Systematic Correspondence between the Self-Generated Frequency Spectrum of a Modulo-30 Statistical Sieve and the Imaginary Parts of Non-Trivial Zeros of the Riemann ζ Function

This paper reports a mathematical discovery that can be independently and inexpensively reproduced: a modulo-30 statistical sieve based on elemen- tary number theory spontaneously generates a prime proportion frequency spectrum Pk that corresponds systematically and precisely to the imagi- nary parts γn of the non-trivial zeros of the Riemann ζ function across multiple scales. Reference values are taken from Odlyzko’s publicly available tables. At N = 10⁶, the pointwise error can be as low as 0. 00345 (for the 7th zero). A waveform synthesized from these frequencies predicts prime locations with 59. 5% accuracy at x ≤ 1000 (p = 0. 005, still significant after Bonferroni correction), and the predictive power decays with x in exact agree- ment with the amplitude factor x1/2/ ln x in Riemann’s explicit formula. The phenomenon is independently replicated at N = 10⁷. The entire experiment can be reproduced on a standard laptop in approximately 2 hours. All source code, raw data, and a detailed reproduction guide are publicly available at Zenodo under the CC BY 4. 0 license. Based on the numerical evidence, I propose two core conjectures and discuss their possible connections with the Riemann hypothesis.