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Volume 877 of the series Lecture Notes in Computer Science pp 116
Date:
On the difficulty of finding reliable witnesses
 W. R. AlfordAffiliated withDepartment of Mathematics, The University of Georgia
 , Andrew GranvilleAffiliated withDepartment of Mathematics, The University of Georgia
 , Carl PomeranceAffiliated withDepartment of Mathematics, The University of Georgia
Abstract
For an odd composite number n, let w(n) denote the least witness for n; that is, the least positive number w for which n is not a strong pseudoprime to the base w. It is widely conjectured, but not proved, that w(n) > 3 for infinitely many n. We show the stronger result that w(n) > (log n)^{1/(3 log log log n)} for infinitely many n. We also show that there are finite sets of odd composites which do not have a reliable witness, namely a common witness for all of the numbers in the set.
 Title
 On the difficulty of finding reliable witnesses
 Book Title
 Algorithmic Number Theory
 Book Subtitle
 First International Symposium, ANTSI Ithaca, NY, USA, May 6–9, 1994 Proceedings
 Pages
 pp 116
 Copyright
 1994
 DOI
 10.1007/3540586911_36
 Print ISBN
 9783540586913
 Online ISBN
 9783540490449
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 877
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 W. R. Alford ^{(1)}
 Andrew Granville ^{(1)}
 Carl Pomerance ^{(1)}
 Author Affiliations

 1. Department of Mathematics, The University of Georgia, 30602, Athens, GA, USA
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