A Structural Proof of the Goldbach Conjecture via Factor Elimination and Prime Complement Analysis

We present a constructive and structural proof of the Goldbach Conjecture, which asserts that every even integer greater than two is the sum of two primes. Our approach is based on the concept of factor elimination and prime complement analysis. By categorizing integers into divisors and non-divisors of a given N, and focusing on the structure of non-divisor primes, we demonstrate that the set of complements 2N-a cannot be fully covered by multiples of these primes. Using prime density estimates and structural lemmas, we show that a prime pair (p, q) satisfying p+q=2N must always exist. Numerical examples further validate the framework, providing an intuitive and elementary alternative to heavy analytic methods traditionally used in this domain