Digit Gaps in Prime Series Products: A Number-Theoretic Analysis of Mod-6 Prime Classes

All primes greater than 3 belong to exactly one of two residue classes modulo 6: the 5-series (p ≡ 5 mod 6) or the 7-series (p ≡ 1 mod 6). We prove that cumulative products of primes from each series exhibit specific digit gaps — scales at which no product exists. At the 10^61 scale, gaps are staggered: the 5-series gaps at 60-61 digits, the 7-series at 62-63 digits. Both require factor 3 to fill. At the 10^80 scale, a striking phenomenon occurs: both series gap at the same location (80-81 digits). The 5-series still requires only factor 3, but the 7-series now requires factor 15 = 3 × 5 for numbers divisible by 15. This transition from staggered to coincident gaps, and from factor 3 to factor 15, represents a phase change in the multiplicative structure of prime products. Version 2.0 extends the analysis from 10^61 to 10^80, discovering the coincident gap phenomenon and the emergence of the mod 5 constraint.