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  • Factorial number
    :<math>n! = 1 \cdot 2 \cdot 3 \cdots (n{-}2) \cdot (n{-}1) \cdot n</math> :5! = 5 * 4 * 3 * 2 * 1 = 120
    729 bytes (93 words) - 13:40, 5 November 2023
  • Subtraction
    ...are, minuend &minus; subtrahend = difference. The expression 7 &minus; 4 = 3 can be spoken as "seven minus four equals three", "seven take away four lea
    893 bytes (128 words) - 16:58, 29 August 2022
  • Division
    :<math>2 \times 3 = 6</math>.
    2 KB (368 words) - 16:58, 29 August 2022
  • Remainder
    ...ng. Dividing 13 into groups of 5 would yield 2 groups, with a remainder of 3.
    245 bytes (34 words) - 14:07, 18 January 2019
  • 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
    ...factors (half of the numbers are multiples of 2, a third are multiples of 3 and so on) it pays to run factorization methods in the first category and t
    4 KB (642 words) - 12:57, 5 March 2019
  • 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
  • M46
    | foundwith=[[Lucas-Lehmer test]] / [[Prime95]] on 3 GHz Core 2 [[Personal computer|PC]] ...since 1996 testing over 1400 candidates. The calculation took 29 days on a 3.0 GHz Intel Core2 processor.
    2 KB (248 words) - 11:45, 18 February 2019
  • Riesel prime 2 187605
    3
    490 bytes (35 words) - 12:22, 11 December 2022
  • Program
    *Knuth, Donald E., The Art of Computer Programming, Volume 3, 3rd Edition, 1997, Addison-Wesley, ISBN 0-201-89685-0
    2 KB (263 words) - 11:53, 7 February 2019
  • M1
    | number= 3
    193 bytes (19 words) - 13:43, 17 February 2019
  • Conjectures 'R Us
    ==Sub-project #3==
    3 KB (503 words) - 02:20, 1 May 2024
  • Fast Fourier transform
    ...key algorithm is O(&epsilon; log ''n''), compared to O(&epsilon; ''n''<sup>3/2</sup>) for the naive DFT formula (Gentleman and Sande, 1966), where &epsi ...achlass: Theoria interpolationis methodo nova tractata," ''Werke'' band '''3''', 265&ndash;327 (K&ouml;nigliche Gesellschaft der Wissenschaften, G&ouml;
    17 KB (2,684 words) - 18:50, 28 September 2023
  • GpuOwL
    Apart from the LL test, gpuOwL also implements a base-3 [[probable prime|PRP]] test with [[Gerbicz error checking]] ensuring correc
    1 KB (216 words) - 05:22, 1 December 2020
  • M32
    ...nski was notified and tested the number on a 16 CPU Cray-C90, taking about 3 hours. Later it was verified on a different computer architecture, using di
    2 KB (279 words) - 08:35, 18 February 2019
  • 2 Plus Tables
    *1 : {{FDBID|3}}
    2 KB (127 words) - 15:28, 17 August 2019
  • Binary
    :0 &rarr; 0 * 2<sup>3</sup> = 0
    1 KB (210 words) - 11:16, 22 January 2019
  • Repunit
    ...) numbers. 111 is a repunit, in base 2 it is equal to 7 (base 10), in base 3 it is equal to 13 (base 10).
    1 KB (207 words) - 08:04, 12 March 2024
  • Parallel computing
    | 3 || 300 || x || 1440 || 432000 || ..., they could all be done in parallel. This would cut a 5 step procedure to 3. If the numbers were each 100 digits long and 10 individuals (or cores in a
    3 KB (416 words) - 06:47, 1 May 2019
  • Trial factoring
    ...trial divisors. If P(i) is the i'th prime number so P(1) = 2, P(2) = 3, P(3) = 5, etc, then the last prime factor possibility for some number N would b ...ce 2*7 is excluded because 2 will have been tried, 3*7 is excluded because 3 will have been tried, and 5*7 is excluded because 5 will have been tried. T
    7 KB (1,221 words) - 13:20, 11 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
  • Odd Magnar Strindmo
    Strindmo's 3 GHz Core 2 Duo PC first reported the prime to GIMPS on 2009-04-12. However,
    991 bytes (141 words) - 00:33, 15 January 2024
  • Modular arithmetic
    ...rithmetic 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>. The set <b>Z</b>/n<b>Z</b> of numbers modulo n contains the numbers 0, 1, 2, 3, ..., n-2 and n-1. The following operations are defined:
    4 KB (625 words) - 10:25, 23 January 2019
  • Montgomery multiplication
    :Let m=5 , n=3 , a = b = 3. :We get: a' = b' = 3 &times; 8 mod 5 = 4
    4 KB (582 words) - 17:01, 29 August 2022
  • Elliptic curve method
    ...cation|multiplying]] lots of different prime numbers together. So that 2 x 3 x 5 x 7 x 11 x 13 etc will be a highly composite number. But that is only t ...for ''y''. If we plug in ''x'' = 2, we get out ''y'' = 23. Plug in ''x'' = 3, we get out ''y'' = 48. If we plug in enough different values for ''x'' and
    19 KB (3,181 words) - 22:27, 6 July 2023
  • Raphael M. Robinson
    ...ey.edu/sites/default/files/imagecache/photo_album_main/photo_albums/ROBINS~3.jpg ...[Mersenne number]]s were all composite except for 17 values of ''n'' = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, [[M12|127]], [[M13|521]], [[M14|607]],
    4 KB (526 words) - 14:51, 19 September 2021
  • Sierpiński problem
    *{{Kbn|+|78557|2n}} is multiple of 3. *{{Kbn|+|78557|9n+3}} is multiple of 73.
