On the $\mathcal{A}$-transcendence of a Champernowne-type constant

Abstract

Let $p_n$ denote the $n$-th prime. We prove that for every nonzero polynomial $f(x)\in \mathbb{Z}[x]$, there exist infinitely many positive integers $n$ such that $p_n\nmid f(n)$.

arXiv comment5 pages, to appear in the Canadian Mathematical Bulletin