Further investigations with the strong probable prime test

Author:

Burthe Ronald

Abstract

Recently, Damgård, Landrock and Pomerance described a procedure in which a k k -bit odd number is chosen at random and subjected to t t random strong probable prime tests. If the chosen number passes all t t tests, then the procedure will return that number; otherwise, another k k -bit odd integer is selected and then tested. The procedure ends when a number that passes all t t tests is found. Let p k , t p_{k,t} denote the probability that such a number is composite. The authors above have shown that p k , t 4 t p_{k,t}\le 4^{-t} when k 51 k\ge 51 and t 1 t\ge 1 . In this paper we will show that this is in fact valid for all k 2 k\ge 2 and t 1 t\ge 1 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference5 articles.

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