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	1064	15,743,264
3-symbol	0	4	4,747,566
4-symbol	0	11,362,197
5-symbol	65
6-symbol	412,086

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(5)

Date	Shared by	Number of holdouts	File	Notes
July 2nd, 2024	bbchallenge	0	List of 0 holdouts	BB(5) is solved!
circa May 13th, 2003	Georgi Georgiev (Skelet)	43	List of 43 holdouts

BB(6)

Date	Shared by	Number of holdouts	File	Notes
July 28th, 2026	@mxdys	1064	BB6_holdouts_1064.txt
June 29th, 2026	@mxdys	1094	BB6_holdouts_1094.txt
April 29th, 2026	@mxdys	1104	BB6_holdouts_1104.txt	More reduction by equivalences
April 25th, 2026	@mxdys	1119	BB6_holdouts_1119.txt	Reduction by equivalences, one halting TM
March 25th, 2026	@mxdys	1161	BB6_holdouts_1161.txt
February 28th, 2026	@mxdys	1214	BB6_holdouts_1214.txt
February 19th, 2026	@mxdys	1226	BB6_holdouts_1226.txt
January 29th, 2026	@mxdys	1314	BB6_holdouts_1314.txt
December 30th, 2025	@mxdys	1326	BB6_holdouts_1326.txt
November 22nd, 2025	Robin Rovenszky	Variable	Google Sheets	Annotated list, including links to Discord discussions, always up-to-date.
December 16th, 2025	@mxdys	1343	BB6_holdouts_1343.txt
November 28th, 2025	@mxdys	1416	BB6_holdouts_1416.txt
November 14th, 2025	@mxdys	1534	BB6_holdouts_1534.txt
October 20th, 2025	@mxdys	1618	BB6 holdouts 1618.txt
September 21, 2025	@mxdys	1691	BB6_holdouts_1691.txt
August 30 2025	@mxdys	2592	BB6 holdouts 2592.txt
July 29 2025	@mxdys	2728	BB6 holdouts 2728.txt
July 13, 2025	@mxdys	2891	BB6_holdouts_2891.txt
July 5, 2025	@mxdys	3094	BB6_holdouts_3094.txt
June 18, 2025	@mxdys	3335	BB6_holdouts_3335.txt
March 1, 2025	@mxdys	3571	BB6_holdouts_3571.txt
November 25, 2024 (@icy)	@tjligocki	4319	Spreadsheet of holdouts	Keeping track of BB(6) progress - informal.
November 8, 2024	@mxdys	4408	BB6_holdouts_4408.txt
October 19, 2024	@mxdys	4521	BB6_holdouts_4521.txt
September 23, 2024	@mxdys	4741	BB6_holdouts_4741.txt
September 7, 2024	@mxdys	4986	BB6_holdouts_4986.txt
September 2, 2024	@mxdys	5394	File:BB6 holdouts 5394.txt
August 4, 2024	@mxdys	5877	File:BB6 holdouts 5877.txt
July 28, 2024	@mxdys	6417	BB6_holdouts_6417.txt
July 15, 2024	@mxdys	7013	BB6_holdouts_7013.txt
July 14, 2024	@Justin Blanchard	7255	BB6_holdouts_7255.txt	Work done by Justin Blanchard
July 6, 2024	@mxdys	7296	File:BB6 holdouts 7296.txt
July 6, 2024	@Justin Blanchard	7430	BB6_holdouts_7430.txt	Work done by Justin Blanchard
July 5, 2024	@mxdys	7449	BB6_holdouts_7449.txt
June 28, 2024	@mxdys	9366	BB6_holdouts_9366.txt
June 24, 2024	@Justin Blanchard	9853	BB6_holdouts_9853.txt
June 21, 2024	@mxdys	10,020	BB6_holdouts_10020.txt	Work done by Justin Blanchard
June 20, 2024	@mxdys	10,944	BB6_holdouts_10944.txt
June 13, 2024	@tjligocki	12,091	File:BB6 holdouts 12091.txt	Work done with @Shawn Ligocki
June 7, 2024	@mxdys	12,325	File:BB6 holdouts 12325.txt	Some equivalent machines are removed.
May 28, 2024	@mxdys	18,560	BB6_holdouts_18560.txt
May 13, 2024	@mxdys	35,788	BB6_holdouts_35788.txt	C++ version of the deciders from Coq-BB5 ran on Shawns 181,851 holdouts
May 27, 2023	@sligocki	181,851	6x2.holdouts_181851.txt.gz	This was posted to the BBChallenge Forum (before Discord)
May 10, 2023	@sligocki	1,458,704	6x2.holdouts_1458704.txt.gz	This was posted to the BBChallenge Forum (before Discord)

