Number Theory

    

Restrictions to Goldbach’s Conjecture Using Bertrand’s Postulate, Initiation to a Proof

Authors: Anass Massoudi

The Goldbach conjecture, also named the binary Goldbach’s conjecture, proposed by the Russian mathematician Christian Goldbach in 1742, states that for every even integer n bigger than 2, there is always two primes a and b such that n = a + b, and until now this conjecture remained unproven, in this paper, we use what’s known as Bertrand’s postulate to restrict the conditions for the two primes a and b that verify this conjecture for every even number n = 2p, namely proving the interesting fact that the Goldbach statement is valid if and only if we have p < a < 2p – 2 and b < p, leading to a clue to prove this conjecture in a simpler manner than attack it brutally without any knowledge about the properties of a and b and the inequality that we will prove, making at last an initiation for a proof of the Goldbach statement .

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[v1] 2021-09-21 21:28:29

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