User blog comment:Swooped me in one hit/Franks number/@comment-29310326-20170213171620/@comment-30754445-20170213173326

As written, it isn't well defined. Saying that number of factorials "exceeds" a given number does not tell us how many factorials there are.

If we ignore the "exceeds" then it is a well-defined number, very close to FF(65 octillion). Note that using the Library of Babel thing doesn't have any noticable effect on the number's size. You could replace it by a "10" or even a "2" and it won't change the final estimate by any considerable amount. Either way, the number of factorials will be a power tower of 65 octillion 10's (give or take a handful).

At any rate, an octillion is 1 followed by 27 zeros, so "65 octillion" is 6.5x1028. So the final number is about 10↑↑10↑↑(6.5x1028). That's higher than a tria-taxis (10↑↑↑3 = G3) and lower than a tetra-taxis (10↑↑↑4 = G4). In Letter notation it can be approximated as G3.335.