...ime; so is 7 = 8 &minus; 1 = {{Kbn|3}}. On the other hand, 15 = 16 &minus; 1 = {{Kbn|4}}, for example, is not a prime, because 15 is divisible by 3 and :<math>M_n=2^n{-}1</math> .
    5 KB (857 words) - 14:53, 19 September 2021
  • Mersenne number
    A '''Mersenne number''' is a number of the form <math>2^n{-}1</math> where <math>n</math> is a non-negative [[integer]]. ...r <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
  • Leonhard Euler
    ...to its diameter in 1755, <math>\large i</math> for the <math>\large\sqrt{-1}</math> in 1777, the notation for finite differences <math>\large\delta y</
    16 KB (2,614 words) - 11:48, 14 January 2024
  • Marin Mersenne
    <math> f=\frac{1}{2L}\sqrt{\frac{T}{\mu}}, </math> ...would be explained if the ratio of the air oscillation frequencies is also 1&nbsp;:&nbsp;2, which in turn is consistent with the source-air-motion-frequ
    11 KB (1,582 words) - 01:17, 15 January 2024
  • Euclid
    ...with the definitions of the most basic and fundamental parts of geometry; 1. A point is that which has no part. 2. A line is breadthless length. From t
    2 KB (341 words) - 11:43, 14 January 2024
  • Laura 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 international news because N
    2 KB (254 words) - 01:23, 15 January 2024
  • David Slowinski
    | [[M27]] || 2<sup>{{Num|44497}}</sup>-1 || 1979-04-08 | [[M28]] || 2<sup>{{Num|86243}}</sup>-1 || 1982-09-25
    1 KB (213 words) - 23:53, 14 January 2024
  • Fermat number
    :{{V|F}}<sub>{{Vn}}</sub> = {{Kbn|+|1|2|2<sup>n</sup>}} :{{V|F}}<sub>0</sub> = {{Kbn|+|1}} = 3
    12 KB (1,913 words) - 14:35, 9 August 2021
  • M50
    The official discovery date for prime 2<sup>77 232 917</sup>-1 was 2017-12-26. See the [https://www.mersenne.org/primes/press/M77232917.ht *[[Aaron Blosser]] verified it using [[Prime95]] on an Intel Xeon server in 1.5 days
    2 KB (333 words) - 13:16, 17 February 2019
  • M49
    The official discovery date for 2<sup>{{Num|74207281}}</sup>-1 was 2016-01-07. See the [http://www.mersenne.org/primes/?press=M74207281 pr
    2 KB (283 words) - 11:50, 18 February 2019
  • Curtis Cooper
    ...prime]], 2<sup>32 582 657</sup>-1. As of 2008-09-15 his account is ranked #1 on [[PrimeNet]] in [[Lucas-Lehmer test|LL testing]], with over 242 000 P90 ...3-01-25 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
  • Derrick Henry Lehmer
    ...vement to the [[Lucas primality test]] for [[Mersenne prime]]s <math>2^p{-}1</math>, extending its application to all odd prime exponents ''p'', and ena
    6 KB (1,033 words) - 01:13, 15 January 2024
  • Base 2 Home Prime Results
    {| border="1" cellpadding="4px" style="border:3px; border-color:#000; border-collapse:co {| border="1" cellpadding="4px" style="border:3px; border-color:#000; border-collapse:co
    2 KB (175 words) - 18:45, 14 December 2023
  • Cunningham project
    ...to find the complete [[factorization]] 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 ex :<math>(b^{kn}-1) = (b^n-1) \sum _{r=0}^{k-1} b^{rn}</math>
    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. ...heory 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
    ...905 - 1991) provided a complete proof that this was not only true when p = 1 (mod 4), but for all odd prime exponents. The test therefore takes its name ...> - 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
    ...ucas-Lehmer test]]. In 1876, Lucas proved the primality of <math>2^{127}{-}1</math> ([[M12]]) and this remained the highest [[Mersenne prime]] for almos
    2 KB (296 words) - 01:09, 15 January 2024
  • Decimal
    ...rious 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.
