BB(2,6)

The 2-state, 6-symbol Busy Beaver problem, BB(2,6), is unsolved. With cryptids like Hydra in the preceding domain BB(2,5), we know that we must solve a Collatz-like problem in order to solve BB(2,6).

The current BB(2,6) champion 1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch) was discovered by Pavel Kropitz in May 2023, proving the lower bound:

$$S(2,6)>\Sigma (2,6)>10\uparrow \uparrow 10\uparrow \uparrow 10^{10^{115}}>10\uparrow \uparrow \uparrow 3$$

Top Halters

The highest known scoring machines are:

TM	Approximate sigma score	Discoverer
1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch)	10 ↑↑↑ 3	Pavel Kropitz
1RB3LA4LB0RB1RA3LA_2LA2RA4LA1RA5RB1RZ (bbch)	10 ↑↑ 91	Pavel Kropitz
1RB2LA1RA4LA5RA0LB_1LA3RA2RB1RZ3RB4LA (bbch)	10 ↑↑ 70	Shawn Ligocki
1RB2LA1RZ5LB5LA4LB_1LA4RB3RB5LB1LB4RA (bbch)	1.9 × 10^4933	Terry and Shawn Ligocki
1RB1LB3RA4LA2LA4LB_2LA2RB3LB1LA5RA1RZ (bbch)	6.9 × 10^4931	Terry and Shawn Ligocki