Abstract
Let \(c \geq 2\) be any fixed real number. Matomäki [4] inverstigated the set of \(A > 1\) such that the integer part of \( A^{c^k}\) is a prime number for every \(k \in \mathbb{N}\). She proved that the set is uncountable, nowhere dense, and has Lebesgue measure 0. In this article, we show that the set has Hausdorff dimension 1.
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The author would like to thank the referee for finding mistakes and giving useful comments.
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This work was supported by JSPS KAKENHI Grant Number JP19J20878.
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Saito, K. Prime-representing functions and Hausdorff dimension. Acta Math. Hungar. 165, 203–217 (2021). https://doi.org/10.1007/s10474-021-01170-6
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DOI: https://doi.org/10.1007/s10474-021-01170-6