User:XnoobSpeakable/Holdouts-temp

The top table may or may not match the one found at Holdouts lists depending on the timing of when these lists get updated. I will keep track of the list on this page seperately. The bottom list will include unfinished work that I have noticed on Discord that will not be in other wiki pages.

Number of holdouts (latest exact counts)

	2-state	3-state	4-state	5-state	6-state	7-state
2-symbol	0	0	0	0	1691*	23,314,388
3-symbol	0	6***	97,701,052
4-symbol	0	434,787,751
5-symbol	75
6-symbol	873,469

*The 1691 holdouts are based on equivalence classes. The amount of individual unsolved TMs in TNF is currently 3171. The holdouts for every other entry use the unsolved TNF TM count as well.

Number of holdouts (in-progress and approximate values)

	2-state	3-state	4-state	5-state	6-state	7-state
2-symbol	0	0	0	0	1689* / 3169*	23,314,388
3-symbol	0	6***	88,914,343
4-symbol	0	<434,787,751**
5-symbol	75
6-symbol	873,469

**I am currently working on BB(3,4) and have removed some holdouts, however, the partial progress has not been merged and the reduction has not been counted.

After the work is done, I will upload my results and update the value in the table. I suspect a reduction to ~65M will be achievable.

Said work was supposed to be done by the end of this week as I am typing (which is tomorrow, 2025-09-28), however, I have delayed it to the end of next week, which is 2025-10-05 to those reading in the future.

Other technicalities:

***This addendum applies to both tables. For BB(3,3), the most commonly accepted value is 6 holdouts, however, there are other values that I want to highlight in the table below:

BB(3,3) holdouts	Unproven	Proven
By TNF	6	10
By Equivalence Classes	4	Not Applied Yet.