No, it's the halting problem all the way down.
But if it's true that there doesn't exist a proof that it halts, then it will run forever searching for one.
Not remotely! There's no proof that it halts, and there's no proof that it doesn't halt. It will run until it halts or the universe ends - there is no forever. The key is that there can be programs for which nobody can tell which one they are without actually trying them until they halt or the universe ends.
The key is that there can be programs for which nobody can tell which one they are without actually trying them until they halt or the universe ends.
The halting problem doesn't actually imply this.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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