Holdouts lists: Difference between revisions

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Updated BB(6), BB(4,3) and BBlambda(42) holdout counts
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Updated BB(6) and BBlambda(42) holdout counts
 
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|[https://discord.com/channels/960643023006490684/1239205785913790465/1543436534831906926 August 30th, 2026]
|@mxdys
|1003
|[https://wiki.bbchallenge.org/w/images/e/e0/BB6_holdouts_1003.txt BB6_holdouts_1003.txt]
|-
|-
|[https://discord.com/channels/960643023006490684/1239205785913790465/1538109685033607198 August 15th, 2026]
|[https://discord.com/channels/960643023006490684/1239205785913790465/1538109685033607198 August 15th, 2026]
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|[https://discord.com/channels/960643023006490684/1355653587824283678/1517130491512492083 June 18, 2026]
|[https://discord.com/channels/960643023006490684/1355653587824283678/1517130491512492083 June 18, 2026]
|@C++DSucker
|@C++DSucker
|Variable (207)
|Variable (158)
|[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=1544675322#gid=1544675322 Spreadsheet]
|[https://docs.google.com/spreadsheets/d/1jZ6TK9m3xmXUlC69727T-8WwvhALcsp8FrK6DzgThtw/edit?gid=1544675322#gid=1544675322 Spreadsheet]
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Latest revision as of 09:34, 31 August 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 1003 15,743,264
3-symbol 0 4 4,720,332
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
August 30th, 2026 @mxdys 1003 BB6_holdouts_1003.txt
August 15th, 2026 @mxdys 1016 BB6_holdouts_1016.txt
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[1]
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 Programs simulated to halting were removed
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(3,3) August 11, 2026 @creeperman7002 19368 3x3_holdouts_19368.txt
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 (158) 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.

References

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