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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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    The way you worded your question makes it, imo, highly unclear. It seems to be telling that every irreducible fraction can be written as the quotient of two prime numbers, yet I think you meant that you want to look at the set of all fractions formed with primes numbers. Am I right?2012-12-10
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    IMHO it is a good, clear question: is the set of all fractions of the form $m/n$ where both $m$ and $n$ are prime numbers dense in the $\mathbb{R}_+$ ?2012-12-10
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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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