Looking for Fibonacci Base-2 Pseudoprimes

Document Type

Article

Department or Administrative Unit

Mathematics

Publication Date

11-2012

Abstract

In this paper, we examine computationally the results of combining two well-known, simple, and imperfect tests for primality: the Fermat base-2 test, and the Fibonacci test. Although considerable attention has been paid to various properties of composite integers which pass the base-2 test (base-2 pseudoprimes), no comparable study of Fibonacci and base-2 Fibonacci tests exists in the literature. Our study tabulates various empirical properties of these numbers. Among other things, we conclude that there are no base-2 Fibonacci pseudoprimes less than 1015 which are congruent to 2 or 3 (modulo 5).

Comments

This article was originally published in Missouri Journal of Mathematical Sciences. The full-text article from the publisher can be found here.

Due to copyright restrictions, this article is not available for free download from ScholarWorks @ CWU.

Journal

Missouri Journal of Mathematical Sciences

Copyright

Copyright © 2012 Central Missouri State University, Department of Mathematics and Computer Science

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