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
1RB2LB0RA2RA5RA1LB_2LA4RB3LB2RB0RB1RZ (bbch)	10 ↑↑ 54.90	Andrew Ducharme*
1RB3RB1LB5LA2LB1RZ_2LA3RA4RB2LB0LA4RB (bbch)	10 ↑↑ 42.17	Andrew Ducharme*
1RB3LB0RB5RA1LB1RZ_2LB3LA4RA0RB0RA2LB (bbch)	10 ↑↑ 40.07	Andrew Ducharme*
1RB3LB3RB4LA2LA4LA_2LA2RB1LB0RA5RA1RZ (bbch)	10 ↑↑ 21.54	Andrew Ducharme*
1RB0RA3RB0LB1RA2LA_2LA4LB1RA3LB5LB1RZ (bbch)	10 ↑↑ 17.53	Andrew Ducharme*
1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ (bbch)	10 ↑↑ 17.53	Andrew Ducharme*
1RB3RA4LA1LA0LA1RZ_2LA0LB1RA1LB5LB2RA (bbch)	10 ↑↑ 15.49	Andrew Ducharme*

All decimal places are truncated. Discoverers are asterisked where it is unclear if the TM had been found but unreported by someone previously (namely Shawn Ligocki).