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
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch)	10 ↑↑ 193
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE (bbch)	10 ↑↑ 188
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188
1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA (bbch)	10 ↑↑ 188
1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ (bbch)	10 ↑↑ 117
1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG (bbch)	10 ↑↑ 116.05
1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch)	10 ↑↑ 114.60
1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 113
1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG (bbch)	10 ↑↑ 93.81
1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ (bbch)	10 ↑↑ 93.78
1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0RA (bbch) 1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0LE (bbch)	10 ↑↑ 63
1RB0RE_1LC0RB_1LD0RC_1LE0LF_1RA0LD_1LD1LG_1LF1RZ (bbch)	10 ↑↑ 55
1RB0RG_0RC0RF_1LD0RA_0LE0LA_1RA0LC_0LG1LC_1RE1RZ (bbch)	10 ↑↑ 51
1RB1RZ_1RC0RG_0RD1RB_0LE0RB_0LF0RA_1LB1RF_1RE1LD (bbch)	10 ↑↑ 50
1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC (bbch)	10 ↑↑ 46
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	1,056,253	TBD	TBD
02xxxx	@Iijil	Yes	No	963,486	TBD	TBD
03xxxx	@Iijil	Yes	No	1,052,504	TBD	TBD
04xxxx	@Iijil	Yes	No	955,711	TBD	TBD
13xxxx	Shawn Ligocki	Yes	Yes	1,192,442	1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch)	10 ↑↑ 114.60	Google Drive folder
20xxxx	@C7X	Yes	No	TBD	TBD	TBD	Google Drive folder
243308	@uni	Yes	No	TBE	1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)	$2\uparrow ^{11}2\uparrow ^{11}3$	Discord post
25xxxx	@stokastic	Yes	No	1,056,591	TBD	TBD	Google Drive folder
26xxxx	@stokastic	Yes	No	958,289	TBD	TBD	Google Drive folder
27xxxx	@stokastic	Yes	No	1,052,946	TBD	TBD	Google Drive folder
28xxxx	@stokastic	Yes	No	956,935	TBD	TBD	Google Drive folder
29xxxx	@stokastic	Yes	No	1,052,415	TBD	TBD	Google Drive folder
30xxxx	@stokastic	Yes	No	1,032,095	TBD	TBD	Google Drive folder
31xxxx	@stokastic	Yes	No	1,436,970	TBD	TBD	Google Drive folder
32xxxx	@stokastic	Yes	No	1,036,950	TBD	TBD	Google Drive folder
33xxxx	@stokastic	No	No	TBD	TBD	TBD	Google Drive folder
34xxxx	@stokastic	No	No	TBD	TBD	TBD	Google Drive folder
43xxxx	Andrew Ducharme	Yes	Yes	817,332	1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG (bbch)	10 ↑↑ 93	Google Drive folder
44xxxx		No	No	TBD	TBD	TBD
49xxxx	Tobiáš Brichta	No	No	TBD	TBD	TBD	Google Drive folder
500xxx	@prurq	Yes	No	TBD	TBD	TBD	Google Drive folder
69xxxx	@poppuncher	Yes	No	TBD	1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch)	10 ↑↑ 133	Google Drive folder
700xxx - 701xxx	@hipparcos	Yes	Yes	160,792	1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA (bbch)	10 ↑↑ 26	Posted to Discord
80xxxx	@xnoobspeakable	Yes	No	964,396	TBD	TBD	Google Drive folder
85xxxx	Terry Ligocki	Yes	No	1,050,753	TBD	TBD	Google Drive folder
86xxxx	Terry Ligocki	Yes	No	952,102	TBD	TBD
87xxxx	Terry Ligocki	Yes	Yes	813,349	1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ (bbch)	10 ↑↑ 117
88xxxx	Terry Ligocki	Yes	Yes	727,990	1RB0RE_1LC0RB_1LD0RC_1LE0LF_1RA0LD_1LD1LG_1LF1RZ (bbch)	10 ↑↑ 55
89xxxx	Terry Ligocki	Yes	Yes	804,470	1RB1LD_1LC1RE_0RA0LB_1LA0LE_1RC0RF_0RC1RG_1RZ0RB (bbch)	10 ↑↑ 32
9xxxxx	Terry Ligocki	Yes	Yes	9,516,852	1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch) 1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch) 1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch) 1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 286 10 ↑↑ 193 10 ↑↑ 188 10 ↑↑ 113