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.