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)	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

Current Progress

This is a summary of the 1 million subtasks from mxdys's code that have been processed, including further processing by Shawn Ligocki's linear rule code ("TBD" = "To Be Determined", "TBE" = "To Be Entered"):

Task range	Done by	Completed		# holdouts	Maximum Score TM	~Sigma	Source
		enumeration	linear rule
00xxxx	@Iijil	Yes	Yes	728495	1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC (bbch)	10 ↑↑ 46	Google Drive folder
01xxxx	@Iijil	Yes	No	1056253	TBD	TBD
02xxxx	@Iijil	Yes	No	963486	TBD	TBD
03xxxx	@Iijil	Yes	No	1052504	TBD	TBD
04xxxx	@Iijil	Yes	No	955711	TBD	TBD
13xxxx	Shawn Ligocki	No	No	TBD	TBD	TBD	TBE
138xxx	Shawn Ligocki	Yes	Yes	129930	1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC (bbch)	10 ↑↑ 35
139xxx	Shawn Ligocki	Yes	No	155407	TBD	TBD
243308	@uni	Yes	No	TBE	1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)	$2\uparrow ^{11}2\uparrow ^{11}3$	Discord post
25xxxx	@stokastic	No	No	TBD	TBD	TBD	Google Drive folder
43xxxx	Andrew Ducharme	No	No	TBD	1RB0RF_1RC0LF_0LC1RD_1LE1LG_0RB1LA_1RE1LD_1RZ0LF (bbch)	10 ↑↑ 24	TBE
500xxx	@prurq	Yes	No	TBD	TBD	TBD	Google Drive folder
700000-701999	@hipparcos	Yes	Yes	160792	1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA (bbch)	10 ↑↑ 26	Posted to Discord
90xxxx	Terry Ligocki	Yes	No	1025733	TBD	TBD	Google Drive folder
91xxxx	Terry Ligocki	Yes	No	1437031	TBD	TBD
92xxxx	Terry Ligocki	Yes	No	1037736	TBD	TBD
93xxxx	Terry Ligocki	Yes	No	1436093	TBD	TBD
94xxxx	Terry Ligocki	Yes	No	1040565	TBD	TBD
95xxxx	Terry Ligocki	Yes	No	1434203	TBD	TBD
96xxxx	Terry Ligocki	Yes	No	1036863	TBD	TBD
97xxxx	Terry Ligocki	Yes	Yes	1436051	1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 113
98xxxx	Terry Ligocki	Yes	Yes	797084	1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188
99xxxx	Terry Ligocki	Yes	Yes	1105427	1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch)	10 ↑↑ 286