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• Williams prime
  ...er''' is a [[natural number]] of the form {{Kbn|(b-1)|b|n}} for integers ''b'' ≥ 2 and ''n'' ≥ 1. Lists of primes for bases ''b'' and ''n''-values can be found here:
  5 KB (744 words) - 07:30, 5 August 2019
• Examples
  <pre><math>\sideset{_1^2}{_3^4}\prod_a^b</math></pre> :<math>\sideset{_1^2}{_3^4}\prod_a^b</math>
  11 KB (1,236 words) - 14:41, 3 September 2020
• Mersenne prime
  :<math>(2^a-1)\cdot \left(1+2^a+2^{2a}+2^{3a}+ ... +2^{(b-1)a}\right)=2^{ab}-1</math>
  5 KB (857 words) - 14:53, 19 September 2021
• Fermat number
  ...} &equiv; (2^{{V|a}})^{{V|b}} + 1 &equiv; (-1)^{{V|b}} + 1 &equiv; 0 (mod 2^{{V|a}} + 1).) In other words, every :<math>F_{n} = (F_{n-1}-1)^{2}+1</math>
  12 KB (1,913 words) - 14:35, 9 August 2021
• Home prime
  Notations for other bases of 10 are HP_base(n) for base ''b''.
  980 bytes (143 words) - 13:22, 6 March 2019
• Cunningham project
  ...e [[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 exponent <math>n</mat ...split into two parts directly, for certain combination of values of <math>b</math> and <math>n</math>.
  7 KB (1,150 words) - 23:48, 19 April 2023
• Lucas-Lehmer test
  ...ber denoted S_n where S₀=4 and S_n = (S_n-1)² &minus; 2. In 1930, the American mathematician [[Derrick ...th> is the element) must divide N-1. Now exhibit an element whose order is N-1 and we are done.
  20 KB (3,572 words) - 14:30, 17 February 2019
• Multiplication
  ...elf b times. The result of a multiplication is called the product of a and b, and each of the numbers is called a [[factor]] of the product ab. Multiplication is denoted a&times;b,(a)(b), or simply ab. The symbol '&times;' is known as the multiplication sign.
  2 KB (271 words) - 17:00, 29 August 2022
• Conjectures 'R Us
  For every base ({{Vb}} &le; 1030) for the forms {{Kbn|±|k|b|n}} there is a {{Vk}}-value for each form that has been conjectured to be t
  3 KB (503 words) - 04:44, 27 March 2024
• Rational number
  ...h> where <math>a</math> (the '''numerator''') is any [[integer]] and <math>b</math> (the '''denominator''') is an integer different from zero. The set o The notation <math>a/b</math> is called '''fraction'''. A fraction is irreducible when both number
  3 KB (541 words) - 15:01, 26 March 2023
• Repunit
  :<math>(b^n-1)\over (b-1)</math>.
  1 KB (207 words) - 08:04, 12 March 2024
• Modular arithmetic
  ...ers representing the hours 0, 1, 2, 3,..., 11 is known as <b>Z</b>/12<b>Z</b>. ...o numbers ''A'' and ''B'' are said to be congruent modulo ''n'' if ''A''-''B'' is a multiple of ''n''.
  4 KB (625 words) - 10:25, 23 January 2019
• Montgomery multiplication
  The Montgomery multiplication computes <math>c'\,=\,2^{-n}\,a'b'\bmod{m}</math>. Notice that <math>pq\,\equiv \, r</math> implies <math>p'q ...e perform the actual Montgomery multiplication <math>c' \,\equiv \,2^{-n}a'b'</math>.
  4 KB (582 words) - 17:01, 29 August 2022
• Elliptic curve method
  ...expression to <math>y^2\,\equiv \,x^3\,+\,ax\,+\,b</math> (where ''a'', ''b'', ''x'' and ''y'' are integers like 3 or -12, and the sign <math>\equiv</m which is an elliptic curve when <math>B\neq 0</math> and <math>A\neq \pm 2</math>.
  19 KB (3,181 words) - 22:27, 6 July 2023
• Mfakto
  %d - date (Mon nn) "%b %d" (strftime format)
  17 KB (2,524 words) - 12:39, 24 January 2019
• Lucas primality test
  ...es whether a number N is prime or not, using the complete factorization of N-1. ...up>(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
• Primality testing program
  | [[Mersenne number]]s<br/>a &times; bⁿ±c (only factoring and [[probable prime|PRP]]-testing) | k &times; bⁿ±c general numbers
  2 KB (314 words) - 21:23, 29 August 2019
• LLR
  **{{V|N}}-1 [[Pocklington algorithm]] for {{Kbn|+|k|b|n}} numbers. **{{V|N}}+1 [[Morrison algorithm]] for {{Kbn|k|b|n}} numbers.
  2 KB (300 words) - 22:00, 16 December 2023
• P-1 factorization method
  :<math>E = 2^{E_2} * 3^{E_3} * 5^{E_5} * ... * B</math> ...ath>2^{E_2}</math> is about B1 and the same for the other prime numbers. ''B'' is the greatest prime number less than or equal to B1.
  5 KB (814 words) - 01:35, 12 March 2019
• Self-initializing quadratic sieve
  ...t^2\equiv u\,\pmod N</math> where <math>t = ax+b</math> and <math>u = g_{a,b}(x)</math>. ...agraph does not depend on the particular values of <math>a</math> or <math>b</math>, so the factor base can be computed at the beginning of SIQS. The up
  10 KB (1,763 words) - 02:56, 12 March 2019

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