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• 100 Million Digit Prefactor Project
  Uncwilly has resumed a leadership role in prefactoring numbers in this range. Many other users are now signed up to [[Lucas-Lehmer test|LL
  3 KB (534 words) - 10:06, 7 March 2019
• FermatSearch
  361 bytes (46 words) - 13:48, 29 January 2019
• Sieve of Eratosthenes
  The '''sieve of Eratosthenes''' is a method to find all [[prime]] numbers smaller than a given integer <math>N</math>. It's invention is credited to ...be divisible by <math>2</math>, we cross out every second number; all such numbers are composite.
  4 KB (657 words) - 01:17, 11 August 2024
• Aliquot sequence
  An '''aliquot sequence''' is a sequence of numbers generated from an initial number using the sigma <math>\sigma(n)</math> fun The naive way to find the divisors of a number are to check the numbers from 1 to <math>\sqrt{n}</math> to see if they divide the number. Easy to d
  6 KB (914 words) - 19:49, 21 February 2023
• Abundant number
  ==Abundant numbers and aliquot sequences== Abundant numbers increase the size of an [[aliquot sequence]] because when an abundant numbe
  674 bytes (92 words) - 00:58, 11 August 2024
• Prime
  ...greater than 1 that is only divisible by itself and 1. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19. ...er Q, larger than P, that is equal to the product of the consecutive whole numbers from 2 to P plus the number 1. In other words, Q = (2 x 3 x 4 x 5 ... x P)
  2 KB (447 words) - 00:22, 10 July 2023
• Nomenclature and notation
  Either [[Marin Mersenne]] or one of the special class of numbers that bear his name. ...omposite]] or [[prime]] of the form <math>2^{x}-1</math>. For one of these numbers to be prime, <math>x</math> (the exponent) must also be prime. Thus, the no
  3 KB (467 words) - 08:48, 15 May 2024
• Seventeen or Bust/Primes
  These are the [[prime|prime numbers]] found by the [[Seventeen or Bust]] project so far.
  2 KB (163 words) - 14:20, 7 March 2019
• Seventeen or Bust/Factoring
  The programs commonly used to P-1 factor these numbers are [[Prime95]] and [http://linux.redbird.com/~alien88/sbfactor12.zip SBFac
  3 KB (491 words) - 13:39, 1 February 2019
• Why participate in GIMPS?
  ...28=1+2+4+7+14). He realized that the even perfect numbers (no odd perfect numbers are known) are all closely related to the primes of the form 2^p- ...elementary number theory was developed while deciding how to handle large numbers, how to characterize their [[factor]]s and discover those which are prime.
  7 KB (1,253 words) - 07:15, 17 October 2024
• Sieving
  '''Sieving''' is an algorithm to discover [[smooth number]]s and [[prime]] numbers from a sequence of [[integer]]s much faster than [[trial factoring]], even The next step depends on whether we need to find prime number or smooth numbers.
  3 KB (521 words) - 11:14, 6 February 2019
• Sieving program
  *[[Gcwsieve]] (performing sieving of generalized Cullen/Woodall numbers n &times; bⁿ+-1) http://sites.google.com/site/geoffreywalterreyn *[[PPSieve]] (sieving for factors of numbers of the form K &times; 2ⁿ + 1 or - 1. Independent of K's, but goo
  2 KB (220 words) - 11:42, 7 March 2019
• NewPGen
  ...by Paul Jobling that is used to [[Sieving|sieve]] a set of many candidate numbers, of the following forms: ...t any k or n divisible by small primes. Since it works with a large set of numbers and uses fast implementations, it is a lot better than performing [[trial f
  3 KB (529 words) - 09:32, 7 March 2019
• Proth prime
  A '''Proth prime''' is not a true class of numbers, but primes in the form {{Kbn|+|k|n}} with 2^''n'' > ''k'' are of
  656 bytes (91 words) - 07:02, 31 August 2020
• Riesel Sieve
  ...nd primes for all the remaining k values to prove that they are not Riesel numbers.
  2 KB (326 words) - 10:29, 26 March 2024
• Introductory stuff
  *[[Elliptic curve method|ECM]] curves on Mersenne numbers and Fermat numbers ...basically the same as a standard primality test, but test the primality of numbers with more than 100 000 000 digits. These work units take a very long time t
  14 KB (2,370 words) - 15:15, 17 August 2019
• What use are prime numbers anyway?
  ==So it would seem to be a fair question "What use are prime numbers?"== ...e would not exist as we know it, and all of this security depends on prime numbers.
  3 KB (497 words) - 07:17, 22 May 2020
• Overclocking
  ...mark, which uses 19 iterations in the test, is set 1 Million digits. Lower numbers denote faster calculation times (seconds), and hence, better performance.
  14 KB (2,326 words) - 15:17, 11 February 2019
• Triangular number
  ...angular) after a number) represents the summing of a number with all whole numbers smaller than it.
  658 bytes (81 words) - 00:59, 11 August 2024
• Pocklington's theorem
  ...mada. It includes a program written in C language that proves primality of numbers of several thousand digits using this theorem.
  2 KB (347 words) - 01:15, 11 August 2024

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