Spectral Periodicity in Prime Gaps and Riemann Zero Spacings

Abstract We report Fast Fourier Transform analysis of prime number gaps and Riemann zeta function zero spacings, revealing shared spectral periodicity near 0.356 cycles per index. This observed frequency shows 99.93% agreement with the theoretical prediction √5/(2π) ≈ 0.3559. Analysis of 254,832 prime gaps and 2,000 nontrivial Riemann zeros demonstrates convergence to this common spectral signature, suggesting an underlying harmonic structure connecting prime distribution to the Riemann Hypothesis. Authored and compiled by Michael K. Nowlin, this document is part of the open-access public release of FUNt (2025 edition), archived for independent and institutional review. 10.5281/zenodo.17298395