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!)

Is it logically possible that it is both true and also impossible to prove that all even integers can be expressed as the sum of two odd primes?

I say, "yes".

Is my restatement of the question accurate?