The Quantum Mechanical Potential for the Prime Numbers

G. Mussardo

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arXiv · cond-mat/9712010

The Quantum Mechanical Potential for the Prime Numbers

G. Mussardo

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Abstract

A simple criterion is derived in order that a number sequence ${\cal S}_n$ 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.

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G. Mussardo. 1997-12-01. The Quantum Mechanical Potential for the Prime Numbers. https://arxiv.org/abs/cond-mat/9712010

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