Verifying Sierpiński and Riesel Numbers in ACL2

John R. Cowles
(University of Wyoming)
Ruben Gamboa
(University of Wyoming)

A Sierpinski number is an odd positive integer, k, such that no positive integer of the form k * 2^n + 1 is prime. Similar to a Sierpinski number, a Riesel number is an odd positive integer, k, such that no positive integer of the form k * 2^n + 1 is prime. A cover for such a k is a finite list of positive integers such that each integer j of the appropriate form has a factor, d, in the cover, with 1 < d < j. Given a k and its cover, ACL2 is used to systematically verify that each integer of the given form has a non-trivial factor in the cover.

In David Hardin and Julien Schmaltz: Proceedings 10th International Workshop on the ACL2 Theorem Prover and its Applications (ACL2 2011), Austin, Texas, USA, November 3-4, 2011, Electronic Proceedings in Theoretical Computer Science 70, pp. 20–27.
Published: 20th October 2011.

ArXived at: http://dx.doi.org/10.4204/EPTCS.70.2 bibtex PDF
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