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arXiv:2407.02426math.CO

Skelet #17 and the fifth Busy Beaver number

Chris Xu

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Abstract

We prove nonhalting of the Turing machine dubbed "Skelet #17", known to be one of the toughest 5-state, 2-symbol Turing machines to analyze. Combined with the efforts of The Busy Beaver Challenge, we are therefore able to show that BB(5), the fifth Busy Beaver number, equals 47,176,870.

arXiv comments
added more references, fixed a broken link, and streamlined Proposition 3.4
Journal reference
DOI
Subjects
math.COCombinatorics math.LOLogic

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  1. BusyBeaver(6) Is Quite Large 1 comment

    • While that question depends on what you count as an 'enumeration', there's the related question of "What's the richest logic that cannot prove the halting status of all 5-state TMs?" That is, what's the richest logic that some 5-state TM's halting status is independent of? I've…

      LegionMammal978View on HNParent context

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