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
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	@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
1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch)	10 ↑↑ 114.60	Shawn Ligocki
1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 113.37	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

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
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	@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
1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch)	10 ↑↑ 114.60	Shawn Ligocki
1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 113.37	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
1RB1LC_1RC0RC_1RD1LA_0RE1RF_1LC0LG_1LA1LE_1RZ1LF (bbch)	10 ↑↑ 76.36	Andrew Ducharme
1RB0LD_1RC0RF_0RD1RA_1LE0RB_0LA0LB_1RA1RG_0RA1RZ (bbch)	10 ↑↑ 64.03	Terry Ligocki
1RB1RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_1RG1RZ_0LG0LE (bbch)	10 ↑↑ 63.56	Terry Ligocki
1RB0LD_1RC0RF_0RD1RA_1LE0RB_0LA0LB_1RA1RG_1LE1RZ (bbch)	10 ↑↑ 61.02	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 ↑↑ 46	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	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	Yes	No	1,432,081	TBD	TBD	Google Drive folder
34xxxx	@stokastic	Yes	No	1,032,970	TBD	TBD	Google Drive folder
35xxxx - 38xxxx	Terry Ligocki	No	No	TBD	TBD	TBD	Google Drive folder
39xxxx	Terry Ligocki	Yes	Yes	1,093,938	1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ (bbch)	10 ↑↑ 193	Google Drive folder
40xxxx	Andrew Ducharme	No	No	TBD	TBD	TBD	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		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
60xxxx	@gerbil5709	No	No	TBD	TBD	TBD
69xxxx	@poppuncher	Yes	No	TBD	1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch)	10 ↑↑ 133	Google Drive folder
70xxxx	@hipparcos	No	No	TBD	1RB0LF_1LC1LE_1RE0LD_0LC0LA_1LB1RA_0LG0RC_1RZ0LA (bbch)	10 ↑↑ 26	Posted to Discord
75xxxx	Terry Ligocki	Yes	Yes	1,103,089	1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188	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) 1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch) 1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch) 1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ (bbch) 1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 286 10 ↑↑ 193 10 ↑↑ 188 10 ↑↑ 117 10 ↑↑ 113	Google Drive folder