Journal of Advances in Mathematics and Computer Science

An Example of the Application of Provability Logic to Unsolved Problems in Number Theory: The Cullen Numbers and Conway’s Supposition

Alexander Bolotin *

Open University of Israel, Beersheba, Israel

*Author to whom correspondence should be addressed.

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Abstract

This short paper offers an example of possibly fruitful interactions between modal logic and number theory. In the paper, Conway's remark that p and p.2^p + 1  can both be prime numbers is formulated as a formula of modal logic and then analyzed for its decidability.

Keywords: Modal logic, provability logic, Fermat’s last theorem, Cullen numbers, Conway's remark, decidability

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