Proof of the Binary Goldbach Conjecture

In this article the proof of the binary Goldbach conjecture is established (Any integer greater than one is the mean arithmetic of two positive primes) . To this end the weak Chen conjecture is proved (Any even integer greater than One is the difference of two positive primes) and a " located " algorithm is developed for the construction of two recurrent sequences of primes ( and ( ), (( ) dependent of ( )) such that for each integer n their sum is equal to 2n . To form this a third sequence of primes ( ) is defined for any integer n by = Sup (p ∈ : p ≤ 2n - 3) , being the infinite set of positive primes. The Goldbach conjecture has been proved for all even integers 2n between 4 and 4. In the table of terms of Goldbach sequences given in Appendix 12 values of the order of 2n = are reached. An analogous proof by recurrence « finite ascent and descent method » is developed and a majorization of by 0.7 (2n) is justified.. In addition, the Lagrange-Lemoine-Levy conjecture and its generalization called ’’ Bezout-Goldbach ’’ conjecture are proven by the same type of algorithm.