Every even number greater than 2 is the sum of two primes provided Riemann hypothesis holds

Abstract

We solve Goldbach's conjecture for all the evens greater than 2. This solution is based upon the proof of Sabihi's first and second conjectures (my own conjectures on Goldbach's one) and Riemann Hypothesis is supposed to be correct. Our essential method goes through compleax integral analysis. The first conjecture states that $L(N(k))-D(N(k))\geq K(N(k),m)\geq 2$ and $N(k)\geq 120$, but since the proof can be exhaustive for special case $N(k)=n$, we therefore prove it in such a case. The second conjecture states that $\log(N)=\frac{4e^{-\gamma}\prod_{p>2}(1-\frac{1}{(p-1)^2})\prod_{p>2~,p\mid N}\frac{p-1}{p-2}(1+O(\frac{1}{\log(N)}))}{\prod_{p>\sqrt{N}, gcd(p,N)=1}(1-\frac{1}{p-1})}\$ for every sufficiently large even integer $N$. In this paper and in order to present an exhaustive proof, we combine both methods applied in our previously published papers, one for when $n\geq 120$ and the other one for when $n$ is a sufficiently large even integer and prove both two Sabihi's conjectures . Then, it follows that Goldbach's conjecture is solved for all the even numbers greater than 120 to infinity and implies that it holds for all the even integers greater than 2.Comment: 47 pages.This paper solves completely strong Goldbach's conjecture. In this paper, we firstly prove both Sabihi's first and second conjectures stated in 1605.08273v1 and 1605.08938v2, then combining these two conjectures, we imply that Goldbach's conjecture is completely solve