    1 KB (190 words) - 10:23, 18 January 2019
  • Base
    | 1 || '''1''' || 1
    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
    ...positive [[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 u ...e operation of [[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
  • Addition
    :1 + 5 = 6
    333 bytes (43 words) - 16:55, 29 August 2022
  • Multiplication
    ...ponent|exponentiation]] (<math>a^0=1</math>) and [[factorial number]]s (0!=1).
    2 KB (271 words) - 17:00, 29 August 2022
  • Exponent
    ...<math>a^p</math> means that we are notating the number <math>\large \frac{1}{a*a*a*a...}</math> where, you guess it, the [[absolute value]] of p repres ...th> equals the reciprocal (or the multiplicative inverse) of a, that means 1/a.
    1 KB (273 words) - 16:56, 29 August 2022
  • Factorial number
    :<math>n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n</math> for <math>n \ge 1</math>.
    729 bytes (93 words) - 13:40, 5 November 2023
  • Factor
    ...is a [[prime]] number, and a number that has factors other than itself and 1 is called a [[composite number]].
    576 bytes (107 words) - 19:03, 5 February 2019
  • Composite number
    ...ive [[integer]] is '''composite''' if it is neither [[prime]] nor equal to 1. The smallest composite is 4. ...where the integers <math>a</math> and <math>b</math> are both greater than 1, the number is composite.
    358 bytes (56 words) - 23:30, 26 October 2020
  • 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
    ...ion method|p-1]]: It finds a factor ''p'' if the largest prime factor of p-1 is small. *[[p+1 factorization method|p+1]]: Similar to p-1, but succeeds if p+1 has no large factors.
    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.org/primes/?press=M57885161 pr .../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
    ...ormally refers to the 47th [[Mersenne prime]] 2<sup>{{Num|43112609}}</sup>-1, in order of size from the smallest to greatest. This is the primary usage On 2018-04-08 all tests below 2<sup>{{Num|43112609}}</sup>-1 were verified by [[GIMPS]], officially making it the 47th Mersenne prime.
    5 KB (694 words) - 13:17, 21 August 2019
  • Prime95
    ...ehmer test|LL]], PRP, [[Trial factoring|TF]], [[P-1 factorization method|P-1]], [[Elliptic curve method|ECM]]|release=1996|latest=30.3b6<br/><small>2020 {| style="font-size: 85%; text-align: center" border="1" style="border: 1px solid #afafaf; background-color: #f9f9f9; border-collap
    11 KB (1,586 words) - 12:24, 7 August 2021
  • Odd number
    When expressed in decimal 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
  • CUDALucas
    CUDALucas -cufftbench 1 22680 5 CUDALucas -threadbench 1 22680 5 10
    2 KB (275 words) - 11:11, 21 August 2019
  • M41
    ...used to refer to the 41st [[Mersenne prime]] 2<sup>{{Num|24036583}}</sup>-1. ...nce using half of a Bull NovaScale 5000 HPC running Linux on 16 Itanium II 1.3 GHz CPUs for five days using the [[Glucas]] program by Guillermo Balleste
    1 KB (203 words) - 11:26, 18 February 2019
  • M43
    ...used to refer to the 43rd [[Mersenne prime]] 2<sup>{{Num|30402457}}</sup>-1. *by Tony Reix of Bull S.A. in Grenoble, France, in 5 days using 16 Itanium2 1.5 GHz [[CPU]]s of a Bull NovaScale 6160 HPC at Bull Grenoble Research Cente
    1 KB (191 words) - 11:31, 18 February 2019
  • M46
    ...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 102765
    1
    935 bytes (70 words) - 18:56, 10 December 2022
  • Riesel prime 2 187605
    1;T:S
    490 bytes (35 words) - 12:22, 11 December 2022

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