We present the first experimental evidence that prime-ratio frequency networks outperform composite-ratio networks in a physical resonator. Using a 12-cell torsion ring constructed from SLG47004V GreenPAK chips and LM324 op-amps, connected by twin copper torsion traces on a PCB, we injected six simultaneous square-wave frequencies at various divisor ratios of a common fundamental f0 = 1024 Hz and measured the combined network response. In controlled comparisons on the same board with identical probes and instrumentation, prime-ratio divisors 1, 3, 5, 7, 11, 13 produced +28% higher peak spectral amplitude, +22% greater inter-channel coherence, and 48% fewer intermodulation products than composite-ratio divisors 4, 6, 8, 9, 10, 12. Progressive addition of prime frequencies yielded monotonic superlinear amplitude growth from 320 mV to 1160 mV over six channels. A systematic investigation of 15 distinct frequency sets revealed a Four-Factor hierarchy governing network response: (1) structural resonance with number-theoretic building blocks, (2) anchor frequency inclusion, (3) pairwise coprimality of the divisor set, and (4) factor depth. The Tusk-resonant set 1, 2, 3, 5, 6, 7 exceeded pure primes by 24% on spectral structure, while Riemann zeta zero frequency ratios achieved 85–90% of prime coupling power with superior spectral uniformity. All integer divisors of f0 produced identical peak-to-peak voltage (1140 mV) regardless of number-theoretic classification, establishing that coprimality governs spectral quality rather than coupling power. These results constitute the first physical demonstration that the fundamental theorem of arithmetic has measurable engineering consequences in analog resonator networks.
Adrian *Tusk Sutton (Thu,) studied this question.