On the Elementary Solution of Goldbach's Binary Conjecture

In this paper, we present a solution to a famous open problem of number theory - Goldbach’s binary conjecture. The proof of Goldbach’s binary conjecture is elementary and based on a combinatorial covering argument. We show that the proof of Goldbach’s binary conjecture is reduced to the proof of a conjecture on the covering for the set of natural numbers except 1 by means of the set of sums of pairs of natural numbers, each of which corresponds to a prime or twin primes. We construct a Generating set 𝕂 of integers and prove a Covering lemma, which shows that the set 𝕂 is an additive basis of order 2 for the set of natural numbers ℕ except 1. The proof of this lemma proceeds by contradiction, using Bertrand's Postulate (the Bertrand–Chebyshev theorem) to rule out the existence of a counterexample. From this lemma, Goldbach’s binary conjecture follows directly. The approach does not rely on analytic methods or heavy machinery.