A Hypothesis on Upper Bound of Goldbach Counting Function

TL;DR

This paper introduces hypotheses on the upper bounds of the Goldbach counting function, providing proofs that imply the truth of the Goldbach and twin prime conjectures if these hypotheses hold.

Contribution

It proposes new upper bound hypotheses for the Goldbach counting function and demonstrates their implications for longstanding conjectures.

Findings

Proposes hypotheses on upper bounds of the Goldbach counting function.

Shows that Goldbach conjecture is true under these hypotheses.

Shows that twin prime conjecture is true under these hypotheses.

Abstract

I define Goldbach counting function with N > 0 and square-free P > 0. Decomposition of this function is discovered and deduction formula is found. I propose a hypothesis on upper bound of Goldbach counting function and prove that Goldbach conjecture is true under this hypothesis. Also, I propose a second hypothesis on upper bound of Goldbach counting function and prove that the twin prime conjecture is true under this hypothesis