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  • Double check
    ...volved 2 independent double checks. [[Mlucas]] and [[Glucas]] are used and 2 different processor types are used. [[Landon Curt Noll]]'s [[Mprime (Cray)|
    2 KB (373 words) - 15:08, 5 June 2019
  • Residue
    Here is the Lucas test for <math>2^7-1</math>, which is 127: :S1 = (4 * 4 - 2) mod 127 = 14
    1 KB (235 words) - 10:24, 6 February 2019
  • GIMPS clients
    ! rowspan="2" | Hardware ...one, and the average GIMPS participant has completed less than three (mean 2.67).
    8 KB (1,218 words) - 15:37, 13 August 2020
  • Mfaktc
    ...variants) should work. (The [[Mfaktc#Future|next version]] will require CC 2.0 or newer.) **executables: CUDA >= 4.2 capable driver (295 series or newer)
    5 KB (765 words) - 14:54, 25 February 2019
  • Mfakto
    -v <n> verbosity level: 0=terse, 1=normal, 2=verbose, 3=debug -tf <exp> <min> <max> trial factor M<exp> from 2^<min> to 2^<max> and exit instead of parsing the worktodo file
    17 KB (2,524 words) - 12:39, 24 January 2019
  • Rho factorization method
    *x<sub>2</sub> = f(x<sub>1</sub>) ...<sub>n+1</sub> = x<sub>n</sub><sup>2</sup> + a, where a <math>\neq </math>-2.
    3 KB (558 words) - 10:28, 6 February 2019
  • Riesel number
    ...ński problem]] article, [[Hans Riesel]] found in 1956 that [[Riesel prime 2 509203|{{Kbn|509203|n}}]] is always composite. *[[Riesel 2 Riesel|Riesel numbers]]
    827 bytes (112 words) - 08:21, 25 March 2024
  • M12
    ...son|Robinson]] at [[University of California, Los Angeles]] found [[M13]], 2<sup>521</sup>-1. ...mula (2<sup>2</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
    2 KB (354 words) - 14:52, 19 September 2021
  • Primality test
    *[[Proth's theorem]]: Used to test numbers of the form {{Kbn|+|k|n}} with 2<sup>{{Vn}}</sup> > {{Vk}}, making it useful in several [[distributed comput
    3 KB (501 words) - 05:20, 3 August 2021
  • Lucas primality test
    Prove that N = 811 is prime knowing that N-1 = 2 &times; 3<sup>4</sup> &times; 5 :<math>3^{810/2}\,= \,3^{405}\,\equiv \, 810\,\pmod{811}</math>
    1 KB (177 words) - 14:31, 17 February 2019
  • Square root
    For example, <math>\sqrt 9 = 3</math> since <math>3^2 = 3 \times 3 = 9</math>. ...uadratic equations such as <math>x^2=9</math> or, more generally, <math>ax^2+bx+c=0</math>.
    13 KB (1,873 words) - 16:52, 24 October 2020
  • Pépin's test
    ...r numbers, like the [[Generalized Fermat number]]s <math>F_{n,2} = 4^{3^n}+2^{3^n}+1</math> with k = 5 instead of k = 3. ...<math>F_n = 2^{2^n}+1</math> is a prime if and only if <math>\ 3^{(F_n-1)/2} \ \equiv -1 \ \pmod{F_n}</math>.
