User blog comment:Swooped me in one hit/froggillion/@comment-29310326-20170214212823/@comment-30754445-20170214222733

As for your number...

gg64 is considered a naive extension of Graham's Number. Why a "naive extension"? Because the Graham function does most of the work, and you simply applied it twice.

The "apply it twice" trick is not that bad, actually. That's how we get from a googol (10^100) to the much larger googolplex (10^10^100). It is just that the Graham function is much more powerful.

When people here talk about numbers which are "much greater than Graham's Number", they mean that those numbers are qualitively different. Say, a number like {3,3,3,3} (Bowers' Tetratri) is far beyond anything you could dream up with variations on g. To reach those heights you can either borrow a stronger notation (which really doesn't help you, because then your numbers will be a naive extention of that notation) or create one yourself.