Determination of the fifth Busy Beaver value — mentioned by tsterin

Wed, 17 Sep 2025 14:03:24 GMT

Number of 5-state TMs is 21^10 = 16,679,880,978,201; coming from (1 + writemovestate)^2*state; difference with your formula is that in our model, halting is encoded using undefined transition. "essentially different" is not a statically-checked property. It is discovered by the enumeration algorithm (Tree Normal Form, see Section 3 of https://arxiv.org/pdf/2509.12337); in particular, for each machine, the algorithm needs to know it if will ever reach an undefined transition because if it does it will visit the children of that machine (i.e. all ways to set that reached undefined transition).…

Paper and discussion history. A mention is not an endorsement.

Determination of the fifth Busy Beaver value — HN submission

Wed, 17 Sep 2025 10:26:18 GMT

Determination of the fifth Busy Beaver value

288 points; 116 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Determination of the fifth Busy Beaver value · HackerPapers discussions

Determination of the fifth Busy Beaver value — mentioned by tsterin

Determination of the fifth Busy Beaver value — HN submission