Holdouts lists: Difference between revisions

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A '''holdout''' (or undecided machine) is a [[Turing machine]] for which it is not known whether the machine halts or not from all-0 input tape. Holdouts are the machines which [[Decider|deciders]] are unable to decide.
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 [[Decider|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 [[Tree Normal Form|TNF enumeration]].


Holdout lists are often shared by contributors. There is a [[#Downloadable Holdout Lists|Downloadable Holdout Lists]] table where people have added lists with no restriction or independent verification. After that table are several tables, [[#Verifiable Holdout Lists|Verifiable Holdout Lists]], that attempt to document a reproducible path from the initial enumeration of TMs of a given size tracking the holdout lists.
Here is a table that summarises the number of holdout per busy beaver domain based on the Downloadable Holdout Lists:
{| class="wikitable"
{| class="wikitable"
|+Number of holdouts
|+Number of holdouts
Line 12: Line 9:
!5-state
!5-state
!6-state
!6-state
!7-state
|-
|-
!2-symbol
!2-symbol
Line 18: Line 16:
|0
|0
|0
|0
|4408
|1104
|17,823,260
|-
|-
!3-symbol
!3-symbol
|0
|0
|6
|4
|460,916,384
|5,641,006
|
|
|
|
|
Line 29: Line 29:
!4-symbol
!4-symbol
|0
|0
|434,787,751
|12,435,284
|
|
|
|
|
Line 35: Line 36:
|-
|-
!5-symbol
!5-symbol
|273
|66
|
|
|
|
|
Line 42: Line 44:
|-
|-
!6-symbol
!6-symbol
|22,302,296
|536,112
|
|
|
|
|
Line 49: Line 52:
|}
|}


