It would not surprise me at all for bb7 to exceed Graham's number. Just a Kirby-Paris hydra or a Goodstein sequence gets you to epsilon zero in the fast-growing hierarchy, where Graham is around omega+2.
It would not surprise me at all for bb7 to exceed Graham's number. Just a Kirby-Paris hydra or a Goodstein sequence gets you to epsilon zero in the fast-growing hierarchy, where Graham is around omega+2.
The 79-bit lambda term λ1(λλ2(λλ3(λ312))(1(λ1)))(λλ1)(λλ211)1 in de-Bruijn notation exhibits f_ε0 growth without all the complexities of computing Kirby-Paris hydra or Goodstein sequences. Even that is over 60% larger than the 49-bit Graham exceeder (λ11)(λ1(1(λλ12(λλ2(21))))). I think one should be quite surprised if you can climb from f_4 (2↑↑2↑↑2↑↑9) to f_{ω+1} (Graham) with just 1 additional state.