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 May 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.

Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, 1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB (bbch) and 1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC (bbch), with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found 1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB (bbch), with sigma score ~10 ↑↑ 46. These were all outpaced by Pavel's champion.

Pavel's champion is enumerated in subtask 243308.

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
1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD (bbch)	10 ↑↑ 192.67	Andrew Ducharme
1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_1RG0LA_0LE1RZ (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE (bbch)	10 ↑↑ 192.67	Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LD0RF_0RA1RE_1RZ0RA (bbch)	10 ↑↑ 188.28	@XnoobSpeakable, @Peacemaker II
1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188.28	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_0RF0LF_0RA1RE_1RZ0LE (bbch)	10 ↑↑ 188.28	Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_1LG1RE_0RF0LF_0RA1RE_1RZ0RA (bbch)	10 ↑↑ 188.28	Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_1LG1RE_1LF0RF_0RA1RE_1RZ0RA (bbch)	10 ↑↑ 188.28	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
1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC (bbch)	10 ↑↑ 140.28	@stokastic
1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch)	10 ↑↑ 133.85	@poppuncher
1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF (bbch)	10 ↑↑ 129.24	@Iijil
1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD (bbch)	10 ↑↑ 126.20	@stokastic
1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ (bbch)	10 ↑↑ 116.98	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 ↑↑ 113.38	Terry Ligocki
1RB1RZ_1RC1RA_1RD0RB_1LE0RC_1LF0LD_1RG0LF_1RC0LG (bbch)	10 ↑↑ 108.77	Terry Ligocki
1RB0LA_1RC0RA_0RD0RB_1LE0RC_0LD1LF_0LA1LG_0LC1RZ (bbch)	10 ↑↑ 105.37	Terry Ligocki
1RB0LE_1RC1RA_1RD0RG_1LA1RZ_1RA1LF_1LA0LE_0RF1RG (bbch)	10 ↑↑ 93.81	Andrew Ducharme

