Recursive Prime Prediction Theorem

This paper introduces the Recursive Prime Prediction Theorem, a novel recursive process that generates the entire set of prime numbers in order, without sieving, probabilistic methods, or external primality tests. Starting from the base case T₀ = 1, each subsequent term is defined as the smallest number greater than the previous term not divisible by any earlier output. The transformation inherently produces all primes and only primes, revealing that prime distribution is not random but arises from recursive constraint and convergence.

The theorem is formally defined and proven, with computational validation up to 400,000. The paper identifies “gates”—periods of recursive tension corresponding to large prime gaps—and connects them to known anomalies in the prime sequence. This work reframes primes as emergent stability points within a recursive field architecture, suggesting a deterministic and structurally necessary origin of primes. It lays foundational ground for further exploration of recursion-based number theory and geometric interpretations of prime emergence.