The Recursive Exclusion Framework for Prime Prediction: A Complete, Non- Probabilistic Model of Prime Distribution

We present a novel deterministic algorithm that precisely predicts the distribution of prime numbers using a recursive exclusion model grounded in base-10 modular residues and diagonal lattice structures. This method provides a complete prime sieve without trial division, probability, or zeta function dependency. By filtering numerical space through structured congruence and recursive elimination of composite residues from ( p^2 ) onward for all primes ( p ), we establish a predictive mechanism that holds across extensive numerical ranges. Empirical validation confirms zero false positives and false negatives up to 30,000, with the structure generalizable to larger domains. This discovery resolves the ancient problem of prime localization by geometric and arithmetic constraints alone.