Resonance-Based Detection of Prime Numbers Using Riemann Zeta Zeros: A Rigorous Study

Prime numbers occupy a fundamental role in number theory. Traditionalmethods for their identification rely on divisibility tests. A complementaryapproach leverages spectral properties of the Riemann zeta function ζ(s),whose non-trivial zeros encode deep information about the distribution ofprimes. In this study, I associate each integer n with a resonance amplitudeRn that reflects its primality. Properly constructed, this resonance functionproduces distinct peaks for primes, whereas composites yield lower amplitudes. This allows the detection of primes without explicit factorization.