On the A A script upper A-transcendence of a Champernowne-type constant

Let p n pₙ p Subscript n denote the n th prime. We prove that, for every nonzero polynomial f ( x ) ∈ Z [ x ] f(x)∈ Z[x] f left parenthesis x right parenthesis element of double struck upper Z left bracket x right bracket , there exist infinitely many positive integers n such that p n ∤ f ( n ) pₙ f(n) p Subscript n Baseline does not divide f left parenthesis n right parenthesis .