On the subsequence of primes having prime subscripts

Abstract

We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimates for its counting function. We obtain bounds for the weighted gaps between elements of the subsequence and show that for every positive integer m there is an integer arithmetic progression (an+b : n ∈ ℕ) with at least m of the (qn) satisfying qn = an+b.