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  • M47
    **One on 4 quad-core SPARC64 VII 2.52GHz CPUs of a Sun SPARC Enterprise M8000 Server
    5 KB (694 words) - 13:17, 21 August 2019
  • Prime95
    |style="text-align:left"|Intel Pentium 4||3078||1||72.40||162.02||14.91||86 |style="text-align:left"|AMD Phenom II X4||3414||4||34.86||76.27||4.59||125
    11 KB (1,586 words) - 12:24, 7 August 2021
  • Even number
    All numbers ending in 0, 2, 4, 6, or 8 are even.
    425 bytes (61 words) - 11:19, 7 March 2019
  • M41
    | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 2.4 GHz Pentium 4 [[Personal computer|PC]] The discovery took 14 days of computing on 2.4 GHz Pentium 4 Windows XP PC.
    1 KB (203 words) - 11:26, 18 February 2019
  • M43
    | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 2 GHz Pentium 4 [[Personal computer|PC]]
    1 KB (191 words) - 11:31, 18 February 2019
  • Riesel prime 2 21143
    4
    403 bytes (26 words) - 18:40, 2 January 2023
  • Proth prime 2 12321
    4
    498 bytes (31 words) - 13:34, 2 January 2023
  • Program
    ...Programming, Volume 1, 3rd Edition, 1997, Addison-Wesley, ISBN 0-201-89683-4
    2 KB (263 words) - 11:53, 7 February 2019
  • M42
    | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 2.4 GHz Pentium 4 [[Personal computer|PC]]
    934 bytes (118 words) - 11:26, 18 February 2019
  • Fast Fourier transform
    ...he history of the fast Fourier transform," ''IEEE ASSP Magazine'' '''1''' (4), 14-21 (1984).
    17 KB (2,684 words) - 18:50, 28 September 2023
  • Primo
    |latest=4.3.2<br><small>2020-02-06</small> ...ood]] with Primo 4.3.0. The certification process took 21.5 months using a 4 x 12 core AMD 6174.
    1 KB (191 words) - 20:33, 12 May 2020
  • M32
    :"Took 26.562767 minutes to calculate using Maple 4.0 on a 512-MW 4 CPU Cray 2"
    2 KB (279 words) - 08:35, 18 February 2019
  • 2 Plus Tables
    *4 : {{FDBID|17}}
    2 KB (127 words) - 15:28, 17 August 2019
  • Binary
    :1 &rarr; 1 * 2<sup>4</sup> = 16
    1 KB (210 words) - 11:16, 22 January 2019
  • Parallel computing
    | 4 || 7200 || + || 86400 || 93600 ||
    3 KB (416 words) - 06:47, 1 May 2019
  • M40
    The discovery took 19 days of computation on a 2 GHz Pentium 4 Dell Dimension PC at a Michigan State University lab.
    1 KB (189 words) - 11:17, 18 February 2019
  • M44
    | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 3 GHz Pentium 4 [[Personal computer|PC]]
    997 bytes (129 words) - 11:35, 18 February 2019
  • Modular arithmetic
    ...3 hours = 2 PM). We can also subtract: 2-3 = 11 and even multiply: 5&times;4 = 8 (because 5+5+5+5 = 8). This is arithmetic modulo 12 and the set of numb
    4 KB (625 words) - 10:25, 23 January 2019
  • Montgomery multiplication
    :We get: a' = b' = 3 &times; 8 mod 5 = 4 :x = a' b' = 4 &times; 4 = 16
    4 KB (582 words) - 17:01, 29 August 2022
  • Elliptic curve method
    ...''' = '''S'''. Given a point '''P''', we could compute 2'''P''', 3'''P''', 4'''P''', and so on. For some value <math>g</math>. we will have <math>g</mat where: <math>S = \frac {A+2}4</math> which can be precomputed when the elliptic curve is selected and
    19 KB (3,181 words) - 22:27, 6 July 2023
  • University of California, Los Angeles
    ...ty. [[University of Central Missouri]] has contributed to the discovery of 4, making it second to UCLA.
    2 KB (347 words) - 14:54, 19 September 2021
  • Raphael M. Robinson
    ...universal Turing machine," describing a universal [[Turing machine]] with 4 symbols and 7 states;
    4 KB (526 words) - 14:51, 19 September 2021
  • M36
    | top5000id=4
    2 KB (279 words) - 11:01, 18 February 2019
  • Sierpiński problem
    |0||1||2||3||4||5||6||7||8||9||10||11||12||13||14||15||16||17||18||19||20||21||22||23||24|
    5 KB (650 words) - 10:25, 26 March 2024
  • M4
    | rank= 4 | pdigits= 4
    195 bytes (19 words) - 13:44, 17 February 2019
  • M5
    | digits= 4
    204 bytes (18 words) - 13:46, 17 February 2019
  • Perfect number
    ...sitive 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. :for ''n'' = 5: &nbsp; 2<sup>4</sup>(2<sup>5</sup> - 1) = 496
    6 KB (885 words) - 11:33, 7 March 2019
  • Residue
    ...roneaous residues (meaning they both missed a prime) out of a pool of ~ 18.4 pentillion numbers, this is considered to be impossible. :S0 = 4
    1 KB (235 words) - 10:24, 6 February 2019
  • Mfakto
    ...this will start happening at vector size 8. On a HD6870, a vector size of 4 is fastest except for the barrett92 and barrett72 kernels which run slightl Allowed sizes are 1, 2, 4, 8, 16.
