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!)

It's the principle, not that actual example.

I believe he means that some statements have an infinite number of solutions - and because it's infinite it cannot definitely be proved even though it is obviously true.