In this article, we define a โ recursive localโ algorithm in order to construct two reccurent numerical sequences of positive prime
numbers (๐2๐) and (๐2๐), ((๐2๐) function of (๐2๐)), such that for any integer nโฅ 2, their sum is 2n. To build these , we use a third
sequence of prime numbers (๐2๐) defined for any integer nโฅ 3 by : ๐2๐ = Sup(pโIP : p โค 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 ยง 10, we reach values of the order of 2n= 101000
. Thus, thanks to this algorithm of โascent and
descentโ, we can validate the strong Euler-Goldbach conjecture.