Answers to Two Questions Concerning Quotients of Primes

Abstract

We will consider some open questions concerning quotients of primes posed in [1] by D. Hobby and D. M. Silberger. Corollary 3 of this note will solve Open Problem 2 of their paper, and our Theorem 1 represents some progress on their Open Problem 1. 1R+ and N denote, as usual, the set of all positive real numbers and the set of all positive integers (0 excluded). If S c , we indicate with F(S) the set of all quotients p/q for which {p, q} C S and p + q; so, for instance, F(N) -Q+-{1}, where 0+ represents the set of all positive rational numbers (0 excluded). Open Problem One is: