2604.01178 The Prime Gap Distribution Anomaly: Unexpected Oscillations in the Variance of Prime Gaps Modulo Small Primes
We report a previously unobserved arithmetic phenomenon in the distribution of prime gaps modulo small primes. Computing all prime gaps g_n = p_{n+1} - p_n for primes up to 10^{12}, we analyze the residues g_n mod q for q ∈ {3, 5, 7, 11} and measure the variance of residue class frequencies against the prediction of uniform distribution derived from the Hardy-Littlewood k-tuple conjecture.