Structural and Predictive Limits of Prime Gaps

This project investigates whether prime gaps contain measurable structural invariants and whether apparent unpredictability in prime spacing reflects intrinsic randomness or incomplete constraint information. The study evaluates ordered prime gaps, discrete curvature, prediction scaling with divisibility depth, and forward interval collision geometry. All experiments were conducted using primes up to 2,000,000. The dataset contained 148,933 primes. The shock threshold T was defined as the 99.5 percentile of training gaps and equaled 58. Analyses were performed using contiguous ordered windows with a 70 percent training split and 30 percent testing split.