Logical Methods pp 130-142

# Prime Isols and the Theorems of Fermat and Wilson

• J. Barback
Chapter
Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 12)

## Abstract

Let pr denote the principal function of the set of prime numbers, and let prΛ. denote its extension to the isols of A. Nerode. Because pr is an increasing recursive function, then prΛ will map regressive isols into regressive isols. It is a well-known property that if A is a regressive isol, then prΛ(A) is a prime isol. In our paper we study these primes and show that there are very general analogues in the isols to both Fermat’s Theorem and Wilson’s Theorem.

## Keywords

Prime Number Infinite Series Recursive Function Principal Function Positive Isol
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