Decomposing Even Integers into Prime and Composite Parts

Abstract

Let n ≥ 10 be an even integer. It is proved that there exists a prime number p and a composite number c such that n = p + c . The proof is constructed using elementary number theory, incorporating inductive reasoning, deterministic candidate filtering, and contradiction-based exclusion. This result provides a structural decomposition of even integers as prime-Composite sums, without reliance on probabilistic or analytic methods.