    2 KB (401 words) - 14:40, 6 March 2019
  • Proof by induction
    *'''Step 2''' :<math>\sum_{k=1}^{n}\,(2k-1)\,=\,n^{2}</math>
    4 KB (679 words) - 13:57, 20 February 2019
  • Floating-point
    ...and scaled using an [[exponent]]. The [[base]] for the scaling is normally 2, 10 or 16. The typical number that can be represented exactly is of the for
    2 KB (294 words) - 22:56, 3 February 2019
  • Complex number
    ...on is <math>z = x + iy</math>. From the previous paragraph we get: <math>i^2 = -1</math>. ..._1 y_1 + x_2 y_2}{x_2^2 + y_2^2}\,+\,\frac {x_2 y_1 - x_1 y_2}{x_2^2 + y_2^2} \,i</math>
    2 KB (280 words) - 14:59, 26 March 2023
  • Operation Billion Digits
    *'''M(''exponent'') no factor from 2^(''startdepth'') to 2^(''end depth'')'''. ...system. They're currently at Level 21.07 (around twenty one candidates to 2^87). Their greatest factor was found at bit depth 85 by Åke Tilander, a fa
    6 KB (918 words) - 16:28, 24 July 2020
  • M37
    ...hort hand used to refer to the 37th [[Mersenne prime]]. Specifically it is 2<sup>{{Num|3021377}}</sup>-1. This number was discovered to be [[prime]] on
    877 bytes (111 words) - 11:04, 18 February 2019
  • Team Prime Rib
    ...ting power#P90 years|P90 CPU years]] of [[Lucas-Lehmer test|LL testing]] (#2 in [[PrimeNet]]) and over 7200 P90 CPU years of [[GIMPS factoring and sievi
    620 bytes (88 words) - 11:46, 12 February 2019
  • GIMPS factoring and sieving
    It is known that any factor of the Mersenne number <math>2^p-1</math> must be of the algebraic form <math>2kp+1</math> for some positi ...t an efficient way to do this, however! It is much easier to compute <math>2^p\,\bmod n</math>, i.e., the remainder after division by <math>n</math> by
    6 KB (962 words) - 10:08, 7 March 2019
  • Quadratic residue
    :<math>{x^2}\equiv{q}\ (mod\ p)</math>
    823 bytes (117 words) - 20:11, 26 October 2020
  • Modular square root
    :<math>r^2 \equiv a\ \pmod m</math> ...ulus. When this modulus is odd, we assume that the quantity <math>a^{(m-1)/2} \bmod m</math> equals 1 (otherwise there is no square root if <math>a \not
    5 KB (726 words) - 10:38, 6 February 2019
  • Legendre symbol
    ...h; that is to say there exists an integer <math>k</math> such that <math>k^2 \equiv a \pmod{p}</math>, or in other words <math>a</math> is a quadratic r #<math>\left(\frac{-1}{p}\right) = (-1)^{(p-1)/2} = \begin{cases} 1 & \text{if } p \equiv 1 \pmod{4} \\ -1 & \text{if } p \e
    2 KB (348 words) - 18:57, 28 September 2023
  • Law of quadratic reciprocity
    This does not cover the cases where we want to know whether -1 or 2 are quadratic residues or non-residues modulo <math>p</math>. *2 is a quadratic residue modulo <math>p</math> if and only if <math>p</math>
    1 KB (208 words) - 18:19, 2 October 2022
  • Ten million digits
    In a period just over 2 weeks in summer 2008, the first two [[Mersenne prime]]s greater than {{Num|
    979 bytes (146 words) - 14:23, 6 March 2019
  • LLR
    ...gram]] available to perform primality test on numbers of the form {{Vk}}•2<sup>{{Vn}}</sup>±{{V|c}}. *the fastest algorithms are for base two numbers (with {{Vk}} < 2<sup>{{Vn}}</sup>):
    2 KB (300 words) - 22:00, 16 December 2023
  • Double Mersenne number
    ...d as '''MM<sub>p</sub>''', '''MMp''', or '''MM(p)''' and refer to <math>2^{2^p-1}-1</math>. Early on it was thought that if M(p) was prime so too was MM *MM(2) = <math>2^3-1</math> = 7, known prime since antiquity
    4 KB (655 words) - 14:50, 19 September 2021
  • P-1 factorization method
    :<math>E = 2^{E_2} * 3^{E_3} * 5^{E_5} * ... * B</math> where <math>E_2</math> is selected so that <math>2^{E_2}</math> is about B1 and the same for the other prime numbers. ''B'' is
    5 KB (814 words) - 01:35, 12 March 2019
  • Brent-Suyama extension
    A naive stage 2 would then compute T=S<sup>q</sup> = 3<sup>E*q</sup> for successive prime q ...s > 3 are of form 6k+/-1. Suppose instead that we compute T=S<sup>(6k)<sup>2</sup>-1</sup> = 3<sup>E*(6k-1)*(6k+1)</sup> whenever one of 6k+1 or 6k-1 is
    2 KB (421 words) - 11:51, 28 January 2019
  • Self-initializing quadratic sieve
    ...power. If somehow we find two integers X and Y such that <math>X^2\equiv Y^2\,\pmod N</math> and <math>X\not\equiv \pm Y\pmod N</math>, then <math>\gcd( ...values X and Y the method finds ''relations'' which have the form <math>t^2 \equiv u\,\pmod N</math> where u is the product of small [[prime]] numbers.
