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 ${\displaystyle >f_{\omega }(2{\uparrow }^{15}5)>f_{\omega }^2(15)}$ steps to halt. It was constructed by Racheline in 2024 by modifying the BB(3,4) champion.^[1] Due to the discoveries of Bigfoot in BB(3,3) and Hydra in BB(2,5), the existence of Cryptids in BB(3,5) is certain.

It is expected that an enumeration of BB(3,5) will leave about 11,300,000,000,000 holdouts.^[2]

References