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• Lucas-Lehmer test
  ...>, or <math>S_{p-2}\,= \,0\,\pmod Q</math>. Since the left-hand side is an integer, this means therefore that <math>S_{p-2}</math> must be divisible by <math> ...h>\omega^d=1</math>. We claim that if <math>n</math> is any other positive integer satisfying <math>\omega^n=1</math>, then <math>n</math> must be a multiple
  20 KB (3,572 words) - 14:30, 17 February 2019
• Trial factoring
  ...nd P(6542) = 65521, the largest prime fitting into an unsigned sixteen bit integer. ...must escalate to multiple-digit arithmetic. If your CPU supports unsigned integer arithmetic of 32 bits, the straightforward implementations of long multipli
  7 KB (1,221 words) - 13:20, 11 February 2019
• Square root
  Square roots of positive [[integer]]s are often ''[[irrational number]]s'', i.e., numbers not expressible as a ...ot after finitely many steps. It can thus be used to check whether a given integer is a [[square number]].
  13 KB (1,873 words) - 16:52, 24 October 2020
• Floating-point unit
  ...architectures, there is some division of floating-point operations from [[integer]] operations. This division varies significantly by architecture; some, lik ...cution, floating-point operations were sometimes pipelined separately from integer operations. Since the early and mid-1990s, many microprocessors for desktop
  2 KB (323 words) - 06:49, 1 May 2019
• Quadratic residue
  ...atic residue''' [[modular arithmetic|modulo]] {{V|p}} if there exists an [[integer]] {{V|x}} such that:
  823 bytes (117 words) - 20:11, 26 October 2020
• Modular square root
  ...umber <math>a</math> modulo an integer <math>m</math> greater than 1 is an integer such that:
  5 KB (726 words) - 10:38, 6 February 2019
• Legendre symbol
  If <math>p</math> is an odd [[prime]] number and <math>a</math> is an [[integer]], then the Legendre symbol ...arithmetic|modulo]] <math>p</math> &mdash; that is to say there exists an integer <math>k</math> such that <math>k^2 \equiv a \pmod{p}</math>, or in other wo
  2 KB (348 words) - 18:57, 28 September 2023
• Self-initializing quadratic sieve
  ...ng the logarithms in base 2 of the different primes rounded to the nearest integer, storing these values in the arrays <math>\operatorname{tsqrt}</math> and < ...xity of the quadratic sieve is O(exp(sqrt(log n log log n))) where n is an integer. The constant ''e'' is usually used as the base of the logarithm.
  10 KB (1,763 words) - 02:56, 12 March 2019
• Sieving
  ...to discover [[smooth number]]s and [[prime]] numbers from a sequence of [[integer]]s much faster than [[trial factoring]], even when trial factoring runs qui
  3 KB (521 words) - 11:14, 6 February 2019
• Multiple polynomial quadratic sieve
  ...ng the logarithms in base 2 of the different primes rounded to the nearest integer, storing these values in the arrays <math>\operatorname{tsqrt}</math> and <
  6 KB (1,068 words) - 14:33, 13 February 2019
• Square number
  ...some other integer. (In other words, a number whose [[square root]] is an integer.) So for example, 9 is a square number since it can be written as 3 &times;
  3 KB (408 words) - 13:56, 19 February 2019
• Aurifeuillian factor
  ...n(b)</math>, where <math>b = s^2 \cdot t</math> with [[Square-free integer|square-free]] <math>t</math>, have aurifeuillean factorization if and only if one of th :Thus, when <math>b = s^2\cdot t</math> with square-free <math>t</math>, and <math>n</math> is [[Congruence relation|congruent]] to
  10 KB (1,257 words) - 08:04, 24 June 2019
• Carol-Kynea prime
  .... If {{Vn}} is negative then <math>(b^n±1)^2</math> is not necessarily an integer. *{{Vb}} may be a perfect power of another integer. However these form a subset of another base’s primes (ex. Base 4 Carol/K
  8 KB (1,172 words) - 00:38, 6 July 2023