Prime Number Harmonics Predict the Helical Periodicities of DNA and Protein α-Helices

Hello,I investigate a mathematical relationship between the spectral properties of prime number distributions and the geometric periodicities of biological helical structures. By constructing a scalar field Ω(x, q) as a weighted superposition of cosine waves with frequencies determined by modular inverses of prime numbers, we observe that dominant Fourier peaks emerge at wavelengths closely matching known biological structures. For modulus q = 7, we find a harmonic at λ = 3.504 (error 2.68% vs. the canonical α-helix pitch of 3.6 residues/turn). For q = 21, a harmonic appears at λ = 10.511 (error 0.10% vs. B-form DNA’s 10.5 bases/turn). These wavelengths arise from exact arithmetic: λ = q/k where k = p−1 mod q for specific primes p. Notably, the prime p = 11 generates both biological periodicities through its modular inverse 11−1 ≡ 2 in q ∈ {7, 21}. We perform a systematic survey of moduli q ∈ [3, 30] and calculate the statistical significance of these correspondences (p < 0.01). While our results demonstrate a striking numerical correlation, we emphasize that causality remains unestablished. We discuss potential physical mechanisms and propose experimental tests to determine whether this correspondence reflects fundamental biophysical principles or numerical coincidenceCordialy