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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
  • CPU
    ...uction takes a very small time to happen. Many CPUs today can do more than 1 billion instructions in a single second. In general, the more a CPU can do
    2 KB (366 words) - 09:57, 13 February 2019
  • Program
    *Knuth, Donald E., The Art of Computer Programming, Volume 1, 3rd Edition, 1997, Addison-Wesley, ISBN 0-201-89683-4
    2 KB (263 words) - 11:53, 7 February 2019
  • GPU
    :P-1 testing
    2 KB (250 words) - 08:44, 13 February 2019
  • M42
    '''M42''' refers to the 42nd [[Mersenne prime]] 2<sup>{{Num|25964951}}</sup>-1.
    934 bytes (118 words) - 11:26, 18 February 2019
  • M1
    | rank= 1 | digits= 1
    193 bytes (19 words) - 13:43, 17 February 2019
  • Conjectures 'R Us
    ...|Riesel value]]' (-1 form) that is composite for all values of {{Vn}} &ge; 1. Conjectures must have a finite covering set. {{Vk}}-values are not conside ==Sub-project #1==
    3 KB (503 words) - 02:20, 1 May 2024
  • Fast Fourier transform
    Let ''x''<sub>0</sub>, ...., ''x''<sub>''n''-1</sub> be [[complex number]]s. The DFT is defined by the formula ...f_j = \sum_{k=0}^{n-1} x_k e^{-{2\pi i \over n} jk } \qquad j = 0, ... ,n-1.</math>
    17 KB (2,684 words) - 18:50, 28 September 2023
  • GpuOwL
    ...://github.com/preda/gpuowl/tree/V1 gpuOwL V.1.x branch] at GitHub (version 1 uses 4M FFT and is about 50% faster than version 2) [http://www.mersennefor
    1 KB (216 words) - 05:22, 1 December 2020
  • M32
    :2<sup>756 839</sup>-1, a number {{Num|227832}} [[decimal]] [[digit]] long was found to be [[prime
    2 KB (279 words) - 08:35, 18 February 2019
  • M33
    '''M33''' refers to 33rd [[Mersenne prime]] number 2<sup>{{Num|859433}}</sup>-1.
    814 bytes (97 words) - 08:38, 18 February 2019
  • M34
    ...and in order of discovery. Specifically M34 is 2<sup>{{Num|1257787}}</sup>-1, which is a number {{Num|378632}} [[decimal]] [[digit]]s long. The number w
    3 KB (513 words) - 08:42, 18 February 2019
  • 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
  • Rational number
    :<math>\large a + \frac{k(b-a)}{n+1}</math> by varying the number <math>k</math> from 1 to <math>n</math>. Then we can make the value <math>n</math> as high as we
    3 KB (541 words) - 15:01, 26 March 2023
  • Binary
    ...em, a representation for numbers using only two [[digit]]s (usually, 0 and 1). Thus it is a [[base]] 2 numbering system. ...the next digit to the right; the place value of the rightmost digit being 1.
    1 KB (210 words) - 11:16, 22 January 2019
  • Repunit
    ...digit]]. All [[Mersenne number]]s are repunit ('''rep'''eated '''unit''', "1" being the number referred to as "unity") numbers. 111 is a repunit, in bas :(10<sup>n</sup> - 1) / 9
    1 KB (207 words) - 08:04, 12 March 2024
  • Parallel computing
    ==Example 1== ! Step !! Input 1 !! Operation !! Input 2 !! Result !! 1440<br>x 365
    3 KB (416 words) - 06:47, 1 May 2019
  • Trial factoring
    ...last prime factor possibility for some number N would be P(m) where P(m + 1) squared exceeds N. ...factor candidates would be close to <math>\frac {\sqrt{N}}{Ln(\sqrt{N}) - 1}</math> which for <math>N = 10^{20}</math> is 450 million.
    7 KB (1,221 words) - 13:20, 11 February 2019
  • M40
    ...e 40th [[Mersenne prime]]. Specifically it is 2<sup>{{Num|20996011}}</sup>-1. This number was discovered to be [[prime]] on 2003-11-17 by [[Michael Shaf ..., California (author of program [[Mlucas]]) using three weeks of time on a 1 GHz HP Alpha workstation.
