In this article, we define a β recursive localβ algorithm in order to construct two reccurent numerical sequences of positive prime
numbers (π2π) and (π2π), ((π2π) function of (π2π)), such that for any integer nβ₯ 2, their sum is 2n. To build these , we use a third
sequence of prime numbers (π2π) defined for any integer nβ₯ 3 by : π2π = Sup(pβIP : p β€ 2n-3), where IP is the infinite set of positive
prime numbers. The Goldbach conjecture has been verified for all even integers 2n between 4 and 4.1018.
. In the Table of Goldbach
sequence terms given in paragraph Β§ 10, we reach values of the order of 2n= 101000
. Thus, thanks to this algorithm of βascent and
descentβ, we can validate the strong Euler-Goldbach conjecture.