Measuring Decidability as Related to Busy Beaver Numbers
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910237164830720 |
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| author | Tandi, Gurpreet Gonzalez-Hendrix, Josue Brown, Jonathan |
| author_facet | Tandi, Gurpreet Gonzalez-Hendrix, Josue Brown, Jonathan |
| contents | The theoretical existence of Busy Beaver numbers provides a new notion for decidability and corresponding heuristic for conjectures. The minimum number of states in which a conjecture can be modeled gives a classification of what logic system can describe said conjecture. In this work, we construct explicit Turing machines that search for a solution to Brocard's problem greater than 7 and a Fermat prime beyond the 4th which halt if and only if such a solution exists. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_20215 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Measuring Decidability as Related to Busy Beaver Numbers Tandi, Gurpreet Gonzalez-Hendrix, Josue Brown, Jonathan Computational Complexity Logic in Computer Science Logic Number Theory The theoretical existence of Busy Beaver numbers provides a new notion for decidability and corresponding heuristic for conjectures. The minimum number of states in which a conjecture can be modeled gives a classification of what logic system can describe said conjecture. In this work, we construct explicit Turing machines that search for a solution to Brocard's problem greater than 7 and a Fermat prime beyond the 4th which halt if and only if such a solution exists. |
| title | Measuring Decidability as Related to Busy Beaver Numbers |
| topic | Computational Complexity Logic in Computer Science Logic Number Theory |
| url | https://arxiv.org/abs/2605.20215 |