Author(s)

Jie Hou

HQ Building Design Inc., Oshawa, Canada.

Let $2m>2$ , $m\in \mathbb{Z}$ , be the given even number of the Strong Goldbach Conjecture Problem. Then, m can be called the median of the problem. So, all Goldbach partitions $\left(p,q\right)$ exist a relationship, $p=m-d$ and $q=m+d$ , where $p\le q$ and d is the distance from m to either p or q. Now we denote the finite feasible solutions of the problem as $S\left(2m\right)=\left\{\left(2,2m-2\right),\left(3,2m-3\right),\cdot \cdot \cdot ,\left(m,m\right)\right\}$ . If we utilize the Eratosthenes sieve principle to efface those false objects from set $S\left(2m\right)$ in $p_i$ stages, where $p_i\in P$ , $p_i\le \sqrt{2m}$ , then all optimal solutions should be found. The Strong Goldbach Conjecture is true since we proved that at least one optimal solution must exist to the problem. The Weak Goldbach Conjecture is true since it is a special case of the Strong Goldbach Conjecture. Therefore, the Goldbach Conjecture is true.

Median, The Feasible Goldbach Partitions, The Optimal Goldbach Partitions, Congruences, Effacement

Hou, J. (2024) The Goldbach Conjecture Is True. Open Journal of Discrete Mathematics, 14, 29-41. doi: 10.4236/ojdm.2024.143004.