Per my comment above, Busy Beaver will pass that pretty quickly too, as again, a Busy Beaver contestant will rather early on simulate that entire problem (and BB has ready access to numbers like a mere googol). As large as that number is, I'd guess it's probably under BB(30), and certainly under BB(100) as I'd bet even a mere human could write a 100-state TM to simply simulate that answer.
Why? Perhaps I misunderstand something, but why can't I define a turing machine and the upper bound, and then BB with first order set theory. It is therefore my misunderstanding, that this gives me a lower bound of
BB( googol -n),
whith n the number of symbols I need to define BB.