== Downloadable Holdout Lists ==
== 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.
{| class="wikitable sortable"
{| class="wikitable sortable"
|+
|+
Line 58: Line 62:
!File
!File
!Notes
!Notes
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1499000732236382358 April 29th, 2026]
|@mxdys
|1104
|[https://wiki.bbchallenge.org/w/images/b/bf/BB6_holdouts_1104.txt BB6_holdouts_1104.txt]
|More reduction by equivalences
|-
|[[BB(4,3)]]
|[https://drive.google.com/drive/folders/1HBPZ17llVE_8wCy5FvRUFQ5MJsaYXAW- April 26th, 2026]
|@Andrew Ducharme
|5,641,006
|[https://drive.google.com/file/d/1z8oBXUECL5dpUNAIqik2z_yI5JGmW79t/view 4x3_holdouts_5641006.txt.zip]
|Work done by Andrew Ducharme
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1497651809773289552 April 25th, 2026]
|@mxdys
|1119
|[https://wiki.bbchallenge.org/w/images/a/ab/BB6_holdouts_1119.txt BB6_holdouts_1119.txt]
|Reduction by equivalences, one halting TM
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1486207538843222116 March 25th, 2026]
|@mxdys
|1161
|[https://wiki.bbchallenge.org/w/images/2/2a/BB6_holdouts_1161.txt BB6_holdouts_1161.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1477224991136419983 February 28th, 2026]
|@mxdys
|1214
|[https://wiki.bbchallenge.org/w/images/0/0e/BB6_holdouts_1214.txt BB6_holdouts_1214.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1473945366821998684 February 19th, 2026]
|@mxdys
|1226
|[https://wiki.bbchallenge.org/w/images/8/80/BB6_holdouts_1226.txt BB6_holdouts_1226.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1466438332677619956 January 29th, 2026]
|@mxdys
|1314
|[https://discord.com/channels/960643023006490684/1239205785913790465/1466438332677619956 BB6_holdouts_1314.txt]
|
|-
|[[BB(3,4)]]
|[https://drive.google.com/drive/folders/1pj0MJBCA1hk6NxSj0mYvu5iXbTtVRt64 December 31st, 2025]
|
|12,435,284
|[https://drive.google.com/file/d/15e-Lwl_F6Jn_HoYFPA2a94jLTjX1mmHd/view 3x4st10c_holdouts_12435284.txt]
|Work done by [[User:XnoobSpeakable|XnoobSpeakable]] and [[User:WarpedWartWars|Lúkos]].
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1455369448264568904 December 30th, 2025]
|@mxdys
|1326
|[https://wiki.bbchallenge.org/w/images/f/f0/BB6_holdouts_1326.txt BB6_holdouts_1326.txt]
|
|-
|[[BB(6)]]
|November 22nd, 2025
|Robin Rovenszky
|Variable
|[https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Google Sheets]
|Annotated list, including links to Discord discussions, always up-to-date.
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1450455364179857410 December 16th, 2025]
|@mxdys
|1343
|[https://wiki.bbchallenge.org/w/images/9/9a/BB6_holdouts_classified_1343.txt BB6_holdouts_1343.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1443989662019354647 November 28th, 2025]
|@mxdys
|1416
|[https://wiki.bbchallenge.org/w/images/9/98/BB6_holdouts_1416.txt BB6_holdouts_1416.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1438983076662477004 November 14th, 2025]
|@mxdys
|1534
|[https://wiki.bbchallenge.org/w/images/0/02/BB6_holdouts_1534.txt BB6_holdouts_1534.txt]
|
|-
|[[BB(4,3)]]
|[https://drive.google.com/drive/folders/1HBPZ17llVE_8wCy5FvRUFQ5MJsaYXAW- October 26th, 2025]
|
|9,401,447
|[https://drive.google.com/file/d/1r99v3dcdNTgGkmaydLKiZCp5KD3jGWeE/view 4x3_holdouts_9401447.txt.gz]
|
|-
|[[BB(7)]]
|[https://drive.google.com/drive/folders/1_lIqfvj4_J7WWl5LOBUp_pntoI99QYui October 25th, 2025]
|
|20,405,295
|[https://drive.google.com/file/d/12riXHC3Vz4tk_5mMV7__gZsF7hqAsZ_S/view bb7_holdouts_20405295.txt.gz]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1429892916763033601 October 20th, 2025]
|@mxdys
|1618
|[https://wiki.bbchallenge.org/w/images/e/e3/BB6_holdouts_1618.txt BB6 holdouts 1618.txt]
|
|-
|[[BB(4,3)]]
|[https://drive.google.com/drive/folders/1qNssnvK3W2jJ68VBq9FJZMy9TvwbQk4_ October 20th, 2025]
|@tjligocki
|18,138,027
|[https://drive.google.com/file/d/1vHufk09pI7JcTSAOj1XOzcZXJoX1Wa2a/view 4x3_holdouts_18138027.txt.gz]
|
|-
|[[BB(2,6)]]
|[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT October 6th, 2025]
|@tjligocki
|870,085
|[https://drive.google.com/file/d/1xZqEZFPke02pwBHX0EYsyDVaNU5o_OuO/view 2x6_holdouts_870085.txt.zip]
|Work done by Andrew Ducharme.
|-
|[[BB(3,4)]]
|[https://drive.google.com/drive/folders/1_5j19qrvo1q7jN_c0pYnjBOrIXAP6b7i October 4th, 2025]
|@tjligocki
|64,777,377
|[https://drive.google.com/file/d/1I3s3w-T4NPLn-eCdaZLPgC2Mya51pyvH/view?usp=drive_link 3x4_holdouts_64777377.txt.gz]
|Work done by [[User:XnoobSpeakable|XnoobSpeakable]] and [[User:WarpedWartWars|Lúkos]].
|-
|[[BB(7)]]
|[https://discord.com/channels/960643023006490684/1369339127652159509/1423806362072256676 October 4th, 2025]
|Andrew Ducharme
|22,721,168
|[https://drive.google.com/file/d/1xAFSPh6qAR8VxsF4QVipmdc0UpdPC1hn/view bb7_holdouts_22721168.txt.zip]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734 September 21, 2025]
|@mxdys
|1691
|[https://discord.com/channels/960643023006490684/1239205785913790465/1419290767767240734 BB6_holdouts_1691.txt]
|
|-
|[[BB(2,6)]]
