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, the top 20 scoring known machines are:

TM	Approximate sigma score	Discoverer
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)	$2\uparrow ^{11}2\uparrow ^{11}3$	Pavel Kropitz
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch)	10 ↑↑ 519.20	Andrew Ducharme
1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch)	10 ↑↑ 286.17	Terry Ligocki
1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch)	10 ↑↑ 246.32	@Iijil
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188.28	Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ0RE (bbch)	10 ↑↑ 188.28	Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LF0RF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188.28	Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA (bbch)	10 ↑↑ 188.28	Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA (bbch)	10 ↑↑ 188.28	@XnoobSpeakable, @Peacemaker II
1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch)	10 ↑↑ 133.85	@poppuncher
1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF (bbch)	10 ↑↑ 129.24	@Iijil
1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ (bbch)	10 ↑↑ 116.97	Terry Ligocki
1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG (bbch)	10 ↑↑ 116.05
1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch)	10 ↑↑ 115.52	@prurq
1RB0RF_1RC0RB_0RD0RF_1LE0LG_1LC0RD_1LA0LD_1LF1RZ (bbch)	10 ↑↑ 114.61	Andrew Ducharme
1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch)	10 ↑↑ 114.60	Shawn Ligocki
1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ (bbch)	10 ↑↑ 114.57	Andrew Ducharme
1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 113.37	Terry Ligocki

The top 20 known halters with unique scores are:

TM	Approximate sigma score	Discoverer
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)	$2\uparrow ^{11}2\uparrow ^{11}3$	Pavel Kropitz
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch)	10 ↑↑ 519.20	Andrew Ducharme
1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch)	10 ↑↑ 286.17	Terry Ligocki
1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch)	10 ↑↑ 246.32	@Iijil
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188.28	Terry Ligocki
1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch)	10 ↑↑ 133.85	@poppuncher
1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF (bbch)	10 ↑↑ 129.24	@Iijil
1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ (bbch)	10 ↑↑ 116.97	Terry Ligocki
1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG (bbch)	10 ↑↑ 116.05
1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch)	10 ↑↑ 115.52	@prurq
1RB0RF_1RC0RB_0RD0RF_1LE0LG_1LC0RD_1LA0LD_1LF1RZ (bbch)	10 ↑↑ 114.61	Andrew Ducharme
1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch)	10 ↑↑ 114.60	Shawn Ligocki
1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ (bbch)	10 ↑↑ 114.57	Andrew Ducharme
1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 113.37	Terry Ligocki
1RB1RZ_1RC1RA_1RD0RB_1LE0RC_1LF0LD_1RG0LF_1RC0LG (bbch)	10 ↑↑ 108.77	Terry Ligocki
1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG (bbch)	10 ↑↑ 93.81	Andrew Ducharme
1RB0RF_1LC0LD_1RC0LB_1LE1RG_1RA1RE_1RD0RD_0RA1RZ (bbch)	10 ↑↑ 93.78	Terry Ligocki
1RB1LB_1LC1RE_1RD1RC_0RE0RD_1LF0RB_1LF1LG_1RZ0LA (bbch)	10 ↑↑ 86.40	Terry Ligocki
1RB1LC_1RC0LG_1RD0RG_0LE0RA_1LC0LF_0LD1LF_1RZ1RA (bbch)	10 ↑↑ 82.44	Terry Ligocki

