Prime numbers of the form $[{\mathbf{n}}^{\mathbf{c}}\mathbf{ta}{\mathbf{n}}^{\theta }(\mathbf{logn})]$

Abstract

Let $[\cdot ]$ be the floor function. In the present paper we prove that when $1<c<\frac{12}{11}$ and $\theta >1$ is a fixed, then there exist infinitely many prime numbers of the form $[n^c{\tan }^{\theta }(\log n)]$.