|[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT September 16, 2025]
|
|970,101
|[https://drive.google.com/file/d/1Vjm3Qf-4a-Zr-E3EocjPWI5bjqH2YGil/view 2x6_holdouts_970101.txt.gz]
|Work done by Terry Ligocki
|-
|[[BB(2,6)]]
|[https://drive.google.com/drive/folders/1TsSpW27x3LBlu5qmk-cjzCJzgo_3ehyT September 12, 2025]
|
|20,358,011
|[https://drive.google.com/file/d/1YOoh4Zh2Jn5zaq9-C638S6VR_4jzd6pa/view 2x6_holdouts_20358011.zip]
|Work done by Andrew Ducharme
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1411308408220549140 August 30 2025]
|@mxdys
|2592
|[[:File:BB6 holdouts 2592.txt|BB6 holdouts 2592.txt]]
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1399783936019664896 July 29 2025]
|@mxdys
|2728
|[[:File:BB6 holdouts 2728.txt|BB6 holdouts 2728.txt]]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1393808719615361205 July 13, 2025]
|@mxdys
|2891
|[https://discord.com/channels/960643023006490684/1239205785913790465/1393808719615361205 BB6_holdouts_2891.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1390953522379489401 July 5, 2025]
|@mxdys
|3094
|[https://discord.com/channels/960643023006490684/1239205785913790465/1390953522379489401 BB6_holdouts_3094.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1384957116376158228 June 18, 2025]
|@mxdys
|3335
|[https://discord.com/channels/960643023006490684/1239205785913790465/1384957116376158228 BB6_holdouts_3335.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1259770421046411285/1355593937531961365 March 29 2025]
|@mxdys
|83
|[[:File:BB2x5 Coq holdouts 83.txt]]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1345246656769163284 March 1, 2025]
|@mxdys
|3571
|[https://discord.com/channels/960643023006490684/1239205785913790465/1345246656769163284 BB6_holdouts_3571.txt]
|
|-
|-
|[[BB(4,3)]]
|[[BB(4,3)]]
Line 69: Line 282:
|[https://discord.com/channels/960643023006490684/1239205785913790465/1310648046576730124 November 25, 2024 (@icy)]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1310648046576730124 November 25, 2024 (@icy)]
|@tjligocki
|@tjligocki
|4,319
|4319
|[https://docs.google.com/spreadsheets/d/1grhW_0neb2I8TfceN5-v70_3W42Z2U159r9L6FhPGf8/edit?usp=sharing Spreadsheet of holdouts]
|[https://docs.google.com/spreadsheets/d/1grhW_0neb2I8TfceN5-v70_3W42Z2U159r9L6FhPGf8/edit?usp=sharing Spreadsheet of holdouts]
|Keeping track of BB(6) progress - informal.
|Keeping track of BB(6) progress - informal.
Line 83: Line 296:
|[https://discordapp.com/channels/960643023006490684/1239205785913790465/1304303803213942846 November 8, 2024]
|[https://discordapp.com/channels/960643023006490684/1239205785913790465/1304303803213942846 November 8, 2024]
|@mxdys
|@mxdys
|4,408
|4408
|[[:File:BB6 holdouts 4408.txt|BB6_holdouts_4408.txt]]
|[[:File:BB6 holdouts 4408.txt|BB6_holdouts_4408.txt]]
|
|
Line 100: Line 313:
|[https://drive.google.com/file/d/1PLzN3wLw-MRgk1OFmYh4RTwNc30nflR7/view?usp=drive_link 3x4_holdouts_434787751.txt.gz]
|[https://drive.google.com/file/d/1PLzN3wLw-MRgk1OFmYh4RTwNc30nflR7/view?usp=drive_link 3x4_holdouts_434787751.txt.gz]
|[https://drive.google.com/drive/folders/1bZxl7jg5q9IVvHQNZwItx1kPusAWznZk?usp=drive_link Google Drive directory for 3x4 TMs]
|[https://drive.google.com/drive/folders/1bZxl7jg5q9IVvHQNZwItx1kPusAWznZk?usp=drive_link Google Drive directory for 3x4 TMs]
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1297163115179278336 October 19, 2024]
|@mxdys
|4521
|[https://discord.com/channels/960643023006490684/1239205785913790465/1297163115179278336 BB6_holdouts_4521.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1287580515938865225 September 23, 2024]
|@mxdys
|4741
|[https://discord.com/channels/960643023006490684/1239205785913790465/1287580515938865225 BB6_holdouts_4741.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1282002734912110655 September 7, 2024]
|@mxdys
|4986
|[https://discord.com/channels/960643023006490684/1239205785913790465/1282002734912110655 BB6_holdouts_4986.txt]
|
|-
|-
|[[BB(6)]]
|[[BB(6)]]
Line 114: Line 348:
|[[:File:BB6 holdouts 5877.txt]]
|[[:File:BB6 holdouts 5877.txt]]
|
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1267013907910758451 July 28, 2024]
|@mxdys
|6417
|[https://discord.com/channels/960643023006490684/1239205785913790465/1267013907910758451 BB6_holdouts_6417.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1262276904887521300 July 15, 2024]
|@mxdys
|7013
|[https://discord.com/channels/960643023006490684/1239205785913790465/1262276904887521300 BB6_holdouts_7013.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1262126923321180250 July 14, 2024]
|@Justin Blanchard
|7255
|[https://discord.com/channels/960643023006490684/1239205785913790465/1262126923321180250 BB6_holdouts_7255.txt]
|Work done by Justin Blanchard
|-
|-
|[[BB(6)]]
|[[BB(6)]]
Line 120: Line 375:
|7296
|7296
|[[:File:BB6 holdouts 7296.txt]]
|[[:File:BB6 holdouts 7296.txt]]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1259011186192552068 July 6, 2024]
|@Justin Blanchard
|7430
|[https://discord.com/channels/960643023006490684/1239205785913790465/1259011186192552068 BB6_holdouts_7430.txt]
