TITLE: Is it possible that "A counter-example exists but it cannot be found"
QUESTION [57 upvotes]: Then otherwise the sentence  "It is not possible for someone to find a counter-example"  would be a proof.
I mean, are there some hypotheses that are false but the counter-example is somewhere we cannot find even if we have super computers.
Sorry, if this is a silly question. 
Thanks a lot.

REPLY [3 votes]: Here is a very simple wrong hypothesis for which providing a counter-example is impossible:

Every natural number has been said (written, provided, imagined) by someone.

You can't show me a counter-example, but you can prove that there are a bit more numbers than we have ever imagined.