Number Theory

    

The Complete Proof of the Goldbach Binary Conjecture

Authors: Denis Micheal Odwar

For m ∈ Z, let N = 2m ≥ 8 and GN be a set of goldbach primes, p, of N defined as GN = {p : p ≤ N 2 andp ∤ N}. By denoting the cardinality of GN by |GN| or g(N), we show that ∀N, |GN| > 0, and the set of all these cardinalities, {|GN|}, is equal to the set of natural numbers i.e {|GN|} = N = {1,2,3,4,5,6,···}. We finally prove the famous binary |GN| Goldbach conjecture by showing that for all values of |GN|, i=1 µ(bi)Λ(bi) < 0, whenever bi = N −pi with pi ∈ GN,i ∈ N and 1 ≤ i ≤ |GN|. In particular we show that every N is a sum of two distinct primes.

Comments: 8 Pages.

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Submission history

[v1] 2025-07-06 21:08:56
[v2] 2025-07-09 15:01:25
[v3] 2025-07-17 20:32:38

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