|Work done by Justin Blanchard
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1258810921879605298 July 5, 2024]
|@mxdys
|7449
|[https://discord.com/channels/960643023006490684/1239205785913790465/1258810921879605298 BB6_holdouts_7449.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1256254912573079572 June 28, 2024]
|@mxdys
|9366
|[https://discord.com/channels/960643023006490684/1239205785913790465/1256254912573079572 BB6_holdouts_9366.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1254684723955896362 June 24, 2024]
|@Justin Blanchard
|9853
|[https://discord.com/channels/960643023006490684/1239205785913790465/1254684723955896362 BB6_holdouts_9853.txt]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1253478694798884934 June 21, 2024]
|@mxdys
|10,020
|[https://discord.com/channels/960643023006490684/1239205785913790465/1253478694798884934 BB6_holdouts_10020.txt]
|Work done by Justin Blanchard
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1253466035189846056 June 20, 2024]
|@mxdys
|10,944
|[https://discord.com/channels/960643023006490684/1239205785913790465/1253466035189846056 BB6_holdouts_10944.txt]
|
|
|-
|-
Line 126: Line 423:
|@mxdys
|@mxdys
|217
|217
|File
|[[:File:2x5_holdouts_217.txt]]
|273 holdouts minus machines solved by CTL
|273 holdouts minus machines solved by CTL
|-
|-
Line 163: Line 460:
|
|
|'''BB(5) is SOLVED!'''
|'''BB(5) is SOLVED!'''
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1245116022873264129 May 28, 2024]
|@mxdys
|18,560
|[https://discord.com/channels/960643023006490684/1239205785913790465/1245116022873264129 BB6_holdouts_18560.txt]
|
|-
|-
|[[BB(2,5)]]
|[[BB(2,5)]]
Line 169: Line 473:
|499
|499
|[[:File:2x5.todo.txt]]
|[[:File:2x5.todo.txt]]
|
|-
|[[BB(6)]]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1239628496184279080 May 13, 2024]
|@mxdys
|35,788
|[https://discord.com/channels/960643023006490684/1239205785913790465/1239628496184279080 BB6_holdouts_35788.txt]
|C++ version of the deciders from [[Coq-BB5]] ran on Shawns 181,851 holdouts<ref>https://discord.com/channels/960643023006490684/1239205785913790465/1239275863699361813</ref>
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1233154495635259543 April 25, 2024]
|@Justin Blanchard
|920
|[https://discord.com/channels/960643023006490684/1084047886494470185/1233154495635259543 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1232667326126489710 April 24, 2024]
|@Justin Blanchard
|1045
|[https://discord.com/channels/960643023006490684/1084047886494470185/1232667326126489710 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1231941302975987844 April 22, 2024]
|@Justin Blanchard
|1588
|[https://discord.com/channels/960643023006490684/1084047886494470185/1231941302975987844 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230737657076650066 April 19, 2024]
|@Justin Blanchard
|1835
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230737657076650066 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230491507287523409 April 18, 2024]
|@Justin Blanchard
|1921
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230491507287523409 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230132897583857756 April 17, 2024]
|@Justin Blanchard
|2354
|[https://discord.com/channels/960643023006490684/1084047886494470185/1230132897583857756 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1229770471898087506 April 16, 2024]
|@Justin Blanchard
|2438
|[https://discord.com/channels/960643023006490684/1084047886494470185/1229770471898087506 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1229406059274305546 April 15, 2024]
|@Justin Blanchard
|2564
|[https://discord.com/channels/960643023006490684/1084047886494470185/1229406059274305546 2x5.todo.txt]
|
|-
|[[BB(2,5)]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1228351493745152083 April 12, 2024]
|@Justin Blanchard
|3364
|[https://discord.com/channels/960643023006490684/1084047886494470185/1228351493745152083 2x5.todo.txt]
|
|
|-
|-
Line 190: Line 564:
|2,417
|2,417
|[[:File:2023 06 07.3x3.holdouts 2417.txt]]
|[[:File:2023 06 07.3x3.holdouts 2417.txt]]
|
|-
|[[BB(5)]]
|[https://skelet.ludost.net/bb/nreg.html circa May 13th, 2003]
|Georgi Georgiev (Skelet)
|43
|[https://bbchallenge.org/skelet List of 43 holdouts]
|
|
|-
|-
Line 212: Line 579:
|[https://drive.google.com/file/d/14bDnBt0OwuHATFBiubc_5jub0220EyXf/view?usp=drive_link 6x2.holdouts_1458704.txt.gz]
|[https://drive.google.com/file/d/14bDnBt0OwuHATFBiubc_5jub0220EyXf/view?usp=drive_link 6x2.holdouts_1458704.txt.gz]
|This was posted to the BBChallenge Forum (before Discord)
|This was posted to the BBChallenge Forum (before Discord)
|-
|[[BB(5)]]
|[https://skelet.ludost.net/bb/nreg.html circa May 13th, 2003]
|Georgi Georgiev (Skelet)
|43
|[https://bbchallenge.org/skelet List of 43 holdouts]
|
|}
|}
Georgi Georgiev (Skelet) posted [https://skelet.ludost.net/bb/nreg.html a list of 43 holdouts] for BB(5) in 2003. bbchallenge.org successfully reduced the number of holdouts for BB(5) to zero in June 2024.


