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Proof of the Binary Goldbach Conjecture
Version 1
: Received: 15 October 2024 / Approved: 16 October 2024 / Online: 16 October 2024 (11:45:13 CEST)
How to cite: SAINTY, P. Proof of the Binary Goldbach Conjecture. Preprints 2024, 2024101262. https://doi.org/10.20944/preprints202410.1262.v1 SAINTY, P. Proof of the Binary Goldbach Conjecture. Preprints 2024, 2024101262. https://doi.org/10.20944/preprints202410.1262.v1
Abstract
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.
Keywords
Prime numbers; Prime Number Theorem; binary Goldbach conjecture; Lagrange-Lemoine-Levy conjecture; Bezout-Goldbach conjecture; gaps between consecutive primes
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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