    10 KB (1,763 words) - 02:56, 12 March 2019
  • Special number field sieve
    ...a\left(\exp\left( \left(\frac{32}{9}n\right)^{\frac{1}{3}} (\log n)^{\frac{2}{3}} \right)\right).</math>
    1 KB (186 words) - 12:07, 19 February 2019
  • Miller-Rabin pseudoprimality test
    *If <math>m^2\equiv 1\,\pmod p</math> then <math>m\equiv 1\,\pmod p</math> or <math>m\equ ...<math>N</math> be an odd number being tested for primality, and <math>N = 2^n\,k + 1</math> where <math>k</math> is an odd number.
    3 KB (432 words) - 15:33, 28 January 2019
  • Generalized Fermat number
    ...(2^{p^n}-1)</math> where p is the prime of apparition rank r (r(2)=1, r(3)=2, r(5)=3, ...) and n is greater or equal to 0. :<math>F_{n,2}</math> generates the [[Saouter number]]s.
    5 KB (726 words) - 09:57, 12 September 2021
  • Patrick Laroche
    He is credited with discovery of the [[M51|51th known Mersenne prime]] 2<sup>{{Num|82589933}}</sup>-1.
    987 bytes (147 words) - 01:27, 15 January 2024
  • PrimeGrid
    ...Search|321 Prime Search]] searching for mega primes of the form {{Kbn|±|3|2|n}}. ...rch]] searching for primes of the forms {{Kbn|±|27|2|n}} and {{Kbn|±|121|2|n}}.
    3 KB (458 words) - 10:28, 26 March 2024
  • PrimeNet server
    ...software forced into service has had important benefits. Since one of the 2 new primes was 10 million decimal digits long, it qualified for one of the
    2 KB (381 words) - 14:05, 21 August 2019
  • 321 Search
    ...ect|distributed computing project]] to search for [[prime]]s of the form 3*2<sup>n</sup>-1.
    1 KB (185 words) - 09:34, 3 August 2021
  • Sieve of Eratosthenes
    ...>2</math>. Since every second number after that will be divisible by <math>2</math>, we cross out every second number; all such numbers are composite. ...umber is <math>3</math>. We see that <math>3</math> is prime because <math>2 \geq \sqrt{3}</math>. Now we cross out every third number which hasn't been
    4 KB (654 words) - 11:10, 6 February 2019
  • Top GIMPS teams
    | 2 || [[Curtis Cooper|UCM-curtisc]] || 26914623
    2 KB (206 words) - 09:56, 7 March 2019
  • Aliquot sequence
    :<math>s_0\ =\ 10,\ \sigma(10)=1\ +\ 2\ +\ 5\ +\ 10</math> :<math>s_1\ =\ 18\ -\ 10\ =\ 8,\ \sigma(8)\ =\ 1\ +\ 2\ +\ 4\ +\ 8</math>
    6 KB (914 words) - 19:49, 21 February 2023
  • Abundant number
    The divisors of 12 are <math>(1, 2, 3, 4, 6, 12)</math>, so :<math>\sigma(12)\ =\ 1+2+3+4+6+12\ =\ 28</math>
    671 bytes (92 words) - 00:34, 30 January 2019
  • Prime
    ...1 that is only divisible by itself and 1. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19. ...P) + 1. From the form of the number Q, it is obvious that no integer from 2 to P divides evenly into Q, because each division would leave a remainder o
    2 KB (447 words) - 00:22, 10 July 2023
  • Twin prime
    | align="right" | 10<sup>1</sup> || align="right" | 2 | align="right" | 10<sup>2</sup> || align="right" | 8
    2 KB (255 words) - 06:08, 21 February 2023
  • Proth prime 2 28831
    |Pb=2 |PCount=2
    581 bytes (64 words) - 19:18, 5 April 2023
  • Nomenclature and notation
    ...th>x</math> (the exponent) must also be prime. Thus, the notation of <math>2^{p}-1</math> is generally used when discussing the search for a [[Mersenne A number that is itself prime '''and''' can be written in the form <math>2^{x}-1</math>. These are what [[GIMPS]] is searching for.
