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      The Binary Goldbach Conjecture

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            Abstract

            The Goldbach conjecture, one of the oldest problems in mathematics, has fascinated and inspired many mathematicians for ages. In 1742 a German mathematician Christian Goldbach, in a letter addressed to Leonhard Euler proposed a conjecture. The modern day version of the Binary/Strong Goldbach conjecture asserts that:

            Every even integer greater than 2 can be written as the sum of two primes.

            The conjecture had been empirically verified up to 4× 10 18​​​​​, its proof however remains elusive, which seems to confirm that:

            Some problems in mathematics remain buried deep in the catacombs of slow progress ... mind stretching mysteries await to be discovered beyond the boundaries of former thought. Avery Carr (2013)

            The research was aimed at exposition, of the intricate structure of the fabric of the Goldbach Conjecture problem. The research methodogy explores a number of topics, before the definite proof of the Goldbach Conjecture can be presented. The Ternary Goldbach Conjecture Corollary follows the proof of the Binary Goldbach Conjecture as well as the Representation of even numbers by the difference of two primes Corollary.

            The research demonstrates that the Goldbach Conjecture is a genuine arithmetical question.

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            Content

            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            17 May 2021
            Affiliations
            [1 ] N. A.
            Article
            10.14293/S2199-1006.1.SOR-.PPIU46T.v1
            b5d1b931-b7c5-4486-a98f-75166af23b3b

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .


            The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
            Mathematics
            Goldbach conjecture,Binary Goldbach conjecture,Ternary Goldbach conjecture,Representation of even numbers as a difference of two primes,Primes in arithmetic progression,Prime Number Theorem PNT,Structure in primes

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