== Verifiable Holdout Lists ==
== Busy Beaver adjacent holdouts lists ==
=== BB(3,3) ===
 
=== Beeping Busy Beaver ===
{| class="wikitable sortable"
{| class="wikitable sortable"
|+
|+
!Domain
!Date
!Date
!Shared by
!Shared by
!Number of holdouts
!Number of holdouts
!Holdout TMs
!File
!Decided TMs
!Notes
!Notes
|-
|-
|[https://discord.com/channels/960643023006490684/1259770474897080380/1333364755011731456 January 27, 2025]
|BBB(4)
|@tjligocki
|[https://discord.com/channels/960643023006490684/1385498968011575366/1387585253928992831 June 26, 2025]
|367
|@mxdys
|[[:File:3x3.unk.sort.txt|3x3.unk.sort.txt]]
|3713
|For halting and infinte TMs see [https://drive.google.com/drive/folders/101U9htddFdE889agAZnU58VLgQJlfn0v?usp=drive_link Google Drive directory for 3x3 TMs]
|[https://wiki.bbchallenge.org/w/images/6/62/BBB4_holdouts_3713.txt BBB4_holdouts_3713.txt]
|Initial pass at generating a verified holdout list using software from [https://github.com/sligocki/busy-beaver Shawn's BB Github]. See [https://docs.google.com/spreadsheets/d/1PU386wH1wcOpSAhU5BjJqkub7YJv5cRQ/edit?usp=drive_link&ouid=101141952239004788549&rtpof=true&sd=true spreadsheet]. This a subset of the holdouts generated by @sligocki below.
|
|}
 
