Decomposing Even Integers into Prime and Composite Parts

Let $n\ge 10$ 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.