Resonance-Based Detection of Prime Numbers Using Riemann Zeta Zeros

Prime numbers occupy a fundamental place in number theory. Their distribution is deeply connected with the analytic properties of the Riemann zeta function.In analytic number theory, the non-trivial zeros of the zeta function generate oscillatory components in the explicit formulas governing the distribution of primes. Motivated by this spectralviewpoint, I construct a resonance amplitude assigned to each integer n. This amplitude aggregatesoscillatory modes determined by the imaginary parts of the zeta zeros.The resulting quantity provides a spectral indicator which tends to produce larger values forprimes than for composite integers.