Syntactic Primality Filtering via Coefficient Fingerprinting in Balanced Representations

Syntactic Primality Filtering via Coefficient Fingerprinting inBalanced Representations Abstract. We introduce a deterministic, division-free framework for composite exclusion thatoperates purely on digit-pattern syntax in balanced number systems. By mapping integer represen-tations to fixed-width coefficient fingerprints, the method identifies multiples of primes up to onemillion using minimal digit windows—often significantly narrower than theoretical limits imposedby multiplicative orders. Validated across all 78,498 primes in this range, the approach enablesdivision-free, modular-arithmetic-free screening at inference time—requiring no floating-point opera-tions, or probabilistic checks. It delivers ultra-low-latency, constant-time validation with minimalcomputational footprint, enabling high-throughput, low-power applications in cryptographic keyscreening (e.g., pre-sieving for RSA-2048/4096), in-storage structured computation, and hardware-native primality filtering. This work demonstrates a paradigm shift: from semantic (value-based) tosyntactic (structure-based) primality cues—where divisibility is decoded not by magnitude, but byform.