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 10⁸0 to 10³09, and 20 paired trials for Barreto-Naehrig pairing-friendly curve parameters at 10⁸0. Median speedups of 11. 44x at 10⁸0 and 8. 52x at 10¹00 over sequential odd-integer search. Empirical estimation of the twin-prime constant C₂ achieves 99. 9% accuracy at 10⁸0 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).