Accelerated Sampling of Prime Constellations via Admissible Residue Conditioning: Computational Experiments at Cryptographic Scales

We report large-scale computational experiments on the sampling efficiency of prime constellations and polynomial prime families when candidates are restricted to admissible residue classes modulo a finite set of small primes. Using a C++/GMP implementation with 25-round Miller-Rabin testing, we conduct 100 paired trials for prime triplets {0,2,6} across four digit scales from 10^80 to 10^309, and 20 paired trials for Barreto-Naehrig pairing-friendly curve parameters at 10^80. Median speedups of 11.44x at 10^80 and 8.52x at 10^100 over sequential odd-integer search. Empirical estimation of the twin-prime constant C_2 achieves 99.9% accuracy at 10^80 across 2,000 trials. The polynomial extension to BN254 curve parameter search yields a consistent 2.03x median speedup over an optimized Rust implementation. Files include the manuscript (PDF + LaTeX source) and supplementary data (100 paired speedup ratios, 8,000 safe prime gap measurements).