2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/27926A 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.9 pages, 3 figuresCondensed MatterQuantum Physicstext