    17 KB (2,524 words) - 12:39, 24 January 2019
  • Rho factorization method
    ...rating the polynomial, and at the same time computing x<sub>2</sub>, x<sub>4</sub>, x<sub>6</sub> and so on by iterating the polynomial twice. Then we c ...o compute gcd(x<sub>1</sub> - x<sub>2</sub>, N), gcd(x<sub>2</sub> - x<sub>4</sub>, N), gcd(x<sub>3</sub> - x<sub>6</sub>, N), and so on until we find a
    3 KB (558 words) - 10:28, 6 February 2019
  • M12
    ...} [http://www.garlic.com/~wedgingt/MMPstats.txt], a [[bit level]] over 169.4. The current version of [[Prime95]] cannot handle numbers this large, nor c
    2 KB (354 words) - 14:52, 19 September 2021
  • Lucas primality test
    Prove that N = 811 is prime knowing that N-1 = 2 &times; 3<sup>4</sup> &times; 5
    1 KB (177 words) - 14:31, 17 February 2019
  • Square root
    ...= 1 + \frac{1}{2}x - \frac{1}{8}x^2 + \frac{1}{16} x^3 - \frac{5}{128} x^4 + ...</math> <u> 1 2. 3 4 </u>
    13 KB (1,873 words) - 16:52, 24 October 2020
  • Pépin's test
    ...of other 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.
    2 KB (401 words) - 14:40, 6 March 2019
  • Proof by induction
    ...ally taken to be 1, but that is not essential. In some proofs (see example 4 below) we have to show that the statement is true for several values of n. :<math>\sum_{k=1}^{n}k^{3}\,=\,\frac{n^{2}(n+1)^{2}}{4}</math>
    4 KB (679 words) - 13:57, 20 February 2019
  • Pseudoprime
    ...of the Miller-Rabin test, for example, has a probability of only <math>{1/4}^{100}</math> of being composite, which is less than <math>10^{-60}</math>.
    1 KB (155 words) - 20:32, 25 July 2020
  • Modular square root
    ===Modulus congruent to 3 modulo 4=== :<math>r\equiv \pm a^{(m+1)/4}\ \pmod m</math>
    5 KB (726 words) - 10:38, 6 February 2019
  • Legendre symbol
    ...es} 1 & \text{if } p \equiv 1 \pmod{4} \\ -1 & \text{if } p \equiv 3 \pmod{4} \end{cases}</math> ...property is known as the [[law of quadratic reciprocity]]. The properties 4 and 5 are traditionally known as the ''supplements'' to quadratic reciproci
    2 KB (348 words) - 18:57, 28 September 2023
  • Law of quadratic reciprocity
    *If at least one of <math>p</math> or <math>q</math> are congruent to 1 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if *If both of <math>p</math> or <math>q</math> are congruent to 3 mod 4: <math>p</math> is a quadratic residue modulo <math>q</math> if and only if
    1 KB (208 words) - 18:19, 2 October 2022
  • Double Mersenne number
    This holds true for the first 4 terms: However this does not hold true for next 4 terms:
    4 KB (655 words) - 14:50, 19 September 2021
  • Self-initializing quadratic sieve
    :<math>45^2\,\equiv \,2^4*7^0*13^1</math>
    10 KB (1,763 words) - 02:56, 12 March 2019
  • Miller-Rabin pseudoprimality test
    ...strated that a composite <math>N</math> will only pass at most <math>(N-1)/4</math> such tests. ...35. Since the exponent is 4, the sequence will use exponents from zero to 4.
    3 KB (432 words) - 15:33, 28 January 2019
  • Generalized Fermat number
    3*2^41+1 is a Factor of xGF(38,4,3)!!!! (0.000000 seconds)
    5 KB (726 words) - 09:57, 12 September 2021
  • Patrick Laroche
    ...hunting on his media server to "give back" to the project. After less than 4 months and on just his fourth try, he discovered the new prime number. By w
    987 bytes (147 words) - 01:27, 15 January 2024
  • Top GIMPS teams
    | 4 || [[Team Prime Rib|Ars Technica Team Prime Rib]] || 4457877
    2 KB (206 words) - 09:56, 7 March 2019
  • Aliquot sequence
    :<math>s_1\ =\ 18\ -\ 10\ =\ 8,\ \sigma(8)\ =\ 1\ +\ 2\ +\ 4\ +\ 8</math> :<math>2^4\ *\ 31</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
    ...whole numbers from 2 to P plus the number 1. In other words, Q = (2 x 3 x 4 x 5 ... x P) + 1. From the form of the number Q, it is obvious that no inte :the remainder r can be only 0, 1, 2, 3, 4, or 5
    2 KB (447 words) - 00:22, 10 July 2023
  • Twin prime
    | align="right" | 10<sup>4</sup> || align="right" | 205
    2 KB (255 words) - 06:08, 21 February 2023
  • Proth prime 2 28831
    4
    581 bytes (64 words) - 19:18, 5 April 2023

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