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	728,495	1RB0RF_1RC1LF_0RD0RD_1LE0LB_1RA1RZ_1LG1RA_1LD0RC (bbch)	10 ↑↑ 45.64	Google Drive folder
01xxxx	@Iijil	Yes	Yes	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
05xxxx	@Iijil	Yes	No	TBD	TBD	TBD
06xxxx	@Iijil	Yes	No	TBD	TBD	TBD
07xxxx	@Iijil	Yes	No	TBD	TBD	TBD
08xxxx	@Iijil	Yes	No	TBD	TBD	TBD
09xxxx	@Iijil	Yes	No	TBD	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 - 21xxxx	@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	1RB1RZ_1LC0LE_0LD0LC_0RE1LB_1RF0RG_0LD1RB_1RD1RA (bbch)	10 ↑↑ 31.33	Google Drive folder
26xxxx	@stokastic	Yes	No	958,289	1RB1RZ_0LC1RB_0LE0LD_1LE1LD_0RF0LC_0RG1RF_1RD0RA (bbch)	10 ↑↑ 36.26
27xxxx	@stokastic	Yes	No	1,052,946	1RB0RG_1LC1LB_0RE0LD_0LC1RF_0RA1RE_0LF0LB_1RF1RZ (bbch)	10 ↑↑ 63.56
28xxxx	@stokastic	Yes	No	956,935	TBD	TBD
29xxxx	@stokastic	Yes	No	1,052,415	TBD	TBD
30xxxx	@stokastic	Yes	No	1,032,095	TBD	TBD
31xxxx	@stokastic	Yes	No	1,436,970	TBD	TBD
32xxxx	@stokastic	Yes	No	1,036,950	TBD	TBD
33xxxx	@stokastic	Yes	No	1,432,081	TBD	TBD
34xxxx	@stokastic	Yes	No	1,032,970	TBD	TBD
35xxxx	Terry Ligocki	Yes	No	1,437,841	TBD	TBD	Google Drive folder
36xxxx		Yes	Yes	798,364	1RB1LD_0LC1LE_1RD1LB_1RD0RA_1LB0RF_0RG1RE_1RZ0RA (bbch)	10 ↑↑ 26.82
37xxxx		Yes	Yes	1,098,681	1RB0LA_1RC0LB_1RD0RF_1LE0RC_1LA0LD_1RC1RG_1RF1RZ (bbch)	10 ↑↑ 108.77
38xxxx		Yes	Yes	801,308	1RB1RZ_1RC1RA_1RD0RB_1LE0RC_1LF0LD_1RG0LF_1RC0LG (bbch)	10 ↑↑ 108.77
39xxxx		Yes	Yes	1,093,938	1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ (bbch)	10 ↑↑ 192.67
40xxxx	Andrew Ducharme	Yes	Yes	730,310	1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch)	10 ↑↑ 519.20	Google Drive folder
41xxxx		No	No	TBD	TBD	TBD
42xxxx		No	No	TBD	TBD	TBD
43xxxx		Yes	Yes	817,332	1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG (bbch)	10 ↑↑ 93.81
44xxxx		Yes	Yes	729,686	1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF (bbch)	10 ↑↑ 76.36
45xxxx		Yes	Yes	812,973	1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ (bbch)	10 ↑↑ 114.57
49xxxx	Tobiáš Brichta	No	No	TBD	TBD	TBD	Google Drive folder
500xxx	@prurq	Yes	No	TBD	TBD	TBD	Google Drive folder
60xxxx	@gerbil5709	Yes	No	TBD	TBD	TBD	Google Drive folder
61xxxx		No	No	TBD	TBD	TBD
62xxxx		No	No	TBD	TBD	TBD
69xxxx	@poppuncher	Yes	No	TBD	1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch)	10 ↑↑ 133.85	Google Drive folder
70xxxx	@hipparcos	Yes	Yes	798,304	1RB0LF_1RC1LE_0RD1RA_1RE1RG_0LA1LB_1LE1RG_0RC1RZ (bbch) 1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA (bbch)	10 ↑↑ 33.81 10 ↑↑ 26.63	Github release
75xxxx	Terry Ligocki	Yes	Yes	1,103,089	1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188.28	Google Drive folder
80xxxx	@xnoobspeakable	Yes	No	964,396	TBD	TBD	Google Drive folder
81xxxx	@xnoobspeakable	No	No	TBD	TBD	TBD
85xxxx - 9xxxxx	Terry Ligocki	Yes	Yes	13,396,923	1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch)	10 ↑↑ 286.17	Google Drive folder