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Further investigations
with the strong probable prime test


Author: Ronald Joseph Burthe Jr.
Journal: Math. Comp. 65 (1996), 373-381
MSC (1991): Primary 11Y11; Secondary 11A51
DOI: https://doi.org/10.1090/S0025-5718-96-00695-3
MathSciNet review: 1325864
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Abstract | References | Similar Articles | Additional Information

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


References [Enhancements On Off] (What's this?)

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Additional Information

Ronald Joseph Burthe Jr.
Email: ronnie@alpha.math.uga.edu

DOI: https://doi.org/10.1090/S0025-5718-96-00695-3
Received by editor(s): May 3, 1994
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society