BB(7)

Date	Shared by	Number of holdouts	File	Notes
May 25th, 2026		17,823,260	7x2_holdouts_17823260.txt.zip	Work done by Andrew Ducharme
October 25th, 2025		20,405,295	bb7_holdouts_20405295.txt.gz
October 4th, 2025	Andrew Ducharme	22,721,168	bb7_holdouts_22721168.txt.zip

BB(3,3)

Date	Shared by	Number of holdouts	File	Notes
November 10, 2024		6	3x3 holdout 6.txt
June 9, 2024	@Justin Blanchard	22	File:3x3.todo.txt, File:Mugshots small.pdf
June 8, 2023	@Iijil	925	File:2023 06 08.3x3.holdouts intersect sligocki iijil 925.txt	Intersection of @sligocki and @Iijil from below
June 8, 2023	@Iijil	2,480	File:2023 06 08.3x3.holdouts iijil 2380.txt
June 7, 2023	@sligocki	2,417	File:2023 06 07.3x3.holdouts 2417.txt

BB(4,3)

Date	Shared by	Number of holdouts	File	Notes
May 9th, 2026	@Andrew Ducharme	5,127,263	4x3_holdouts_5127263.txt.zip	Work done by Andrew Ducharme
April 26th, 2026	@Andrew Ducharme	5,641,006	4x3_holdouts_5641006.txt.zip	Work done by Andrew Ducharme
October 26th, 2025		9,401,447	4x3_holdouts_9401447.txt.gz
October 20th, 2025	@tjligocki	18,138,027	4x3_holdouts_18138027.txt.gz
December 21, 2024	@tjligocki	460,916,384	4x3_holdouts_460916384.txt.gz	Google Drive directory for 4x3 TMs

BB(3,4)

Date	Shared by	Number of holdouts	File	Notes
May 11th, 2026	@XnoobSpeakable	11,362,197	3x4_holdouts_11362197.zip	Work done by XnoobSpeakable
April 30th, 2026	@Andrew Ducharme	12,049,358	3x4_holdouts_12049358.txt.zip	Work done by Andrew Ducharme
December 31st, 2025		12,435,284	3x4st10c_holdouts_12435284.txt	Work done by XnoobSpeakable and Lúkos.
October 4th, 2025	@tjligocki	64,777,377	3x4_holdouts_64777377.txt.gz	Work done by XnoobSpeakable and Lúkos.
November 3, 2024	@tjligocki	434,787,751	3x4_holdouts_434787751.txt.gz	Google Drive directory for 3x4 TMs

BB(2,5)

