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About the strong EULER-GOLDBACH conjecture
  • PHILIPPE SAINTY
PHILIPPE SAINTY
university

Corresponding Author:[email protected]

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Abstract

Abstract. In this article, we define a β€œ recursive local” algorithm in order to construct two reccurent numerical sequences of positive prime  numbers (π‘ˆ2𝑛) and (𝑉2𝑛), ((π‘ˆ2𝑛) function of (𝑉2𝑛)), such that for any integer nβ‰₯ 2, their sum is 2n. To build these , we use a third  sequence of prime numbers (π‘Š2𝑛) defined for any integer nβ‰₯ 3 by : π‘Š2𝑛 = 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 Β§ 10, we reach values of the order of 2n= 101000 . Thus, thanks to this algorithm of β€œascent and  descent”, we can validate the strong Euler-Goldbach conjecture.