Goldbach Conjecture and Integer Programming Madjid Zerafat Angiz Langroudi School of Mathematics, University Sains Malaysia(USM),Penang,Malaysia email: mzerafat24@yahoo.com & Islamic Azad University,Firoozkoh, Iran Gholamreza Jandaghi Faculty of Information Technology and Quantitative Sciences, UiTM, Malaysia, email: jandaghi@ftmsk.uitm.edu.my & Faculty of Management, Qom Campus, University of Tehran, Iran, email: Adli Ben Mustafa School of Mathematics, University Sains Malaysia(USM),Penang,Malaysia Abstract: making relation among different mathematics branches can expand the thought about solving a mathematical problem. The goldbach Conjecture is one of the mathematical problems which has not been proved since 1742. In this paper we will try to show that one is able to convert a theorem in number theory to a group of Integer Programming Problems that the proof of existence of their solutions is equivalent to the proof of the theorem. Key words: Goldbach Conjecture, Integer programming Math 2000 subject classifications: 90c10;90c90;11p32 Introduction Goldbach wrote in a letter to Euler(1742) that it seems that each integer number can be written in terms of the sum 3 prime numbers. This was then called the Goldbach Ternary Conjecture. In this conjecture, he assumed 1 as a prime number. Euler wrote to Goldbach, as a reply “I realize that the Conjecture is true but I am unable to prove it”. Another equivalent of the above conjecture is called the Strong Goldbach Conjeture which states that each even integer number can be written as sum of two integer numbers which are either 1 or odd prime numbers. Since then the process of solving this problem has moved very slowly. Even some scientific institutes have assigned great prices to attract mathematics scientists for solving the problem. In recent decades there has been considerable progress in this matter. Hardy and Littlwood(1923) the first basic step to prove the Conjecture. Vinogrdov(1937a) showed that each large enough odd integer number is a sum of 3 prime number and each large enough integer number is a sum of 4 prime numbers. Chen and Wang(1989) could lessen the number to 10 43000. Unfortunately, it can not be shown that the conjecture is true for