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We know a positive rational number can be uniquely written as $m/n$ where $m$ and $n$ are coprime positive integers. Particularly, we can pick out those numbers with $m$ and $n$ both prime.

The question is, is the collection of all such numbers dense on the positive half of the real line?

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    It is settled down here http://mathoverflow.net/questions/117191/using-quotient-of-prime-numbers-to-approximation-reals2013-06-14

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