In this article, we define a “ recursive local” algorithm in order to construct two reccurent numerical sequences of positive prime
numbers (𝑈2𝑛) and (𝑉2𝑛), ((𝑈2𝑛) function of (𝑉2𝑛)), such that for any integer n≥ 2, their sum is 2n. To build these , we use a third
sequence of prime numbers (𝑊2𝑛) defined for any integer n≥ 3 by : 𝑊2𝑛 = Sup(p∈IP : p ≤ 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 § 10, we reach values of the order of 2n= 101000
. Thus, thanks to this algorithm of “ascent and
descent”, we can validate the strong Euler-Goldbach conjecture.
Keywords. Prime numbers, Prime Number Theorem, weak and strong Goldbach’s conjectures, Dirichlet’s theorem, Bertrand-Tchebychev theorem