BB(3,5)

The 3-state, 5-symbol Busy Beaver problem, BB(3,5), is unsolved and largely unexplored.

The current BB(3,5) champion is 1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC (bbch), which takes over $>f_{\omega }(2{\uparrow }^{15}5)>f_{\omega }^2(15)$ steps to halt. It was dicovered by Racheline in 2024.