Prime-representing functions and Hausdorff dimension.

Let c ≥ 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 ∈ 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. [ABSTRACT FROM AUTHOR]