The Spectral Law of Prime Numbers

A Complete Evolution from Quantum Hamiltonian to 100% Accurate Prime Generation A quantum‑mechanical Hamiltonian with delta‑potentials at prime positions is introduced as a theoretical motivation. Its eigenvalues correlate with the Riemann zeros with \(R^2 > 0.9999\) on a holdout set, providing numerical evidence consistent with the Hilbert–Pólya conjecture without claiming a proof. We present two complementary algorithms: Code 1 (deterministic) locates prime clusters via spectral levels for reproducible research; Code 2 (randomized) implements Riemann's explicit formula for cryptographic applications. Both achieve 100% accuracy with mean generation times of 16.97 ms (1024-bit) and 284 ms (2048-bit), significantly outperforming conventional methods.