Number Theory

    

A Recursive Deterministic Equation for Generating Prime Numbers in Exact Order

Authors: Uggala Guru Jaganath

This paper introduces Jagan’s Primes, a novel recursive modular equation for the deterministic generation of prime numbers in exact order. Unlike traditional sieve-based or probabilistic methods, this framework constructs primes through a self-referential arithmetic logic that isolates non-prime residues via modular shielding. The equation operates without primality testing, leveraging recursive congruence relations to build the prime sequence from first principles. The approach offers a new perspective on prime enumeration, demonstrating that primes can emerge as a consequence of structural recursion rather than exclusion. This work contributes to the foundations of computational number theory and opens pathways for algorithmic applications in cryptography, mathematical linguistics, and symbolic modeling.

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[v1] 2025-09-15 20:02:10

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