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!)

Start with even integers greater than or equal to 6.

Also, the solution to the problem is more philosophical in nature than logical.  I.e., it doesn't answer anything.