Submit progress

on The sixth Busy Beaver number

The statement

A Turing machine is a mathematical model of computation consisting of a finite set of states, a finite tape alphabet, a transition function, and a designated start state. A machine is halting if it eventually reaches a halting configuration. For a halting machine, the halting number is the total number of steps (or tape shifts) taken before halting. For each positive integer $n$ , the Busy Beaver number $BB(n)$ is defined as the maximum halting number among all halting Turing machines with exactly $n$ states and exactly $2$ tape symbols, when started on an initially blank tape. It is known that $BB(1) = 1$ , $BB(2) = 6$ , $BB(3) = 21$ , $BB(4) = 107$ , and $BB(5) = 47176870$ . Determine the exact value of $BB(6)$ .

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.