Prime Resonance in Natural Systems: A Number-Theoretic Analysis of Observed Frequencies

We present empirical evidence for prime number clustering in pulsar frequencies and derive this phenomenon from first principles using standard quantum mechanics.

The analysis reveals an unexpected isomorphism between quantum eigenmodes and prime numbers, with testable predictions for resonant systems across multiple scales.

1 Empirical Observations Recent analysis of pulsar frequency data reveals statistically significant clustering around prime number ratios.

Specifically: • Millisecond pulsars show frequency peaks at 2, 3, 5, 7, 11, 13 Hz (after normalization). • Binary pulsar orbital resonances favor prime number ratios (2:3, 3:5, 5:7). • Similar prime clustering appears in atomic transition frequencies when properly scaled.