Weighted Stratified Sieve and Lattice Matrix Noise Constraints: Formal Verification of the Twin Prime Conjecture(with Lean 4 Formalization)

Abstract

This paper establishes a stratified weighted sieve framework based on lattice matrix noise identification, studying the asymptotic behavior of the twin prime counting function π2(X). By controlling the sieve remainder, an asymptotic main term estimate for the counting function is established, and the core logical chain is formalized using Lean 4. A numerical experiment scheme introduces GSA global sensitivity analysis to locate noise sources in high-dimensional space. The final conclusion proves that there are infinitely many twin primes. 本文建立基于格点矩阵噪声识别的分层加权筛框架,研究孪生素数计数 函数 π2(X) 的渐近行为。通过控制筛法余项,建立计数函数的渐近主项估 计,并借助 Lean4 完成核心逻辑链的形式化建模。数值实验方案引入 GSA 全局敏感性分析,定位高维空间中的噪声来源。最终证明孪生素数有无穷多 对。 附录(含 Lean 4 形式化验证源码)