On the non-reflective cases we at least see that we can forge small but very hard problems too. The most simple ones are the infinite loops testing some whole n

On the non-reflective cases we at least see that we can forge small but very hard problems too. The most simple ones are the infinite loops testing some whole number related property, like: Goldbach conjecture, Fermat's theorem. Now we know the program of the second case never halts but it was not an easy proof, the first one is still open.