Twin Prime Residue Classes Modulo 2310: Completing the Primorial Hierarchy

We analyze the distribution of 3,424,506 twin prime pairs below 10⁹ modulo the primorial 2310 = 2·3·5·7·11. Among the φ(2310)=480 residue classes coprime to 2310, exactly 135 classes admit twin prime pairs, forming a natural hierarchical structure: 15 families × 9 subclasses. The observed frequencies are nearly identical, with a chi-square statistic χ² = 54.05 (df = 134), far below the critical value at the 5% level. All observed deviations lie within expected statistical fluctuations, with maximum deviation 2.04σ and relative errors below 1.2%. This work provides strong experimental evidence supporting the Hardy--Littlewood equidistribution prediction across the primorial hierarchy 6, 30, 210, 2310.