Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
MathSciNet review: 1325864
Full-text PDF Free Access

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?)


Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 11Y11, 11A51

Retrieve articles in all journals with MSC (1991): 11Y11, 11A51


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00695-3
PII: S 0025-5718(96)00695-3
Received by editor(s): May 3, 1994
Article copyright: © Copyright 1996 American Mathematical Society