    3 KB (467 words) - 08:48, 15 May 2024
  • Computing power
    The work accomplished by one core of a hypothetical 1GHz Core 2 Duo [[CPU]] in one day. One P90 year equals 5.075 GHz-days. 1 TFLOPS equals
    2 KB (258 words) - 08:40, 15 May 2024
  • Seventeen or Bust/Primes
    | 4847 || {{PP|75994|4847 &times; 2<sup>{{Num|3321063}}</sup>+1}} || 999744 || 2005-10-15 || Richard Hassler | 5359 || {{PP|67719|5359 &times; 2<sup>{{Num|5054502}}</sup>+1}} || 1521561 || 2003-12-06 || Randy Sundquist
    2 KB (163 words) - 14:20, 7 March 2019
  • Seventeen or Bust/Factoring
    ...rime95]] and [http://linux.redbird.com/~alien88/sbfactor12.zip SBFactor v1.2]. Be warned that SBFactor doesn't allow resuming a factoring in the middle ...he sievedepth is around 49 and 50, the factorworth is best between 1.5 and 2, around 1.7. Save it and rename it to make_worktodo.bat. Run it. Then start
    3 KB (491 words) - 13:39, 1 February 2019
  • Why participate in GIMPS?
    ...rfect numbers are known) are all closely related to the primes of the form 2<sup>p</sup>-1, for some prime ''p'' (now called [[Mersenne prime|Mersennes] ...g new. Mersennes have one of the simplest possible forms for primes, <math>2^p-1</math>. The proof of their primality has an elegant simplicity (to a ma
    7 KB (1,252 words) - 09:47, 7 March 2019
  • Sieving
    ...+ b</math>, while in the second the sequence has the form <math>m\, =\, an^2 + bn + c</math>. If we need to find prime numbers, for all primes between 2 and the square root of the maximum member of the sequence, set to 1 those e
    3 KB (521 words) - 11:14, 6 February 2019
  • Smooth number
    :900 = 2<sup>2</sup> &times; 3<sup>2</sup> &times; 5<sup>2</sup>
    436 bytes (63 words) - 21:36, 3 February 2019
  • Sieving program
    *[[PPSieve]] (sieving for factors of numbers of the form K &times; 2<sup>n</sup> + 1 or - 1. Independent of K's, but good for many N's too) and *[[AthGFNSieve]] (performing sieving of generalized Fermat numbers b<sup>2<sup>n</sup></sup>+1) http://www.underbakke.com/AthGFNsv/
    2 KB (220 words) - 11:42, 7 March 2019
  • NewPGen
    *k&times;2<sup>n</sup>+1, k&times;2<sup>n+1</sup>+3 (Sophie Germain) ...sup>n</sup>+1, 2k&times;b<sup>n</sup>+1 (Cunningham Chain 2nd kind, length 2)
    3 KB (529 words) - 09:32, 7 March 2019
  • Sophie Germain prime
    ...prime. For example, 23 is a Sophie Germain prime because it is a prime and 2*23+1 = 47, also prime. | 1 || 2 || -
    1 KB (171 words) - 04:26, 3 November 2020
  • M13
    '''M13''' is the 13th known [[Mersenne prime]] 2<sup>521</sup>-1 found on 1952-01-30 by [[Raphael M. Robinson]].
    419 bytes (48 words) - 14:50, 19 September 2021
  • M14
    '''M14''' is the 14th known [[Mersenne prime]] 2<sup>607</sup>-1 found on 1952-01-30 by [[Raphael M. Robinson]].
    420 bytes (48 words) - 14:49, 19 September 2021
  • M15
    '''M15''' is the 15th known [[Mersenne prime]] 2<sup>{{Num|1279}}</sup>-1 found on 1952-06-25 by [[Raphael M. Robinson]].
    430 bytes (49 words) - 14:49, 19 September 2021
  • M16
    '''M16''' is the 16th known [[Mersenne prime]] 2<sup>{{Num|2203}}</sup>-1 found on 1952-10-07 by [[Raphael M. Robinson]].
    431 bytes (49 words) - 14:49, 19 September 2021
  • M17
    '''M17''' is the 17th known [[Mersenne prime]] 2<sup>{{Num|2281}}</sup>-1 found on 1952-11-09 by [[Raphael M. Robinson]].
