Symbolic Primality Certification via Modular Irreducibility: The AMIT Framework

We introduce a symbolic and deterministic method for primality certification based on modular irreducibility conditions over reduced residue systems. This framework, called the Abdeslam Modular Irreducibility Theorem (AMIT), enables the identification of prime numbers without relying on trial division or probabilistic tests. By analyzing structured numerical candidates through a layered system of modular filters, AMIT certifies primality using purely symbolic, non-factor-based logic. The method supports fast, lightweight prime generation and is well-suited for cryptographic applications, hardware-level filtering, and symbolic mathematical systems.