[elijaht]

“Probably doesn’t halt” is ill defined, it either halts or it doesn’t. In either case, computability of that number is completely separate from whether we can prove that number is BB(N) or decide whether a given beaver halts. Additionally, the way the busy beaver function is defined ensures it has a defined integer output. Computability is just our ability to construct a machine which would print out that number. We can clearly do that for any integer