Prime Numbers as Structural Phenomena – A Two-Layer Model for Their Emergence and Detection

This paper introduces a new structural theory of prime numbers, proposing a two-layer model that explains the emergence and recognition of primes based on principles of structural independence. The concept of “light value” (as structural freedom) and “coding freedom” (as modular resonance) are introduced as foundational mechanisms. Prime numbers are interpreted as emergent phenomena that arise precisely where these two dimensions of freedom converge. The theory matches all classical primes up to 100,000 with 100% accuracy and offers a new algorithmic and philosophical understanding of primality. This preprint version documents the full conceptual and computational framework.