    5 KB (650 words) - 10:25, 26 March 2024
  • Paul Seelhoff
    :28 [[Proth prime]]s for 3 &le; {{Vk}} &le; 97
    2 KB (195 words) - 00:13, 15 January 2024
  • M2
    | nvalue= 3
    193 bytes (19 words) - 13:43, 17 February 2019
  • M3
    | rank= 3 | pdigits= 3
    194 bytes (19 words) - 13:43, 17 February 2019
  • M4
    | digits= 3
    195 bytes (19 words) - 13:44, 17 February 2019
  • Perfect number
    ...ct number, because 1, 2 and 3 are its proper positive divisors and 1 + 2 + 3 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. The next perfect n :for ''n'' = 3: &nbsp; 2<sup>2</sup>(2<sup>3</sup> - 1) = 28
    6 KB (885 words) - 11:33, 7 March 2019
  • Unused computing power
    ..."do nothing". A [[computer]] that is a quad-[[Processor|core]] running at 3 GHz is capable of performing 12 billion instructions a second. Often less t
    971 bytes (156 words) - 13:46, 25 January 2019
  • Mfakto
    -v <n> verbosity level: 0=terse, 1=normal, 2=verbose, 3=debug Maximum: 3 (debug)
    17 KB (2,524 words) - 12:39, 24 January 2019
  • Rho factorization method
    ...ed by Floyd that consists in computing x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub> and so on by iterating the polynomial, and at the same time computing ...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 proper factor of N.
    3 KB (558 words) - 10:28, 6 February 2019
  • Lucas primality test
    Prove that N = 811 is prime knowing that N-1 = 2 &times; 3<sup>4</sup> &times; 5 Let's start with b = 3.
    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>. :<math> = 1 + \frac{1}{2}x - \frac{1}{8}x^2 + \frac{1}{16} x^3 - \frac{5}{128} x^4 + ...</math>
    13 KB (1,873 words) - 16:52, 24 October 2020
  • Primality testing program
    ...e Prime Freeware] by [[Luke Welsh]] and Yuri Sorkin. Last updated on April 3, 2008.
    2 KB (314 words) - 21:23, 29 August 2019
  • Pépin's test
    ...mber]]s <math>F_{n,2} = 4^{3^n}+2^{3^n}+1</math> with k = 5 instead of k = 3. ...n>0</math>, <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 3''' *'''Step 3'''
    4 KB (679 words) - 13:57, 20 February 2019
  • M37
    | top5000id=3
    877 bytes (111 words) - 11:04, 18 February 2019
  • GIMPS factoring and sieving
    ...d is eliminated if it was not previously eliminated in the divisibility by 3 test, and so forth. It is not necessary to carry this sieving process all t
    6 KB (962 words) - 10:08, 7 March 2019
  • Modular square root
    ===Modulus congruent to 3 modulo 4=== *Step 2: <math>x = 2</math>, <math>z = 2^7 \bmod 113 = 15</math>, <math>z^{2^3} \bmod 113 = 1</math>, so we have to repeat step 2.
    5 KB (726 words) - 10:38, 6 February 2019
  • Legendre symbol
    ...egin{cases} 1 & \text{if } p \equiv 1 \pmod{4} \\ -1 & \text{if } p \equiv 3 \pmod{4} \end{cases}</math> ...\text{if } p \equiv 1 \text { or } 7 \pmod{8} \\ -1 & \text{if } p \equiv 3 \text{ or } 5 \pmod{8} \end{cases}</math>
    2 KB (348 words) - 18:57, 28 September 2023
  • Law of quadratic reciprocity
    *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 o
    1 KB (208 words) - 18:19, 2 October 2022
  • LLR
    ..." for Gaussian-Mersenne norms and Wagstaff numbers (2<sup>{{V|p}}</sup>+1)/3. The latter uses a strong Fermat PRP-test and the [[Vrba-Reix algorithm]].
    2 KB (300 words) - 22:00, 16 December 2023
  • Double Mersenne number
    *MM(2) = <math>2^3-1</math> = 7, known prime since antiquity *MM(3) = <math>2^7-1</math> = 127, 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> Then E = 2<sup>3</sup> &times; 3<sup>2</sup> &times; 5 &times; 7 &times; 29.
    5 KB (814 words) - 01:35, 12 March 2019
  • Brent-Suyama extension
    Recall that stage 1 computes S=3<sup>E</sup> where E is the product of prime powers less than B1. Then by [[ A naive stage 2 would then compute T=S<sup>q</sup> = 3<sup>E*q</sup> for successive prime q in the range (B1,B2]. Then p | T-1 if
    2 KB (421 words) - 11:51, 28 January 2019
  • Special number field sieve
    ...eft(\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

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