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arXiv · 2409.04314

The automaticity of the set of primes

Thomas Dubbe
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Abstract

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.

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Thomas Dubbe. 2024-09-06. The automaticity of the set of primes. https://arxiv.org/abs/2409.04314

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