Holdouts lists

A holdout (or undecided machine) is a Turing machine for which it is not known whether the machine halts or not from an all-0 input tape. Holdouts are the machines which deciders are yet unable to decide. Contributors have shared lists of holdouts. Some lists exclude known equivalent machines, i.e., machines whose halting status is implied by the halting status of another machine. If a holdout machine with more than one undefined transitions is found to reach a undefined transition, the number of holdouts may increase as a consequence of TNF enumeration.

Number of holdouts

	2-state	3-state	4-state	5-state	6-state	7-state
2-symbol	0	0	0	0	1161	18,036,852
3-symbol	0	4	9,401,447
4-symbol	0	12,435,284
5-symbol	69
6-symbol	545,005

Downloadable Holdouts Lists

This is a table where people have added lists with no restriction or independent verification. For some of the entries there is a reference to a spreadsheet that documents what was run to achieve the result. For others, there is additional documentation on the specific BB pages.

BB space	Date	Shared by	Number of holdouts	File	Notes
BB(6)	March 25th, 2026	@mxdys	1161	BB6_holdouts_1161.txt
BB(6)	February 28th, 2026	@mxdys	1214	BB6_holdouts_1214.txt
BB(6)	February 19th, 2026	@mxdys	1226	BB6_holdouts_1226.txt
BB(6)	January 29th, 2026	@mxdys	1314	BB6_holdouts_1314.txt
BB(3,4)	December 31st, 2025		12,435,284	3x4st10c_holdouts_12435284.txt	Work done by XnoobSpeakable and Lúkos.
BB(6)	December 30th, 2025	@mxdys	1326	BB6_holdouts_1326.txt
BB(6)	November 22nd, 2025	Robin Rovenszky	Variable	Google Sheets	Annotated list, including links to Discord discussions, always up-to-date.
BB(6)	December 16th, 2025	@mxdys	1343	BB6_holdouts_1343.txt
BB(6)	November 28th, 2025	@mxdys	1416	BB6_holdouts_1416.txt
BB(6)	November 14th, 2025	@mxdys	1534	BB6_holdouts_1534.txt
BB(4,3)	October 26th, 2025		9,401,447	4x3_holdouts_9401447.txt.gz
BB(6)	October 20th, 2025	@mxdys	1618	BB6 holdouts 1618.txt
BB(4,3)	October 20th, 2025	@tjligocki	18,138,027	4x3_holdouts_18138027.txt.gz
BB(2,6)	October 6th, 2025	@tjligocki	870,085	2x6_holdouts_870085.txt.zip	Work done by Andrew Ducharme.
BB(3,4)	October 4th, 2025	@tjligocki	64,777,377	3x4_holdouts_64777377.txt.gz	Work done by XnoobSpeakable and Lúkos.
BB(7)	October 4th, 2025	Andrew Ducharme	22,721,168	bb7_holdouts_22721168.txt.zip
BB(6)	September 21, 2025	@mxdys	1691	BB6_holdouts_1691.txt
BB(6)	August 30 2025	@mxdys	2592	BB6 holdouts 2592.txt
BB(6)	July 29 2025	@mxdys	2728	BB6 holdouts 2728.txt
BB(6)	July 13, 2025	@mxdys	2891	BB6_holdouts_2891.txt
BB(6)	July 5, 2025	@mxdys	3094	BB6_holdouts_3094.txt
BB(6)	June 18, 2025	@mxdys	3335	BB6_holdouts_3335.txt
BB(2,5)	March 29 2025	@mxdys	83	File:BB2x5 Coq holdouts 83.txt
BB(6)	March 1, 2025	@mxdys	3571	BB6_holdouts_3571.txt
BB(4,3)	December 21, 2024	@tjligocki	460,916,384	4x3_holdouts_460916384.txt.gz	Google Drive directory for 4x3 TMs
BB(6)	November 25, 2024 (@icy)	@tjligocki	4319	Spreadsheet of holdouts	Keeping track of BB(6) progress - informal.
BB(3,3)	November 10, 2024		6	3x3 holdout 6.txt
BB(6)	November 8, 2024	@mxdys	4408	BB6_holdouts_4408.txt