Date	Shared by	Number of holdouts	File	Notes
March 29, 2025	@mxdys	83	File:BB2x5 Coq holdouts 83.txt
June 19, 2024	@mxdys	217	File:2x5_holdouts_217.txt	273 holdouts minus machines solved by CTL
June 15th 2024	@dyuan01	273	File:2x5_holdouts_273.txt	@Justin Blanchard's 499 holdouts minus machines solved by @mxdys
May 22, 2024	@Justin Blanchard	499	File:2x5.todo.txt
April 25, 2024	@Justin Blanchard	920	2x5.todo.txt
April 24, 2024	@Justin Blanchard	1045	2x5.todo.txt
April 22, 2024	@Justin Blanchard	1588	2x5.todo.txt
April 19, 2024	@Justin Blanchard	1835	2x5.todo.txt
April 18, 2024	@Justin Blanchard	1921	2x5.todo.txt
April 17, 2024	@Justin Blanchard	2354	2x5.todo.txt
April 16, 2024	@Justin Blanchard	2438	2x5.todo.txt
April 15, 2024	@Justin Blanchard	2564	2x5.todo.txt
April 12, 2024	@Justin Blanchard	3364	2x5.todo.txt

BB(2,6)

Date	Shared by	Number of holdouts	File	Notes
October 6th, 2025	@tjligocki	870,085	2x6_holdouts_870085.txt.zip	Work done by Andrew Ducharme.
September 16, 2025		970,101	2x6_holdouts_970101.txt.gz	Work done by Terry Ligocki
September 12, 2025		20,358,011	2x6_holdouts_20358011.zip	Work done by Andrew Ducharme
November 4, 2024	@tjligocki	22,302,296	2x6_holdouts_22302296.txt.gz	Google Drive directory for 2x6 TMs

Busy Beaver adjacent holdouts lists

Beeping Busy Beaver

Domain	Date	Shared by	Number of holdouts	File	Notes
BBB(4)	August 2nd, 2026	bbchallenge	0		BBB(4) had been proven to be 32,779,478 by August 2nd, 2026. See Coq-BBB4 for more details.
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(23)	August 5, 2026	@-d	13	sz23_13_unofficial.txt	Unofficial holdouts list
BBf(23)	July 25, 2026	@-d	694	sz23_694_unofficial.txt	Unofficial holdouts list, reduction by Claude
BBf(23)	July 25, 2026	@-d	703	sz23_703_unofficial.txt	Unofficial holdouts list, reduction by Claude
BBf(23)	July 24, 2026	@-d	8,021	sz23_8021_unofficial.txt	Unofficial holdouts list, reduction by Claude
BBf(23)	July 11, 2026	@-d	21233	sz23_21233.txt
BBf(23)	June 3, 2026	@-d	21295	sz23_21295.txt	Programs simulated to halting were removed
BBf(23)	June 2, 2026	@-d	21320	sz23_21320.txt	Programs simluated to halting were removed
BBf(23)	June 2, 2026	@-d	28100	sz23_28100.txt
BBf(23)	June 2, 2026	@-d	29188	sz23_29188.txt
BBf(23)	May 31, 2026	@-d	29250	sz23_29250.txt
BBf(23)	May 31, 2026	@-d	94367	sz23_94367.txt
BBf(23)	May 30, 2026	@-d	790,335	sz23_790335.txt
BBf(22)	April 4, 2026	@-d	3	sz22_3.txt	Holdout reduction by Claude Opus 4.6
BBf(21)	March 28, 2026	@-d	0		Claude Opus 4.6's proof of nonhalting of all the 140 remaining BBf(21) holdouts: March 28th, 2026
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 3, 2026	@creeperman7002	630	TT2x4_holdouts_630.txt
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(42)	June 18, 2026	@C++DSucker	Variable (240)	Spreadsheet
BBλ(41)			0	Spreadsheet	BBλ(41) was solved on August 7th, 2026
BBλ(40)	June 10, 2026	@C++DSucker	0	Spreadsheet	BBλ(40) was solved on July 20th, 2026
BBλ(39)	April 10, 2026	@Sligocki	0	Spreadsheet	BBλ(39) was solved on June 10th, 2026
BBλ(38)	April 19, 2025	@Sligocki	0	Spreadsheet	BBλ(38) was solved on April 13th, 2026
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

CounterScript

Domain	Date	Shared by	Number of holdouts	File	Notes
BBCS(11)	July 10, 2026	@Azerty	1	11.txt	The holdout may be resolved by hand.