The Quantum Mechanical Potential for the Prime Numbers

Abstract

A simple criterion is derived in order that a number sequence ${\mathcal{S}}_n$ is a permitted spectrum of a quantized system. The sequence of the prime numbers fulfils the criterion and the corresponding one-dimensional quantum potential is explicitly computed in a semi-classical approximation. The existence of such a potential implies that the primality testing can in principle be resolved by the sole use of physical laws.

9 pages, 3 figures

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