BB(2,6)	November 4, 2024	@tjligocki	22,302,296	2x6_holdouts_22302296.txt.gz	Google Drive directory for 2x6 TMs
BB(3,4)	November 3, 2024	@tjligocki	434,787,751	3x4_holdouts_434787751.txt.gz	Google Drive directory for 3x4 TMs
BB(6)	October 19, 2024	@mxdys	4521	BB6_holdouts_4521.txt
BB(6)	September 23, 2024	@mxdys	4741	BB6_holdouts_4741.txt
BB(6)	September 7, 2024	@mxdys	4986	BB6_holdouts_4986.txt
BB(6)	September 2, 2024	@mxdys	5394	File:BB6 holdouts 5394.txt
BB(6)	August 4, 2024	@mxdys	5877	File:BB6 holdouts 5877.txt
BB(6)	July 28, 2024	@mxdys	6417	BB6_holdouts_6417.txt
BB(6)	July 15, 2024	@mxdys	7013	BB6_holdouts_7013.txt
BB(6)	July 14, 2024	@Justin Blanchard	7255	BB6_holdouts_7255.txt	Work done by Justin Blanchard
BB(6)	July 6, 2024	@mxdys	7296	File:BB6 holdouts 7296.txt
BB(6)	July 6, 2024	@Justin Blanchard	7430	BB6_holdouts_7430.txt	Work done by Justin Blanchard
BB(6)	July 5, 2024	@mxdys	7449	BB6_holdouts_7449.txt
BB(6)	June 28, 2024	@mxdys	9366	BB6_holdouts_9366.txt
BB(6)	June 24, 2024	@Justin Blanchard	9853	BB6_holdouts_9853.txt
BB(6)	June 21, 2024	@mxdys	10,020	BB6_holdouts_10020.txt	Work done by Justin Blanchard
BB(6)	June 20, 2024	@mxdys	10,944	BB6_holdouts_10944.txt
BB(2,5)	June 19, 2024	@mxdys	217	File:2x5_holdouts_217.txt	273 holdouts minus machines solved by CTL
BB(2,5)	June 15th 2024	@dyuan01	273	File:2x5_holdouts_273.txt	@Justin Blanchard's 499 holdouts minus machines solved by @mxdys
BB(6)	June 13, 2024	@tjligocki	12,091	File:BB6 holdouts 12091.txt	Work done with @Shawn Ligocki
BB(3,3)	June 9, 2024	@Justin Blanchard	22	File:3x3.todo.txt, File:Mugshots small.pdf
BB(6)	June 7, 2024	@mxdys	12,325	File:BB6 holdouts 12325.txt	Some equivalent machines are removed.
BB(5)	June 2024	BBChallenge	0		BB(5) is SOLVED!
BB(6)	May 28, 2024	@mxdys	18,560	BB6_holdouts_18560.txt
BB(2,5)	May 22, 2024	@Justin Blanchard	499	File:2x5.todo.txt
BB(6)	May 13, 2024	@mxdys	35,788	BB6_holdouts_35788.txt	C++ version of the deciders from Coq-BB5 ran on Shawns 181,851 holdouts
BB(2,5)	April 25, 2024	@Justin Blanchard	920	2x5.todo.txt
BB(2,5)	April 24, 2024	@Justin Blanchard	1045	2x5.todo.txt
BB(2,5)	April 22, 2024	@Justin Blanchard	1588	2x5.todo.txt
BB(2,5)	April 19, 2024	@Justin Blanchard	1835	2x5.todo.txt
BB(2,5)	April 18, 2024	@Justin Blanchard	1921	2x5.todo.txt
BB(2,5)	April 17, 2024	@Justin Blanchard	2354	2x5.todo.txt
BB(2,5)	April 16, 2024	@Justin Blanchard	2438	2x5.todo.txt
BB(2,5)	April 15, 2024	@Justin Blanchard	2564	2x5.todo.txt
BB(2,5)	April 12, 2024	@Justin Blanchard	3364	2x5.todo.txt
BB(3,3)	June 8, 2023	@Iijil	925	File:2023 06 08.3x3.holdouts intersect sligocki iijil 925.txt	Intersection of @sligocki and @Iijil from below
BB(3,3)	June 8, 2023	@Iijil	2,480	File:2023 06 08.3x3.holdouts iijil 2380.txt
BB(3,3)	June 7, 2023	@sligocki	2,417	File:2023 06 07.3x3.holdouts 2417.txt
BB(6)	May 27, 2023	@sligocki	181,851	6x2.holdouts_181851.txt.gz	This was posted to the BBChallenge Forum (before Discord)
BB(6)	May 10, 2023	@sligocki	1,458,704	6x2.holdouts_1458704.txt.gz	This was posted to the BBChallenge Forum (before Discord)
BB(5)	circa May 13th, 2003	Georgi Georgiev (Skelet)	43	List of 43 holdouts