    431 bytes (49 words) - 14:49, 19 September 2021
  • M18
    '''M18''' is the 18th known [[Mersenne prime]] 2<sup>{{Num|3217}}</sup>-1 found on 1957-09-08 by [[Hans Riesel]].
    415 bytes (47 words) - 22:26, 17 February 2019
  • M11
    '''M11''' is the 11th known [[Mersenne prime]] 2<sup>107</sup>-1</math> found in 1914 by [[Ralph Ernest Powers]].
    412 bytes (47 words) - 14:23, 17 February 2019
  • M10
    '''M10''' is the 10th known [[Mersenne prime]] <math>2^{89}-1</math> found in 1911 by [[Ralph Ernest Powers]].
    403 bytes (44 words) - 13:54, 17 February 2019
  • Proth's theorem
    Let <math>p = k*2^n+1</math> and <math>k < 2^n</math>; then <math>p</math> is prime if there is an integer <math>a</math :<math>a^{(p-1)/2} \equiv -1\pmod{p}</math>.
    549 bytes (88 words) - 18:15, 28 September 2023
  • Proth prime
    ...is not a true class of numbers, but primes in the form {{Kbn|+|k|n}} with 2<sup>''n''</sup> > ''k'' are often called Proth primes.
    656 bytes (91 words) - 07:02, 31 August 2020
  • Riesel prime
    ...ion of a '''Riesel prime''' mostly all primes of the form {{Kbn|k|n}} with 2<sup>{{Vn}}</sup> > {{Vk}} are called like this on many pages. *[https://www.mersenneforum.org/showthread.php?t=8621 "RPS {{Vk}}*2^{{Vn}}-1, {{Vk}}<300 reservations/status"]: [https://www.mersenneforum.org/
    2 KB (279 words) - 03:48, 24 April 2024
  • M26
    '''M26''' is the 26th known [[Mersenne prime]] 2<sup>{{Num|23209}}</sup>-1 found on 1979-02-09 by [[Landon Curt Noll]].
    455 bytes (52 words) - 23:01, 17 February 2019
  • Floor function
    ! 2 | 2 || 2
    813 bytes (111 words) - 16:56, 29 August 2022
  • Power of two
    ...2 &times; 2 &times; 2 &times; ...). They are normally represented as <math>2^n</math> where n is the [[exponent]]. ...refix for multiples of 1024 is kibi-, so 1024 bytes = 1 kibibyte. 1024<sup>2</sup> bytes = 1 mebibyte, 1024<sup>3</sup> bytes = 1 gibibyte, and so on.
    839 bytes (127 words) - 11:38, 6 February 2019
  • Introductory stuff
    ...mple, 3 = 4 - 1 = 2<sup>2</sup> - 1 is a Mersenne prime; so is 7 = 8 - 1 = 2<sup>3</sup> - 1. See [[Mersenne prime]]. ...At the time of writing, a candidate at the current wavefront may take 1 to 2 weeks on a modern PC (say, a quad core Intel with AVX2 instructions or an A
    14 KB (2,370 words) - 15:15, 17 August 2019
  • Overclocking and Prime95
    ...of 1.92 or 2.06 then you know the correct value is 2. If you end up with 2.2 then the calculation is invalid. If you proved that the maximum accumulated ...of 1.92 or 2.06 then you know the correct value is 2. If you end up with 2.2 then the calculation is invalid. If you proved that the maximum accumulated
    12 KB (1,995 words) - 09:55, 7 March 2019
  • Overclocking
    ...GP PORT for your AGP card is set to operate at a fixed fraction, (2/3 or 1/2), of the FSB.
    14 KB (2,326 words) - 15:17, 11 February 2019
  • Area
    An '''area''' is defined as a surface enclosed by a shape. It can be 2 or 3 dimensional. For 3 dimensional shapes, the surface is the area.
    215 bytes (32 words) - 13:43, 18 September 2022
  • Triangular number
    :4△ = 4 + 3 + 2 + 1 = 10 (10 pin bowling uses a triangular arrangement.) :5△ = 5 + 4 + 3 + 2 + 1 = 15 (a common billiards arrangement is 15 balls in a triangle.)
