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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.

##### MSC:
 11A41 Primes 11B05 Density, gaps, topology
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