    1 KB (189 words) - 11:17, 18 February 2019
  • Michael Shafer
    ...scovered the [[M40|40th]] [[Mersenne prime]], 2<sup>{{Num|20996011}}</sup>-1 at [[GIMPS]] project.
    660 bytes (88 words) - 00:39, 15 January 2024
  • Josh Findley
    ...very of the [[M41|41st known Mersenne prime]] 2<sup>{{Num|24036583}}</sup>-1.
    695 bytes (93 words) - 11:46, 14 January 2024
  • M39
    | top5000id=1 ...e 39th [[Mersenne prime]]. Specifically it is 2<sup>{{Num|13466917}}</sup>-1. This number was discovered to be [[prime]] on 2001-11-14 by [[Michael Came
    868 bytes (109 words) - 11:14, 18 February 2019
  • M44
    ...rime]]. Currently that designation belongs to 2<sup>{{Num|32582657}}</sup>-1.
    997 bytes (129 words) - 11:35, 18 February 2019
  • M45
    '''M45''' normally refers to 2<sup>{{Num|37156667}}</sup>-1, the 45th [[Mersenne prime]] in order of size from the smallest to greatest
    2 KB (251 words) - 11:40, 18 February 2019
  • Odd Magnar Strindmo
    ...46th Mersenne prime]] (chronologically 47th), 2<sup>{{Num|42643801}}</sup>-1. Strindmo goes by the alias '''Stig M. Valstad''' on [[GIMPS]].
    991 bytes (141 words) - 00:33, 15 January 2024
  • M38
    ...he 38th [[Mersenne prime]]. Specifically it is 2<sup>{{Num|6972593}}</sup>-1. This number was discovered to be [[prime]] on 1999-06-01 by [[Nayan Hajrat
    1 KB (165 words) - 11:10, 18 February 2019
  • Nayan Hajratwala
    ...ho discovered the [[M38|38th Mersenne prime]], 2<sup>{{Num|6972593}}</sup>-1.
    809 bytes (109 words) - 23:55, 14 January 2024
  • Coprime
    ...ly primes when their [[greatest common divisor]] is 1 (<math>\gcd{(x,y)} = 1</math>). This does not mean that any of these numbers is prime.
    738 bytes (112 words) - 09:50, 23 January 2019
  • Greatest common divisor
    When the greatest common divisor is 1, both numbers are [[coprime]] or relatively prime. This does not mean that #Go back to step 1.
    2 KB (339 words) - 18:38, 27 September 2023
  • Modular arithmetic
    ...can be done when working modulo N, where N is an [[integer]] greater than 1. ...s is 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>.
    4 KB (625 words) - 10:25, 23 January 2019
  • Montgomery multiplication
    ...onentiation]], [[Elliptic curve method|ECM]], [[P-1 factorization method|p-1]], etc.) this method is really fast. ...ation to normal, just perform a Montgomery multiplication using the number 1 as the second factor.
    4 KB (582 words) - 17:01, 29 August 2022
  • Elliptic curve method
    :<math>O(\exp{\sqrt{(\log p \,\log \log p)(1+O(1)}})</math> ...omposite number is a number that has divisors that are neither itself, nor 1. A highly composite number is a number that has lots and lots of divisors.
    19 KB (3,181 words) - 22:27, 6 July 2023
  • M35
    Specifically 2<sup>{{Num|1398269}}</sup>-1, written out in full [http://www.mersenneforum.org/txt/35.txt {{Num|420921}
    2 KB (224 words) - 11:00, 18 February 2019
  • Raphael M. Robinson
    ...t|Lucas-Lehmer]] [[primality test]] to determine whether 2<sup>''n''</sup>-1 was prime for all prime ''n'' < 2304 on a [[SWAC (computer)|SWAC]] at [[Uni ....htm In memoriam : Raphael Mitchel Robinson,]" ''Bull. Symbolic Logic'' '''1''': 340-43.
    4 KB (526 words) - 14:51, 19 September 2021
  • M36
    ...he 36th [[Mersenne prime]], specifically it is 2<sup>{{Num|2976221}}</sup>-1. This number was dicovered to be [[prime]] on 1997-08-24 by [[Gordon Spence ...umber]] is 2<sup>{{Num|2976220}}</sup> &bull; (2<sup>{{Num|2976221}}</sup>-1). This number is {{Num|1791864}} digits long.
