Modular Prime Generation Through Geometric Resonance: The MRPG-30 Framework

We present a systematic approach to prime generation through modular resonance patterns and geometric constraints. The Modular-Resonance Prime Generation framework (MRPG-30) combines structured modular arithmetic with square-trigger exclusions to generate prime sequences with high accuracy across extended ranges. The method employs a three-stage process: harmonic constraint identification, angular pattern application, and composite exclusion at prime squares. Comprehensive validation across four test windows spanning 10,000 to 5,200,000 demonstrates consistent performance,with the framework achieving complete accuracy in identifying prime sequences within tested ranges. The approach integrates classical number-theoretic insights with geometric pattern recognition, providing both theoretical foundation and practical implementation for systematic prime generation.