Holdouts lists

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 deciders are unable to decide.

Holdout lists are often shared by contributors. Here is a table that summarises the number of holdout per busy beaver domain:

Number of holdouts

	2-state	3-state	4-state	5-state	6-state
2-symbol	0	0	0	0	4408
3-symbol	0	6
4-symbol	0	434,787,751
5-symbol	273
6-symbol	22,302,296

Downloadable lists

BB space	Date	Shared by	Number of holdouts	File	Notes
BB(4,3)	December 21, 2024	@tjligocki	434,787,751	4x3_holdouts_460916384.txt.gz	Google Drive directory for 4x3 TMs
BB(6)	November 25, 2024 (@icy)	@tjligocki	4,319	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	4,408	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)	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 6, 2024	@mxdys	7296	File:BB6 holdouts 7296.txt
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 13th 2024	@tjligocki	12,091	File:BB6 holdouts 12091.txt	Work done with @Shawn Ligocki
BB(3,3)	June 9th 2024	@Justin Blanchard	22	File:3x3.todo.txt, File:Mugshots small.pdf
BB(6)	June 7th 2024	@mxdys	12,325	File:BB6 holdouts 12325.txt	Some equivalent machines are removed.
BB(2,5)	May 22nd 2024	@Justin Blanchard	499	File:2x5.todo.txt
BB(5)			0

Georgi Georgiev (Skelet) posted 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.