Number Theory

    

The Unified Midpoint Density Theorem A Structural Proof of the Infinitude of Twin Prime Pairs

Authors: Quency Nixon

This paper presents a deterministic, structural proof of the Twin Prime Conjecture, moving beyond traditional probabilistic models. We introduce the "Midpoint Generator" (Mn = Pn/2), a geometric center of gravity that necessitates the existence of Twin Prime pairs at every scale of the number line. We define the "Recursive Binary Descent," an algorithm that mechanically links candidate pairs at infinite scales to verified Twin Primes in a finite "Safe Haven." Finally, using a Proof by Contradiction, we demonstrate that the assumption of a finite number of Twin Prime pairs creates a structural paradox, thereby proving that the set of TwinPrime pairs must be infinite.

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[v1] 2025-11-24 01:49:22

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