Hmm. This is interesting. I take it that the definition is very precise. By that we don't mean the smallest number after which there is no way to define any larger number in 60 letters. We literally mean some oddball number that is "indescribable." It is probably prime or nearly prime and isn't close to any numbers with a compressible factorization.

But we just described it with the negative statement. This is kind of like Reyo's number but lacks the restriction to "first-order set theory."

What you are going to end up with is the set of all numbers that cannot be described in less then 60 characters, each of which cannot be the answer. So it ends up oscillating between the first two members of the set.

Sounds like U.S. political parties.