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
`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE` (bbch)	10 ↑↑ 519.20	@gerbil5709, Terry Ligocki
`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

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"). A cell in bold font means no one has signed up to do either the enumeration or apply the Ligocki code for that row's subtasks. You can help, especially with applying the Ligocki filters! Download the enumerated TMs from the linked source in the far right column of the table below, put your name alongside the enumerator's in the "Done by" column, turn off the bold font on your chosen task range, and return with the number of holdouts, the maximum score TM, and its approximate sigma value when you're done.

After downloading the Ligocki codebase `busy-beaver-main` here, you can install the dependencies by running `python3 -m pip install -r requirements.txt`, then perform the filtering on holdouts from subtasks between start_number and end_number by running the bash command:

for x in {start_number..end_number}; do busy-beaver-main/Code/Enumerate.py --infile your-path-to-holdouts/holdouts_${x}.txt --outfile your-save-path/bb7_${x}.out.pb -r --no-steps --exp-linear-rules --max-loops=100_000 --block-mult=2 --force --save-freq=100; done

Task range	Done by	Completed		# holdouts	Maximum Score TM	~Sigma	Source
Task range	Done by	enumeration	linear rule	# holdouts	Maximum Score TM	~Sigma	Source
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	@Iijil Andrew Ducharme	Yes	No	950,271	TBD	TBD
07xxxx		Yes	No	1,053,750	TBD	TBD
08xxxx		Yes	No	951,114	TBD	TBD
09xxxx		Yes	Yes	810,098	`1RB1RC_1LC0RA_1RA1RD_0RG1LE_1RD0LF_0LB1LE_1RZ1RB` (bbch)	10 ↑↑ 36.38
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	Yes	1,106,978	`1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LA` (bbch)	10 ↑↑ 188.28
16xxxx		Yes	Yes	797,127	`1RB0LC_1LC0LD_1LA1LB_1LG1RE_0RF0LG_0RA1RE_1RZ0RC` (bbch)	10 ↑↑ 140.28
17xxxx	@gerbil5709	No	No	TBD	TBD	TBD	Google Drive folder
18xxxx		No	No	TBD	TBD	TBD
19xxxx	@isokate	No	No	TBD	TBD	TBD
20xxxx - 21xxxx	@C7X	Yes	Yes	1,543,948	`1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA` (bbch)	10↑↑192.67	Google Drive folder
22xxxx - 23xxxx	@C7X	Yes	No	2,008,495	TBD	TBD	Google Drive folder
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	Tobiáš Brichta	No	No	TBD	TBD	TBD	Google Drive folder
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		Yes	No	1,039,795	TBD	TBD
53xxxx		Yes	No	1,441,903	TBD	TBD
54xxxx - 59xxxx	Terry Ligocki	Yes	Yes	5,689,850	`1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LA` (bbch)	10 ↑↑ 188.28	Google Drive folder
60xxxx	@gerbil5709 Terry Ligocki	Yes	No	957,769	TBD	TBD	@gerbil5709 Google Drive folder Terry Ligocki Google Drive folder
61xxxx		Yes	No	1,052,047	TBD	TBD
62xxxx		Yes	Yes	732,742	`1RB0LG_1RC0RE_1LD1LC_1LA1RE_1RZ1RF_1RD0RC_1LD0LC` (bbch)	10 ↑↑ 126.20
63xxxx		Yes	Yes	813,627	`1RB0RC_1RC1RZ_1LD0RF_0LE1LE_1RG0LF_1LE0LA_1RA0RE` (bbch)	10 ↑↑ 26.01
64xxxx		Yes	Yes	729,885	`1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE` (bbch)	10 ↑↑ 519.20
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	Yes	No	1,046,139	TBD	TBD	Google Drive folder
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.

BB(7)

History

Top Halters

Current Progress

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