    655 bytes (81 words) - 12:49, 25 March 2019
  • Multiple polynomial quadratic sieve
    ...two integers <math>X</math> and <math>Y</math> such that <math>X^2\equiv Y^2\,\pmod N</math> and <math>X\not\equiv \pm Y\pmod N</math>, then <math>\gcd( ...<math>Y</math> the method finds ''relations'' which have the form <math>t^2 \equiv u\,\pmod N</math> where <math>u</math> is the product of small [[pri
    6 KB (1,068 words) - 14:33, 13 February 2019
  • Proth number
    :{{V|N}} = {{Kbn|+|k|2|n}} ...is an odd positive [[integer]] and {{Vn}} is a positive integer such that 2<sup>{{Vn}}</sup> > {{Vk}}.
    670 bytes (104 words) - 10:59, 9 July 2021
  • 27121 Search
    ...r prime numbers of the form: 27 &times; 2<sup>n</sup> ± 1 and 121 &times; 2<sup>n</sup> ± 1. ...s]]. The bigger primes are 27 &times; 2<sup>1902689</sup>-1 and 27 &times; 2<sup>2218064</sup>+1, which weighs in at 572768 digits and 667706 digits, f
    983 bytes (138 words) - 13:25, 8 February 2019
  • 12121 Search
    ...m: 121 &times; 2<sup>n</sup>-1, it also searches for primes of 121 &times; 2<sup>n</sup>+1 after being a partner of [[PrimeGrid]]. ...y 7 primes in the [[The Prime Pages]], their largest number is 121 &times; 2<sup>2033941</sup>-1 which weighs in at 612280 digits. This prime was found
    984 bytes (143 words) - 13:30, 8 February 2019
  • Assignments
    ...php?showsource=1] of FFT sizes and run times as calculated on the baseline 2.0 GHz Core2 Duo machine that set the current GHz-days credit standards. ...php?showsource=1] of FFT sizes and run times as calculated on the baseline 2.0 GHz Core2 Duo machine that set the current GHz-days credit standards (sam
    20 KB (3,473 words) - 18:42, 14 December 2023
  • GIMPS type of work
    *Standard (take the next exponent the server hands out, takes 1 to 2 weeks on typical hardware<ref>By typical, I am referring to a quad core Int ...ll yield a number with at least 100 million digits, these will take around 2 weeks on a Radeon VII, or several weeks on high end consumer hardware <ref>
    4 KB (757 words) - 15:17, 25 July 2020
  • How to get started with GIMPS
    ...taticly linked ''sprimexxx.tar.gz'' for systems that do not have the glibc 2.1 runtime libraries. *'''OS/2''': Max Alekseyev has ported the Linux version to OS/2. Download his ''os2vxxx.zip'' zipped executable.
    4 KB (623 words) - 13:39, 26 March 2019
  • GIMPS chances of finding a prime number
    ...ing as it slows down, and there are [[twin prime]]s - primes that are only 2 apart like 612,107 and 612,109 - and this makes matters more complicated. ...there are only two possible outcomes, so the chance of it being heads is 1:2. From the fact that a number either is prime or it is not one might suppose
    3 KB (593 words) - 10:09, 7 March 2019
  • Worktodo.txt
    *[[Elliptic curve method|ECM]]2=assignment ID,k,b,n,c,B1,B2,curves to do<nowiki>[</nowiki>,specific_sigma,B
    2 KB (273 words) - 22:58, 11 May 2019
  • P+1 factorization method
    <math>\large U_0 = 0\,,\, U_1 = 1\,,\, V_0 = 2\,,\, V_1 = u </math> ...= uU_{n-1} - U_{n-2}\,,\, V_n = uV_{n-1} - V_{n-2}</math> for <math>n\geq 2</math>
    8 KB (1,536 words) - 11:35, 12 February 2019
  • Woodall number
    :W<sub>n</sub> = n &times; 2<sup>n</sup>-1
    374 bytes (59 words) - 16:41, 31 August 2021
  • SNFS polynomial selection
    2. If you want to factor <math>a^{61}-1</math>, you can rewrite the power as ...culty 113) or <math>x^5-100</math> (difficulty 115) by the method of 1. or 2. alone.