Busy Beaver adjacent holdouts lists

Beeping Busy Beaver

Domain	Date	Shared by	Number of holdouts	File	Notes
BBB(4)	June 26, 2025	@mxdys	3713	BBB4_holdouts_3713.txt

Reversible Turing machines

Domain	Date	Shared by	Number of holdouts	File	Notes
BBrev(6)	July 31, 2025	@Sligocki	388	BBrev6_holdouts_388.txt
BBrev(6)	July 31, 2025	@Sligocki	409	BBrev6_holdouts_409.txt

Instruction-limited Busy Beaver

Domain	Date	Shared by	Number of holdouts	File	Notes
BBi(8)	October 7, 2025	@Shawn Ligocki	348	bbi8_holdouts_348.txt
BBi(8)	October 6, 2025	@Peacemaker II	441	BBi8_holdouts_441.txt

Fractran

Domain	Date	Shared by	Number of holdouts	File	Notes
BBf(22)	January 25, 2026	@-d	2003	sz22_2003_unofficial.txt	Result of the beeping permutation decider being run on sz22_5682.txt
BBf(21)	January 25, 2026	@-d	140	sz21_140_unofficial.txt	Result of the beeping permutation decider being run on sz21_345.txt
BBf(21)	January 22, 2026	@-d	143	sz21_143_workinprogress.txt
BBf(22)	January 2, 2026	@-d	5682	sz22_5682.txt
BBf(21)	January 2, 2026	@-d	345	sz21_345.txt
BBf(21)	December 15, 2025	@Sligocki	394	sz21_394.txt
BBf(20)	December 15, 2025	@Sligocki	6	sz20_6.txt	BBf(20) has since been solved
BBf(22)	December 13, 2025	@Sligocki	10441	sz22_10441.txt	17 known halters are removed
BBf(22)	December 11, 2025	@Sligocki	10458	sz22_10457.txt	Known halters are removed
BBf(22)	December 11, 2025	@dyuan01	11130	message.txt
BBf(22)	December 10, 2025	@-d	91123	sz22_91123.txt	Initial enumeration
BBf(21)	November 17, 2025	@Sligocki	760	sz21_760.txt	23 halting machines are removed
BBf(21)	November 16, 2025	@dyuan01	783	message.txt
BBf(20)	November 13, 2025	@dyuan01	279	message.txt
BBf(20)	November 13, 2025	@-d	902	sz20_902.txt

Terminating Turmites

Domain	Date	Shared by	Number of holdouts	File	Notes
TT(2,4)	August 1, 2025	@creeperman7002	2298	holdout_2x4_2298.txt
TT(4)	July 12, 2025	@creeperman7002	99	holdout4x2.txt

Busy Beaver for Lambda Calculus

Domain	Date	Shared by	Number of holdouts	File	Notes
BBλ(38)	April 19, 2025	@Sligocki (tab)	Variable (18)	Spreadsheet
BBλ(37)	March 27, 2025	@Racheline	92	BBλ(37) 92 holdouts progress	BBλ(37) has since been solved
BBλ(37)	March 26, 2025	@Racheline	216	BBL(37)_216.txt
BBλ(37)	March 26, 2025	@Racheline	278	BBL2(37)_278.txt
BBλ(37)	March 26, 2025	@Sam	317	BBL2(37)_317.txt
BBλ(37)	March 26, 2025	@Sam	333	BBL(37).txt