Proof of the Binary Goldbach Conjecture

In this paper, a "local" algorithm is determined for the construction of two recurrent sequences of positive 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 ) , where is the infinite set of 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 10 , values of the order of 2n = are reached. This " finite ascent and descent " method proves the binary Goldbach conjecture ; an analogous proof by recurrence is established and an increase in by 0.7( is justified. Moreover, the Lagrange-Lemoine-Levy conjecture and its generalization, the Bezout-Goldbach conjecture, are proven by the same type of procedure.