BB(7)

The 7-state, 2-symbol Busy Beaver problem, BB(7), refers to the unsolved 7^th value of the Busy Beaver function. With the compilation of the Cryptid machine Bigfoot into a 7-state, 2-symbol machine in May 2024, we now know that we must solve a Collatz-like problem in order to solve BB(7).

The current BB(7) champion 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) was 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. For 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
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_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
1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ (bbch)	10 ↑↑ 228.78	Terry Ligocki
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
1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD (bbch)	10 ↑↑ 192.67	Andrew Ducharme
1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ (bbch)	10 ↑↑ 192.67	Andrew Ducharme
1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA (bbch)	10 ↑↑ 192.67	@C7X
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

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
1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ (bbch)	10 ↑↑ 228.78	Terry Ligocki
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
1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ (bbch)	10 ↑↑ 124.86	Terry Ligocki
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
1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 114.83	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
1RB0RC_1LC1LD_1RA0RD_0LF1LE_0LB1LA_0RE0LG_1LB1RZ (bbch)	10 ↑↑ 114.37	@C7X
1RB0RG_1LC0LE_1LD0LB_1RB1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 113.38	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		Yes	Yes	817,178	1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch)	10 ↑↑ 246.32
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	1,056,745	TBD	TBD
06xxxx	@Iijil	Yes	No	950,271	TBD	TBD
07xxxx	@Iijil	Yes	No	1,053,750	TBD	TBD
08xxxx	@Iijil	Yes	No	951,114	TBD	TBD
09xxxx	@Iijil	Yes	No	1,052,362	TBD	TBD
10xxxx	Andrew Ducharme	Yes	Yes	802,059	1RB0LG_1RC0RA_1LD0LE_1LG1LC_1LF0RB_0LC0RC_1LA1RZ (bbch)	10 ↑↑ 40.79	Google Drive folder
11xxxx		Yes	Yes	1,105,947	1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ (bbch)	10 ↑↑ 114.83
12xxxx		Yes	Yes	800,882	1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE (bbch)	10 ↑↑ 519.20
13xxxx	Shawn Ligocki	Yes	Yes	1,192,442	1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch)	10 ↑↑ 114.60	Google Drive folder
14xxxx	Andrew Ducharme	Yes	Yes	797,532	1RB0LC_1LC0LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LC (bbch)	10 ↑↑ 140.28	Google Drive folder
15xxxx		Yes	No	TBD	TBD	TBD
16xxxx		No	No	TBD	TBD	TBD
17xxxx		No	No
18xxxx		No	No
19xxxx	@isokate	No	No	TBD	TBD	TBD
20xxxx	@C7X	Yes	Yes	728,510	1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA (bbch)	10↑↑192.67	Google Drive folder
21xxxx - 23xxxx		Yes	No	3,065,946	TBD	TBD
24xxxx	Andrew Ducharme	Yes	Yes	712,356	1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)*	$2\uparrow ^{11}2\uparrow ^{11}3^{*}$	Google Drive folder
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	Yes	812120	1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ (bbch)	10 ↑↑ 192.67
48xxxx	Tobiáš Brichta	No	No	TBD	TBD	TBD	Google Drive folder
49xxxx		No	No	TBD	TBD	TBD
50xxxx	@prurq	No	No	~1.08M	1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch)	10 ↑↑ 115.52	Google Drive folder
51xxxx	@gerbil5709	Yes	No	1,436,814	TBD	TBD	Google Drive folder
52xxxx	@gerbil5709	No	No	TBD	TBD	TBD
56xxxx	Terry Ligocki	No	No	TBD	TBD	TBD	Google Drive folder
57xxxx	Terry Ligocki	Yes	Yes	1,100,748	1RB1RC_0RC0RB_0RD0RE_1LD0LE_1LF0RG_1LG1RZ_1LA0LG (bbch)	10 ↑↑ 69.85	Google Drive folder
58xxxx	Terry Ligocki	Yes	Yes	795,772	1RB0RD_1RC0RA_1LA1LD_0LF1LE_0LC1LB_1LA0LG_1LC1RZa (bbch)	10 ↑↑ 115.32	Google Drive folder
59xxxx	Terry Ligocki	Yes	Yes	1,094,678	1RB0LF_0LC0RA_1LA1RD_0RE1RZ_1RC0RE_1LG1RC_0LB1RA (bbch)	10 ↑↑ 124.12	Google Drive folder
60xxxx	@gerbil5709	Yes	No	957,769	TBD	TBD	Google Drive folder
61xxxx	@gerbil5709	Yes	No	1,052,047	TBD	TBD
62xxxx	@gerbil5709	Yes	No	959,753	TBD	TBD
63xxxx	@gerbil5709	Yes	No	1,051,882	TBD	TBD
64xxxx	@gerbil5709	Yes	No	957,669	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
72xxxx - 79xxxx	Terry Ligocki	Yes	Yes	7,627,514	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

*The current BB(7) champion TM 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)* was discovered by Pavel Kropitz in the enumeration of subtask 243308. The remaining subtasks in the 24xxxx range were enumerated and filtered by Andrew Ducharme.