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		Yes	Yes	817,178	1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch)	10 ↑↑ 246.32
02xxxx		Yes	No	963,486	TBD	TBD
03xxxx		Yes	No	1,052,504	TBD	TBD
04xxxx		Yes	No	955,711	TBD	TBD
05xxxx		Yes	No	1,056,745	TBD	TBD
06xxxx		Yes	No	950,271	TBD	TBD
07xxxx		Yes	No	1,053,750	TBD	TBD
08xxxx		Yes	No	951,114	TBD	TBD
09xxxx		Yes	No	1,052,362	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 - 23xxxx	@C7X	Yes	No	4,021,884	TBD	TBD	Google Drive folder
24xxxx	Andrew Ducharme	No	No	TBD	TBD	TBD	Google Drive folder
243308	@uni	N/A	N/A	N/A	1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)	$2\uparrow ^{11}2\uparrow ^{11}3$	Discord May 2025
25xxxx	@stokastic	Yes	Yes	815,919	1RB1RZ_1LC0LE_0LD0LC_0RE1LB_1RF0RG_0LD1RB_1RD1RA (bbch)	10 ↑↑ 31.33	Google Drive folder
26xxxx		Yes	Yes	731,995	1RB1RZ_0LC1RB_0LE0LD_1LE1LD_0RF0LC_0RG1RF_1RD0RA (bbch)	10 ↑↑ 36.26
27xxxx		Yes	Yes	811,486	1RB0RG_1LC1LB_0RE0LD_0LC1RF_0RA1RE_0LF0LB_1RF1RZ (bbch)	10 ↑↑ 63.56
28xxxx		Yes	Yes	956,935	1RB1RZ_0LC1RC_0RE1RD_0RB1RG_1RF0RA_1LG0LC_1LB0LF (bbch)	10 ↑↑ 114.57
29xxxx		Yes	Yes	1,052,415	1RB1LA_1RC1RD_0LA1LG_1RZ0LE_1RB1RF_1RE0LC_0RE1LF (bbch)	10 ↑↑ 31.67
30xxxx		Yes	Yes	1,032,095	1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD (bbch)	10 ↑↑ 126.20
31xxxx		Yes	Yes	1,436,970	1RB1LD_1LC0RF_0RA0LB_0LE1RZ_1LA0LE_1RG1LA_0RC0RF (bbch)	10 ↑↑ 50.27
32xxxx		Yes	Yes	1,036,950	1RB1RD_1LC0RF_0LE0LD_1LE1LE_1RF0LB_1RB0RG_1RA1RZ (bbch)	10 ↑↑ 50.28
33xxxx		Yes	Yes	1,432,081	1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC (bbch)	10 ↑↑ 140.28
34xxxx		Yes	Yes	1,032,970	1RB0RA_1LC0LE_0LD0LB_1RE0RD_0RA0LF_1RD1RG_0RF1RZ (bbch)	10 ↑↑ 72.69
35xxxx - 39xxxx	Terry Ligocki	Yes	Yes	4,894,047	1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE (bbch)	10 ↑↑ 192.67	Google Drive folder
40xxxx	Andrew Ducharme	Yes	Yes	730,310	1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch)	10 ↑↑ 519.20	Google Drive folder
41xxxx		Yes	Yes	814,075	1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD (bbch)	10 ↑↑ 192.67
42xxxx		Yes	Yes	739,729	1RB1LD_0RC1RF_1LD0LE_0LE0LA_1LA1LE_1RG0LA_1RZ1RA (bbch)	10 ↑↑ 46.26
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
46xxxx		Yes	Yes	725,102	1RB1RA_0LC0RE_0LD1LC_1LA0LF_0RB0RA_1LG1RZ_0RE1LG (bbch)	10 ↑↑ 36.26
47xxxx		Yes	No	TBD	TBD	TBD
48xxxx	Tobiáš Brichta	No	No	TBD	TBD	TBD	Google Drive folder
49xxxx		No	No	TBD	TBD	TBD
500xxx	@prurq	Yes	Yes	120,520	1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch)	10 ↑↑ 115.52	Google Drive folder
501xxx		Yes	No	96,102	TBD	TBD
60xxxx	@gerbil5709	Yes	No	957,769	TBD	TBD	Google Drive folder
61xxxx		Yes	No	1,052,047	TBD	TBD
62xxxx		Yes	No	959,753	TBD	TBD
63xxxx		Yes	No	1,051,882	TBD	TBD
64xxxx		No	No	TBD	TBD	TBD
65xxxx - 68xxxx	Terry Ligocki	Yes	Yes	3,076,778	1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD (bbch)	10 ↑↑ 192.67	Google Drive folder
69xxxx	@poppuncher	Yes	Yes	1,053,119	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)	10 ↑↑ 33.81	Github release
71xxxx	@hipparcos	Yes	Yes	1,100,790	1RB1RZ_1LC1RD_0LD0LC_1LE1RA_1LF0LE_1RF0RG_1RG0RD (bbch)	10 ↑↑ 77.50	Github release
75xxxx	Terry Ligocki	Yes	Yes	1,103,089	1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188.28	Google Drive folder
77xxxx	Terry Ligocki	Yes	No	1,435,026	TBD	TBD	Google Drive folder
78xxxx	Terry Ligocki	Yes	Yes	800,141	1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ (bbch)	10 ↑↑ 124.86	Google Drive folder
79xxxx	Terry Ligocki	Yes	Yes	1,104,247	1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ (bbch)	10 ↑↑ 228.78	Google Drive folder
80xxxx	@xnoobspeakable	Yes	No	964,396	TBD	TBD	Google Drive folder
81xxxx	@xnoobspeakable	No	No	TBD	TBD	TBD
82xxxx - 99xxxx	Terry Ligocki	Yes	Yes	15,673,786	1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch)	10 ↑↑ 286.17	Google Drive folder