An approach towards the proof of the strong Goldbach's conjecture for sufficiently large even integers

TL;DR

This paper presents a new approach to prove the strong Goldbach's conjecture for large even integers using complex analysis, sieve functions, and assuming the Riemann Hypothesis, claiming to demonstrate every large even integer as a sum of two primes.

Contribution

It introduces a novel sieve-based function and combines complex analysis with existing theorems to prove the conjecture for large even integers under the Riemann Hypothesis.

Findings

Proves the strong Goldbach's conjecture for sufficiently large even integers

Develops a new sieve function on natural numbers

Utilizes complex analysis and existing theorems to support the proof

Abstract

We approach a new proof of the strong Goldbach's conjecture for sufficiently large even integers by applying the Dirichlet's series. Using the Perron formula and the Residue Theorem in complex variable integration, one could show that any large even integer is demonstrated as a sum of two primes. In this paper,the Riemann Hypothesis is assumed to be true in throughout the paper. A novel function is defined on the natural numbers set.This function is a typical sieve function.Then based on this function,several new functions are represented and using the Prime Number Theorem,Sabihi's theorem, and the Sabihi's second conjecture,the strong Goldbach's conjecture is proved for sufficiently large even integers.