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Symbolic Primality Certification via Modular Irreducibility: The AMIT Framework

12 April 2025, Version 1
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

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.

Keywords

Symbolic primality
Modular irreducibility
Abdeslam Modular Irreducibility Theorem (AMIT)
Reduced residue system
Primality certification
Prime generation
Cryptography
Symbolic number theory
Non-probabilistic primality
Abdeslam Prime Equation (APE)

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