an:00178995
Zbl 0777.11001
Hobby, David; Silberger, D. M.
Quotients of primes
EN
Am. Math. Mon. 100, No. 1, 50-52 (1993).
0002-9890
1993
j
11A41 11B05
quotients of prime numbers between two given real numbers; dense subsets
The motivation of this interesting paper is the answer given to the following problem: Given \(\{a,b\}\) real numbers such that \(a<b\) does there exist primes \(p\), \(q\) such that \(a<p/q<b\)? In the main result the authors prove that the set of quotients of the form \(p/q\), with \(p\), \(q\) primes, \(p\neq q\), is dense in \(\mathbb R^ +\). The proof is based on Bertrand's postulate and the prime number theorem. The paper also contains other results about dense subsets in \(\mathbb R^ +\). The authors propose two open problems.
D.Ştefănescu (Bucureşti)