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Quotients of primes. (English) Zbl 0777.11001
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.

11A41 Primes
11B05 Density, gaps, topology
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