    7 KB (1,238 words) - 16:14, 12 February 2019
  • NFSNET
    |<math>2^{772}+1</math> || 611380852128317600120825600011309662450676630495941840761 |<math>2^{779}+1</math> || 173158781290488639279749054806964483697237470930354987999
    4 KB (237 words) - 12:17, 13 February 2019
  • Mersenneplustwo factorizations
    ...prime) and 2<sup>p</sup> is not divisible by 3 (it's only prime factor is 2). ...159965}}) found by ECMNet, as well as 36-digit factor of M<sub>11213</sub>+2 ({{FDBID|1000000000012161237}}) found using ''mprime'' (the linux version o
    2 KB (215 words) - 13:33, 5 March 2019
  • ECMclient
    ...ized version using the [http://home.roadrunner.com/~mrodenkirch/ecmnet_3.0.2.zip source code]. 2. Move your homemade ecm.exe to the unzipped ecmclient folder (along with yo
    2 KB (383 words) - 11:16, 26 February 2019
  • GMP-ECM
    Distributed under GNU General Public License version 2. :*Get [http://mpir.org/mpir-2.5.1.tar.bz2 MPIR] and [https://gforge.inria.fr/frs/download.php/30965/ecm-6
    4 KB (567 words) - 10:54, 6 December 2019
  • Gerbicz error checking
    ...]] to ensure validity of [[Proth prime|Proth]] tests and PRP tests on base-2 [[Riesel prime]] candidates, and by those programs and [[PRST]] in an exten # <math>u(t) \equiv (a^k)^{2^t} \pmod{p}</math>
    3 KB (528 words) - 14:59, 3 October 2023
  • Jacobi error checking
    ...:Jacobi symbol|Jacobi symbol]] of the residue plus 2 <math>\left(\frac{Res+2}{M_p}\right)</math> has to be +1 *Jacobi symbol of the residue minus 2 <math>\left(\frac{Res-2}{M_p}\right)</math> has to be -1
    1 KB (166 words) - 18:36, 27 September 2023
  • ECPP-DJ
    *[[BPSW test]] (strong PRP-2 test followed by extra strong Lucas-Selfridge test)
    2 KB (237 words) - 18:04, 2 December 2019
  • BLS75
    ...0025-5718-1975-0384673-1.pdf "New Primality Criteria and Factorizations of 2^{{V|m}} ± 1"]. ''Mathematics of Computation.'' Volume 29, Number 130: 620-
    584 bytes (85 words) - 20:12, 26 October 2020
  • Advanced Vector Extensions
    They add 512-bit vector operations capabilities in 2013, with up to 2 FMAs (Fused Multiply Add instructions), to accelerate performance of demand
    1 KB (147 words) - 14:12, 14 February 2019
  • GIMPS PrimeNet reports
    ...eported. If the number has not had a successful [[double check]], the last 2 digits are masked. For unconfirmed results any error code is also displayed
    7 KB (1,137 words) - 15:30, 13 August 2020
  • M29
    | foundwith=[[Lucas-Lehmer test]] / [[NEC SX-2]]
    296 bytes (26 words) - 08:25, 18 February 2019
  • System requirements and compatible hardware
    ...2 / AMD 64-bit / Itanium 64-bit / Itanium 64-bit SP 1 / Itanium 64-bit SP 2) :Windows NT (3 / 4 / 4 SP 1 / 4 SP 2 / 4 SP 3 / 4 SP 4 / 4 SP 5 / 4 SP 6)
    766 bytes (95 words) - 12:25, 19 February 2019
  • Mersenne composite
    A '''Mersenne composite''' is any number of the form 2<sup>n</sup>-1 which is a [[composite number]]. ...e, because it is multiple of both [[Mersenne number]]s 2<sup>p</sup>-1 and 2<sup>q</sup>-1.
    347 bytes (62 words) - 13:07, 19 February 2019
  • Square number
    ...of two square integers is also a square number (e.g. 2/3&nbsp;&times;&nbsp;2/3 = 4/9). :1<sup>2</sup> = 1
    3 KB (408 words) - 13:56, 19 February 2019
  • Square (algebra)
    Example: n squared equals n<sup>2</sup> = n &times; n.
    341 bytes (47 words) - 14:03, 19 February 2019
  • AdvancedFactor
    ...{{Num|1000000}} and {{Num|2000000}} for factors between 2<sup>64</sup> and 2<sup>68</sup>. :bd is where to begin trial-factoring at (2<sup>bd</sup>).
    2 KB (300 words) - 16:08, 19 February 2019

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