User blog comment:Wythagoras/My Turing machines/@comment-6768393-20131012123348/@comment-5150073-20131012225400

If we are able to prove that BB(23) > fω+1(n) for unreasonably large n, just picking one TM from viginitillions of candidates, then I shall not expect that BB(23) is actually close to it. BB(30) could be so large that almost all our notations will be not enough strong to bound it.