The automaticity of the set of primes
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909307519369216 |
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| author | Dubbe, Thomas |
| author_facet | Dubbe, Thomas |
| contents | The automaticity $A(x)$ of a set $\mathcal{X}$ is the size of the smallest automaton that recognizes $\mathcal{X}$ on all words of length $\leq x$. We show that the automaticity of the set of primes is at least $x\exp\left(-c(\log\log x)^2\log\log\log x\right)$, which is fairly close to the maximal automaticity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The automaticity of the set of primes Dubbe, Thomas Number Theory 11B85, 11N36 The automaticity $A(x)$ of a set $\mathcal{X}$ is the size of the smallest automaton that recognizes $\mathcal{X}$ on all words of length $\leq x$. We show that the automaticity of the set of primes is at least $x\exp\left(-c(\log\log x)^2\log\log\log x\right)$, which is fairly close to the maximal automaticity. |
| title | The automaticity of the set of primes |
| topic | Number Theory 11B85, 11N36 |
| url | https://arxiv.org/abs/2409.04314 |