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. In 1964, Milton Green designed a machine that had sigma score 22,961. In 2014, Wythagoras modified a BB(6) champion 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. A few days later, Pavel found a TM that outpaces all of them.

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
1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG (bbch)	10 ↑↑ 243.88	@Iijil, Andrew Ducharme
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
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
1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ (bbch)	10 ↑↑ 192.67	@Iijil, Terry Ligocki
1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_1RG0LA_0LE1RZ (bbch)	10 ↑↑ 192.67	@Iijil, Terry Ligocki
1RB1LA_1LC0RE_0LD1LB_1RE0LG_1RF0RA_0RA0LA_1RB1RZ (bbch)	10 ↑↑ 192.67	@Iijil, 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_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG (bbch)	10 ↑↑ 243.88	@Iijil, Andrew Ducharme
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

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
		enumeration	linear rule
00-01xxxx	@Iijil	Yes	Yes	1,545,673	1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch)	10 ↑↑ 246.32	Google Drive folder
02-04xxxx	@Iijil Terry Ligocki	Yes	Yes	2,279,734	1RB0LF_1RC1RA_1RD0RG_1LE1RZ_1LA0LF_1RA1LE_0RE1RG (bbch)	10 ↑↑ 93.81	@Iijil Terry Ligocki
05-09xxxx	@Iijil Andrew Ducharme	Yes	Yes	3,889,955	1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG (bbch)	10 ↑↑ 243.88	OneDrive folder
10-12xxxx	Andrew Ducharme	Yes	Yes	2,708,888	1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE (bbch)	10 ↑↑ 519.20	Google Drive folder
13xxxx	Shawn Ligocki	Yes	Yes	1,192,442	1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch)	10 ↑↑ 114.60	Google Drive folder
14-16xxxx	Andrew Ducharme	Yes	Yes	2,701,637	1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188.28	Google Drive folder
17xxxx	@gerbil5709 Terry Ligocki	Yes	Yes	1,101,230	1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ (bbch)	10 ↑↑ 192.67	@gerbil5709 Terry Ligocki
18xxxx		Yes	Yes	796,926	1RB0RF_1LC0RA_1LD0LB_1LE0LD_1RA1RE_0RB0RG_1RZ0LE (bbch)	~10 ↑↑ 93.88
19xxxx	Katelyn Doucette	Yes	No	1,433,181	TBD	TBD	Google Drive folder
20-22xxxx	@C7X	Yes	Yes	3,347,034	1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA (bbch)	10 ↑↑ 192.67	Google Drive folder
23xxxx		Yes	No	1,049,137	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
25-34xxxx	@stokastic	Yes	Yes	10,339,816	1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC (bbch)	10 ↑↑ 140.28	Google Drive folder
35-39xxxx	Terry Ligocki	Yes	Yes	4,894,047	1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE (bbch)	10 ↑↑ 192.67	Google Drive folder
40-47xxxx	Andrew Ducharme	Yes	Yes	6,181,327	1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch)	10 ↑↑ 519.20	Google Drive folder
48xxxx	@star	No	No	TBD	TBD	TBD
49xxxx	Tobiáš Brichta	Yes	No	1,049,506	TBD	TBD	Google Drive folder
50xxxx	@prurq Andrew Ducharme	Yes	Yes	797,224	1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch)	10 ↑↑ 115.52	Google Drive folder
51-53xxxx	@gerbil5709 Terry Ligocki	Yes	Yes	3,016,175	1RB0LC_1LC0LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LC (bbch)	10 ↑↑ 140.28	@gerbil5709 Terry Ligocki
54-59xxxx	Terry Ligocki	Yes	Yes	5,689,850	1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LA (bbch)	10 ↑↑ 188.28	Google Drive folder
60-64xxxx	@gerbil5709 Terry Ligocki	Yes	Yes	3,817,876	1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE (bbch)	10 ↑↑ 519.20	@gerbil5709 Terry Ligocki
65-68xxxx	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
70-71xxxx	@hipparcos	Yes	Yes	1,899,094	1RB1RZ_1LC1RD_0LD0LC_1LE1RA_1LF0LE_1RF0RG_1RG0RD (bbch)	10 ↑↑ 77.50	Github release
72-79xxxx	Terry Ligocki	Yes	Yes	7,627,514	1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ (bbch)	10 ↑↑ 228.78	Google Drive folder
80xxxx	@xnoobspeakable	Yes	Yes	733,278	1RB0LD_0RC0RE_1LD0RA_1LA0LF_1RC1RC_1LG1RZ_1LA1LE (bbch)	10 ↑↑ 40.66	Google Drive folder
81xxxx		Yes	Yes	804,255	1RB0LA_0RC1RZ_0RD0RG_1LE1RA_1LF1LD_1RG0RG_1RD1RC (bbch)	10 ↑↑ 74.85
82-99xxxx	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.