BB(2,5)
The 2-state, 5-symbol Busy Beaver problem BB(2,5) is unsolved. With the discovery of the Cryptid 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 is a Counter.