Strongest Goldbach conjecture

The Goldbach's conjecture has been described as the most difficult problem in the history of Mathematics. This conjecture states that every even integer greater than 2 can be written as the sum of two primes. On the other hand, P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? We will define as the strongest Goldbach conjecture when every even integer greater than 6 can be written as the sum of two different primes. We prove if P = NP, then the strongest Goldbach conjecture is false.