User blog comment:Wythagoras/My Turing machines/@comment-6768393-20131012123348/@comment-5529393-20131013123637

LittlePeng9 & Wythagoras: I'm a little perplexed as to why you are talking as if we can only know values of numbers whose decimal expansions will fit within the observable universe. I'm quite certain that BB(7) is much too big for that, as we know that S(6) > 10^36000, so BB(7) should be much larger than that. So if by "known" you mean that we can compute the decimal "expansion", than yes, we can never know BB(n) for n > 6. But I find that a strange definition for a googologist to take! I would imagine that for any Turing machine we could find a set of recursive equations that described the halting time (or number of 1's), so the Busy Beaver number would be "known" in that sense.