BB(2,5)

The 2-state, 5-symbol Busy Beaver problem BB(2,5) is unsolved. With the discovery of the Cryptid machine Hydra by Daniel Yuan in April 2024, we now know that we must solve a Collatz-like problem in order to solve BB(2,5) and thus BB(2,5) is Hard.

The current BB(2,5) champion is 1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch), also discovered by Daniel Yuan in June 2024. It is notable for being the only champion machine that exhibits Counter behavior. It provides the lower bound:

$$S(2,5)>\Sigma (2,5)>10^{10^{10^{3\,314\,360}}}>10\uparrow \uparrow 4$$