=== Reversible Turing machines ===
{| class="wikitable sortable"
|+
!Domain
!Date
!Shared by
!Number of holdouts
!File
!Notes
|-
|BBrev(6)
|[https://discord.com/channels/960643023006490684/1239205785913790465/1400313138611490897 July 31, 2025]
|@Sligocki
|388
|[https://wiki.bbchallenge.org/w/images/8/86/BBrev6_holdouts_388.txt BBrev6_holdouts_388.txt]
|
|-
|BBrev(6)
|[https://discord.com/channels/960643023006490684/1239205785913790465/1400253700986900692 July 31, 2025]
|@Sligocki
|409
|[https://discord.com/channels/960643023006490684/1239205785913790465/1400253700986900692 BBrev6_holdouts_409.txt]
|
|}
 
=== Instruction-limited Busy Beaver ===
{| class="wikitable sortable"
|+
!Domain
!Date
!Shared by
!Number of holdouts
!File
!Notes
|-
|BBi(8)
|[https://discord.com/channels/960643023006490684/1084047886494470185/1425234398919266405 October 7, 2025]
|@Shawn Ligocki
|348
|[https://discord.com/channels/960643023006490684/1084047886494470185/1425234398919266405 bbi8_holdouts_348.txt]
|
|-
|BBi(8)
|[https://discord.com/channels/960643023006490684/1084047886494470185/1424786698537271347 October 6, 2025]
|@Peacemaker II
|441
|[https://discord.com/channels/960643023006490684/1084047886494470185/1424786698537271347 BBi8_holdouts_441.txt]
|
|}
 
=== Fractran ===
{| class="wikitable sortable"
|+
!Domain
!Date
!Shared by
!Number of holdouts
!File
!Notes
|-
|BBf(22)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1464873923647639703 January 25, 2026]
|@-d
|2003
|[https://github.com/int-y1/BBFractran/blob/main/holdout/sz22_2003_unofficial.txt sz22_2003_unofficial.txt]
|Result of the beeping permutation decider being run on sz22_5682.txt
|-
|BBf(21)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1464873923647639703 January 25, 2026]
|@-d
|140
|[https://github.com/int-y1/BBFractran/blob/main/holdout/sz21_140_unofficial.txt sz21_140_unofficial.txt]
|Result of the beeping permutation decider being run on sz21_345.txt
|-
|BBf(21)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1463862950203887811 January 22, 2026]
|@-d
|143
|[https://discord.com/channels/960643023006490684/1438019511155691521/1463862950203887811 sz21_143_workinprogress.txt]
|
|-
|BBf(22)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1456498841334317210 January 2, 2026]
|@-d
|5682
|[https://github.com/int-y1/BBFractran/blob/main/holdout/sz22_5682.txt sz22_5682.txt]
|
|-
|BBf(21)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1456498841334317210 January 2, 2026]
|@-d
|345
|[https://github.com/int-y1/BBFractran/blob/main/holdout/sz21_345.txt sz21_345.txt]
|
|-
|BBf(21)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1450186358474936533 December 15, 2025]
|@Sligocki
|394
|[https://discord.com/channels/960643023006490684/1438019511155691521/1450186358474936533 sz21_394.txt]
|
|-
|BBf(20)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1450186358474936533 December 15, 2025]
|@Sligocki
|6
|[https://discord.com/channels/960643023006490684/1438019511155691521/1450186358474936533 sz20_6.txt]
|BBf(20) has since been solved
|-
|BBf(22)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1449536000098308236 December 13, 2025]
|@Sligocki
|10441
|[https://discord.com/channels/960643023006490684/1438019511155691521/1449536000098308236 sz22_10441.txt]
|17 known halters are removed
|-
|BBf(22)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448806255261913199 December 11, 2025]
|@Sligocki
|10458
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448806255261913199 sz22_10457.txt]
|Known halters are removed
|-
|BBf(22)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448729669263163596 December 11, 2025]
|@dyuan01
|11130
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448729669263163596 message.txt]
|
|-
|BBf(22)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1448214077028569098 December 10, 2025]
|@-d
|91123
|[https://raw.githubusercontent.com/int-y1/BBFractran/refs/heads/main/holdout/sz22_91123.txt sz22_91123.txt]
|Initial enumeration
|-
|BBf(21)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1439799813758648421 November 17, 2025]
|@Sligocki
|760
|[https://discord.com/channels/960643023006490684/1438019511155691521/1439799813758648421 sz21_760.txt]
|23 halting machines are removed
|-
|BBf(21)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1439725735211303003 November 16, 2025]
|@dyuan01
|783
|[https://discord.com/channels/960643023006490684/1438019511155691521/1439725735211303003 message.txt]
|
|-
|BBf(20)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1438560626329784321 November 13, 2025]
|@dyuan01
|279
|[https://discord.com/channels/960643023006490684/1438019511155691521/1438560626329784321 message.txt]
|
|-
|BBf(20)
|[https://discord.com/channels/960643023006490684/1438019511155691521/1438483146864590900 November 13, 2025]
|@-d
|902
|[https://discord.com/channels/960643023006490684/1438019511155691521/1438483146864590900 sz20_902.txt]
|
|}
 
