BB(7)

The 7-state, 2-symbol Busy Beaver problem BB(7) is a mostly unexplored domain with only preliminary information.

The current BB(7) champion is 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) discovered by Pavel Kropitz in 2025 proving the lower bound:

$$S(7)>\Sigma (7)>2\uparrow ^{11}2\uparrow ^{11}3$$

History

Before 2025, the only known BB(7) champions were produced by hand, not by search. Example, Milton Green designed a machine in 1964 that had sigma score 22,961 and Wythagoras modified a BB(6) champion in 2014 to produce a machine that had sigma score $>10\uparrow \uparrow 5$.

In May 2025, mxdys shared C++ code that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.

Top Halters

Based on limited search through a subset of the 1 million subtasks from mxdys's code some of the top known halting machines are:

TM	approximate sigma score
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)	$2\uparrow ^{11}2\uparrow ^{11}3$
1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch)	10 ↑↑ 286
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch) 1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA (bbch)	10 ↑↑ 188
1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 113
1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ (bbch)	10 ↑↑ 93
1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ (bbch)	10 ↑↑ 93
1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0RA (bbch) 1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0LE (bbch)	10 ↑↑ 63
1RB0RG_0RC0RF_1LD0RA_0LE0LA_1RA0LC_0LG1LC_1RE1RZ (bbch)	10 ↑↑ 51
1RB1RZ_1RC0RG_0RD1RB_0LE0RB_0LF0RA_1LB1RF_1RE1LD (bbch)	10 ↑↑ 50
1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC (bbch)	10 ↑↑ 35