A Deterministic Interference Wave Model for Prime Prediction

A deterministic interference wave model for prime prediction is presented. The method is based on the observation that all primes greater than 3 lie on two arithmetic progressions: 6n-1 and 6n+1, collectively referred to as the Crown. Within this Crown, every integer is treated as a wave emitter. Waves propagate forward with a period proportional to the source, creating a deterministic interference field. A number is identified as prime if and only if the total wave density at its coordinate is exactly zero (Φ = 0). This stands in contrast to the Sieve of Eratosthenes, which requires explicit marking of multiples, and to division-based primality tests, which are reactive. The proposed Predictive Sonar Algorithm is proactive: it projects future wave impacts and reads primality directly from the absence of scheduled events. Empirical validation up to 1.1×10^9 confirms that the model achieves 100% accuracy with zero false positives. The implementation is concise, fully deterministic, and does not rely on probabilistic assumptions. The distribution of primes is shown to follow a harmonic law governed by wave interference, resonance nodes, and zero-density corridors.