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      The Binary Goldbach Conjecture

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          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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          ScienceOpen Preprints
          17 May 2021
          [1 ] N. A.

          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.


          Structure in primes, Prime Number Theorem PNT, Primes in arithmetic progression, Representation of even numbers as a difference of two primes, Ternary Goldbach conjecture, Binary Goldbach conjecture, Goldbach conjecture


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