素数集的自动性

arXiv - MATH - Number Theory Pub Date : 2024-09-06 DOI:arxiv-2409.04314

Thomas Dubbe

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摘要

一个集合$\mathcal{X}$的自动性$A(x)$是在所有长度为$\leq x$的词上识别$\mathcal{X}$的最小自动机的大小。我们可以看到，素数集的自动性至少是$x/exp/left(-c(\log/log x)^2\log\log x\right)$ ，这与最大自动性相当接近。

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The automaticity of the set of primes

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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arXiv - MATH - Number Theory

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