A proof of the strong twin prime conjecture

TL;DR

This paper presents a novel proof of the strong twin prime conjecture by developing a sliding model to estimate twin prime pairs and analyzing their distribution with respect to a new average measure, addressing prime dependence errors.

Contribution

The paper introduces a new sliding model for estimating twin prime pairs and establishes their distribution relations, providing a proof of the strong twin prime conjecture.

Findings

Proposes a sliding model to estimate twin prime pair counts.

Derives relations between twin prime counts and their averages.

Addresses errors from prime dependence in the analysis.

Abstract

For integers x and k, let T(x;2k) denote the number of twin prime pairs (p,p+2k) with a distance 2k<=2x**0.5 and p<=x (not p+2k<=x). Let Tg(x;2x**0.5) denote the average of T(x;2k) for all 2k<=2x**0.5. Logically, T(x;2k) should be a function of Tg(x;2x**0.5). We first, propose a sliding model to estimate Tg(x;2x**0.5). Second, derive the relations between T(x;2k) and Tg(x;2x**0.5) from the sieve structure. Third, settle the errors caused by the dependence of primes.