Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers.
Wikipedia: Goldbach's conjecture
We are looking for a optimized way to computing very fast and in a liner speed not in exponential speed, the most biggest even number that culculated with Super Computers is 4×1018. Maybe you think that How can we prove Goldbach conjecture with programming?, So I must say that we dont want to prove it, We are looking for a Counterexample so that's why We insist on speeding up the algorithm.