Suppose I told you that the Goldbach conjecture is one of those. (The Goldbach conjecture supposes that every even integer number can be expressed as the sum of two odd primes.)

Is that logically possible? (And, no, I haven't proved it!)

Ken is right.  The posted solution is completely illogical. 

To infer "the computer will not find a solution" from "the computer has not found a solution yet" is akin to solving the halting problem, which is impossible for any Turing machine to do.