Based on, the well-ordering (N; <) of the set of natural numbers N, and some basic concepts of number theory, and using the proof by contradiction and the inductive proof on N, we prove that the validity of the Goldbachs statement: every even integer 2n 4, with n 2, is the sum of two primes. This result con\u85rms the Goldbach conjecture, which allow to inserting it as theorem in number theory. Key Words: Well-ordering (N; <), basic concepts and theorems on number theory, the indirect and inductive proofs on natural numbers. AMS 2010: 11AXX, 11p32, 11B37. 1 A brief history and some results on the con-jecture Historically, from the reference , the conjecture dating since 1742 in a letter addressed to Euler from Goldbach expresses the following fact
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