The Axiom of Independence Preservation: A Unified Framework for Prime Number Conjectures

This paper proposes a new foundational axiom - the Axiom of Independence Preservation which captures a fundamental truth about prime numbers: their essential independence. Wedemonstrate that this single axiom, once accepted, provides a unified framework from whichseveral major unsolved conjectures in number theory follow as natural corollaries. Theseinclude the Riemann Hypothesis, the Twin Prime Conjecture, and Goldbach's Conjecture.Rather than requiring individual proofs, these conjectures dissolve into consequences ofaccepting the axiomatic nature of prime independence.