Holdouts lists - BusyBeaverWiki
Holdouts lists
From BusyBeaverWiki
Jump to navigation<br>Jump to search<br>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
1064
15,743,264
3-symbol
4,747,566
4-symbol
11,362,197
5-symbol
65
6-symbol
412,086
Contents
1 Downloadable Holdouts Lists
2 Busy Beaver adjacent holdouts lists
2.1 Beeping Busy Beaver
2.2 Reversible Turing machines
2.3 Instruction-limited Busy Beaver
2.4 Fractran
2.5 Terminating Turmites
2.6 Busy Beaver for Lambda Calculus
2.7 CounterScript
3 References
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)
July 28th, 2026
@mxdys
1064
BB6_holdouts_1064.txt
BB(6)
June 29th, 2026
@mxdys
1094
BB6_holdouts_1094.txt
BB(7)
May 25th, 2026
17,823,260
7x2_holdouts_17823260.txt.zip
Work done by Andrew Ducharme
BB(3,4)
May 11th, 2026
@XnoobSpeakable
11,362,197
3x4_holdouts_11362197.zip
Work done by XnoobSpeakable
BB(4,3)
May 9th, 2026
@Andrew Ducharme
5,127,263
4x3_holdouts_5127263.txt.zip
Work done by Andrew Ducharme
BB(3,4)
April 30th, 2026
@Andrew Ducharme
12,049,358
3x4_holdouts_12049358.txt.zip
Work done by Andrew Ducharme
BB(6)
April 29th, 2026
@mxdys
1104
BB6_holdouts_1104.txt
More reduction by equivalences
BB(4,3)
April 26th, 2026
@Andrew Ducharme
5,641,006
4x3_holdouts_5641006.txt.zip
Work done by Andrew Ducharme
BB(6)
April 25th, 2026
@mxdys
1119
BB6_holdouts_1119.txt
Reduction by equivalences, one halting TM
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(7)
October 25th, 2025
20,405,295
bb7_holdouts_20405295.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(2,6)
September 16, 2025
970,101
2x6_holdouts_970101.txt.gz
Work done by Terry Ligocki
BB(2,6)
September 12, 2025
20,358,011
2x6_holdouts_20358011.zip
Work done by Andrew Ducharme
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
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...