Primality Testing — A Deterministic Algorithm

  • S. Harari
Part of the International Centre for Mechanical Sciences book series (CISM, volume 279)


The most ancient and simple method for testing if a number is prime or not consists in factoring n. Using the fact that a non prime has a divisor r such that . We obtain a method usable for numbers up to 1016 on a computer. It necessitates operations, which is large when n is big. Remarkable improvements have been made. On a pocket calculator one can factor numbers up to 1018 and on a large computer up to 1040 with 0(n1/4) algorithms.


Prime Ideal Remarkable Improvement Deterministic Algorithm Primitive Root Riemann Hypothesis 


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  1. [1]
    Test de primalité d’après, Adleman, Rumely, Pomerance, Lenstra. H. Cohen. Université scientifique et medicale de Grenoble.Google Scholar
  2. [2]
    Lenstra, Tests de primalité, Seminaire Bourbaki, Juin 1981.Google Scholar
  3. [3]
    Rabin, Probabilistic algorithms for testing primality. J. Number theory 12 (1980) pp. 128–138.Google Scholar
  4. [4]
    Williams, Primality testing on a computer, Ars combina toria, 5(1978).Google Scholar

Copyright information

© Springer-Verlag Wien 1983

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  • S. Harari

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