The number of rationals determined by large sets of sifted integers (Q2106892)

Let \(\mathcal{H}\) be the set of shifted primes \(p-1\), where \(p\) is a prime such \(p+1\) is a sum of two coprime squares. In the paper under review, the author estimates the number of fractions \(h_1/ h_2\) of integers \(h_1, h_2\) belonging to a subset of \(\mathcal{H}\cap [1,X]\). As a corollary, he estimates the number of fractions of the form \((p_1-1)/(p_2-1)\), where \(p_1\) and \(p_2\) belong to the sequence of primes \(p\leq X\) satisfying \(\|p\pi\|\leq\eta\) for some fixed \(\eta\in(0,1)\).