Some food for thought, perhaps

I was thinking about variations on Turing tests. Say you can communicate with some entity via a text chat, how would you determine the following:
- Is the entity a human or an alien from another planet?
or
- Is it a human from present day or a human from the past? from the future?
or
- Is it a human or is it some sort of entity with intelligence beyond that of humanity in present day?

All of these are really variations on a common theme: what question could a human ask without knowing the answer, but be able to verify a correct answer? (This sort of reminds me of Justice Potter Stewart’s “I know it when I see it”, but that’s unrelated) Carl Sagan suggests that a proof to Fermat’s Last Theorem would be an example of a good way to test a higher intelligence (though, according to what I’ve seen online, a proof was completed in 1996, but I’m not quite sure).