=== Terminating Turmites ===
{| class="wikitable sortable"
|+
!Domain
!Date
!Shared by
!Number of holdouts
!File
!Notes
|-
|TT(2,4)
|[https://discord.com/channels/960643023006490684/1243312334907375676/1400609116103118870 August 1, 2025]
|@creeperman7002
|2298
|[https://discord.com/channels/960643023006490684/1243312334907375676/1400609116103118870 holdout_2x4_2298.txt]
|
|-
|TT(4)
|[https://discord.com/channels/960643023006490684/1243312334907375676/1393363926871310508 July 12, 2025]
|@creeperman7002
|99
|[https://discord.com/channels/960643023006490684/1243312334907375676/1393363926871310508 holdout4x2.txt]
|
|}
 
=== Busy Beaver for Lambda Calculus ===
{| class="wikitable sortable"
|+
!Domain
!Date
!Shared by
!Number of holdouts
!File
!Notes
|-
|BBλ(39)
|[https://discord.com/channels/960643023006490684/1355653587824283678/1492187654429868062 April 10, 2026]
|@Sligocki
|Variable (49)
|[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=1717120706#gid=1717120706 Spreadsheet]
|
|-
|BBλ(38)
|[https://discord.com/channels/960643023006490684/1355653587824283678/1362975027154129056 April 19, 2025]
|@Sligocki
|0
|[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=563816005#gid=563816005 Spreadsheet]
|'''BBλ(38) was solved on April 13th, 2026'''
|-
|BBλ(37)
|[https://discord.com/channels/960643023006490684/1243312334907375676/1354938497848443032 March 27, 2025]
|@Racheline
|92
|[https://docs.google.com/spreadsheets/d/1yoiez7lDjZ-vRzj8NFWKWOxGlkK9IE_KWMUjeSWYWkw/edit?gid=0#gid=0 BBλ(37) 92 holdouts progress]
|BBλ(37) has since been solved
|-
|-
|[https://discord.com/channels/960643023006490684/1084047886494470185/1116351783040716830 June 8, 2023]
|BBλ(37)
|@Iijil
|[https://discord.com/channels/960643023006490684/1243312334907375676/1354421317792694292 March 26, 2025]
|925
|@Racheline
|[[:File:2023 06 08.3x3.holdouts intersect sligocki iijil 925.txt]]
|216
|Derived from TMs in the holdouts generated by @sligocki and @Iijil, see below.
|[https://discord.com/channels/960643023006490684/1243312334907375676/1354421317792694292 BBL(37)_216.txt]
|Intersection of @sligocki and @Iijil from below.
|
|-
|-
|[https://discord.com/channels/960643023006490684/1084047886494470185/1116351783040716830 June 8, 2023]
|BBλ(37)
|@Iijil
|[https://discord.com/channels/960643023006490684/1243312334907375676/1354398010527711345 March 26, 2025]
|2,480
|@Racheline
|[[:File:2023 06 08.3x3.holdouts iijil 2380.txt]]
|278
|Unknown
|[https://discord.com/channels/960643023006490684/1243312334907375676/1354398010527711345 BBL2(37)_278.txt]
|Still gathering information on how this was generated.
|
|-
|-
|[https://discord.com/channels/960643023006490684/1084047886494470185/1116178334620070000 June 7, 2023]
|BBλ(37)
|@sligocki
|[https://discord.com/channels/960643023006490684/1243312334907375676/1354355688763031616 March 26, 2025]
|2,417
|@Sam
|[[:File:2023 06 07.3x3.holdouts 2417.txt]]
|317
|Unknown
|[https://discord.com/channels/960643023006490684/1243312334907375676/1354355688763031616 BBL2(37)_317.txt]
|Initial pass at generating a verified holdout using software from [https://github.com/sligocki/busy-beaver Shawn's BB Github].
|
|-
|-
|BBλ(37)
|[https://discord.com/channels/960643023006490684/1243312334907375676/1354352262562189344 March 26, 2025]
|@Sam
|333
|[https://discord.com/channels/960643023006490684/1243312334907375676/1354352262562189344 BBL(37).txt]
|
|}
|}
== References ==

Revision as of 17:51, 29 April 2026

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 1104 17,823,260
3-symbol 0 4 5,641,006
4-symbol 0 12,435,284
5-symbol 66
6-symbol 536,112

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) 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 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[1]
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(39) April 10, 2026 @Sligocki Variable (49) Spreadsheet
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

References

  1. ↑ https://discord.com/channels/960643023006490684/1239205785913790465/1239275863699361813
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