User blog comment:B1mb0w/The S Function Version 2/@comment-5529393-20160628040514/@comment-10262436-20160628042744

I can add this detail and proofs.

BTW, I have just submitted my candidate for one of the largest named numbers to date.

Last Alpha Number (defined as) alpha(d) where d is a number very close to 10,000 and

alpha(d) = S(2,T^{10,000}(0),1)

Appreciate your thoughts on this if you have a moment.