User blog comment:Wythagoras/My Turing machines/@comment-6768393-20131012123348/@comment-10429372-20131013120216

I think the largest exactly known value of BB(n) will be BB(6) or BB(7), since the whole decimal expansion of BB(8) will not fit in the Observable Universe.

LittlePeng9: I said might reach. I don't believe it too, but I'm quite sure that the ordinal describing dollar function is $$\Pi^1_n$$ indescribable.