Structural Number Theory: Research on Prime Number Rules and Unified Proofs of Several Number-Theoretic Conjectures -- An Original Theory and Complete Demonstration Based on Structural Covering (Part 2: Proofs of Schinzel's Hypothesis H and Related Classical Conjectures)

Abstract

This paper is the second installment of the series "Structural Number Theory: Research on Prime Rules and Unified Proofs of Several Number-Theoretic Conjectures--Original Theory and Complete Demonstration Based on Structural Covering".As an application of structural covering theory to the prime distribution problem of polynomials, this paper continues to construct a one-to-one correspondence between numbers and sets, establishes a dual-operation structural covering based on multiplicative operation structures and the polynomial structure of Schinzel's Hypothesis H, and completes the proof by contradiction.The core objective is to prove that Schinzel's Hypothesis H holds. Based on this result, many classical polynomial prime conjectures in number theory can be derived as its corollaries.