    2 KB (279 words) - 11:01, 18 February 2019
  • Sierpiński problem
    *{{Kbn|+|78557|4n+1}} is multiple of 5. *{{Kbn|+|78557|3n+1}} is multiple of 7.
    5 KB (650 words) - 10:25, 26 March 2024
  • Paul Seelhoff
    ...50?tify={%22pages%22:%5B306%5D,%22view%22:%22%22} "Generalregister zu Band 1-50 der Zeitschrift für Mathematik und Physik"], p.292) ...fy={%22pages%22:%5B412%5D,%22view%22:%22%22} "Die Zahlen von der Form k.2n+1"], Zeitschrift fur Mathematik und Physik, '''Vol. 31''' (1886) p380
    2 KB (195 words) - 00:13, 15 January 2024
  • Covering set
    *[[Riesel problem 1|Riesel problem]]
    380 bytes (56 words) - 10:27, 26 March 2024
  • Seventeen or Bust
    |result=11 k's eliminated as a standalone project, 1 k eliminated as a subproject on PrimeGrid 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 [[Sie
    3 KB (544 words) - 16:44, 21 July 2019
  • M2
    | digits= 1
    193 bytes (19 words) - 13:43, 17 February 2019
  • Perfect number
    ...roper 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. ...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
  • M9
    The ninth [[Mersenne prime]], 2<sup>61</sup>-1 or {{Num|2305843009213693951}}. ...mber, ([[Édouard Lucas]] having shown earlier that [[M12]], <math>2^{127}-1</math> is also prime), and it remained so until 1911. Prior to the develope
    2 KB (213 words) - 14:30, 17 February 2019
  • Residue
    ...of the L-L test. When the numbers being tested are large: <math>\gt2^{64}-1</math> (i.e. exponents larger than 64) and above, the residue is 16 hexadec Here is the Lucas test for <math>2^7-1</math>, which is 127:
    1 KB (235 words) - 10:24, 6 February 2019
  • GIMPS clients
    ! LL test !! PRP test !! Trial factoring !! ECM factoring !! P-1 factoring ...mount of factoring work using (say) Pollard's [[p-1 factorization method|p-1 method]] or the [[elliptic curve method]], both of which involve manipulati
    8 KB (1,218 words) - 15:37, 13 August 2020
  • Mfaktc
    ...CPU resources. However GPU sieving is not supported on compute capability 1.x GPUs in 0.20. Mfaktc 0.21 can do GPU sieving for those old GPUs. *A [[CUDA]] capable GPU with compute capability 1.1 (or newer), any Geforce 8000, 9000, 200, 400, 500 series ''except'' those w
    5 KB (765 words) - 14:54, 25 February 2019
  • Mfakto
    -v <n> verbosity level: 0=terse, 1=normal, 2=verbose, 3=debug -st run built-in selftest (about 1,500 testcases) and exit
    17 KB (2,524 words) - 12:39, 24 January 2019
  • Rho factorization method
    *x<sub>1</sub> = f(x<sub>0</sub>) *x<sub>2</sub> = f(x<sub>1</sub>)
    3 KB (558 words) - 10:28, 6 February 2019
  • Riesel number
    ...ether 509203 is the smallest Riesel number or not (the '''[[Riesel problem 1]]'''), a [[distributed computing project]] was created named [[Riesel Sieve *[[Riesel problem 1]]
    827 bytes (112 words) - 08:21, 25 March 2024
  • M12
    ...t [[University of California, Los Angeles]] found [[M13]], 2<sup>521</sup>-1. .../sup>-1=7) also produces a prime. When this value is tested (2<sup>7</sup>-1=127), another prime is produced. So, Lucas was testing to see if this trend
    2 KB (354 words) - 14:52, 19 September 2021
  • Primality test
    *[[Lucas primality test|Lucas Test]]: Used when the number {{V|N}}-1 is completely factored. ...factors of the input number - 1 are known (the unfactored part of {{V|N}}-1 must be less than the [[square root]] of {{V|N}}).
    3 KB (501 words) - 05:20, 3 August 2021
  • Lucas primality test
    ...whether a number N is prime or not, using the complete factorization of N-1. ...>(N-1)/q</sup> is not congruent to 1 modulo N for any prime divisor q of N-1, then N is a prime.
    1 KB (177 words) - 14:31, 17 February 2019

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