Let $$\Bbb P$$ be the set of all primes, the set

$\{\sin p \mid p\in\Bbb P\}$

is dense  in $$[-1,1]$$.

This problem appeared in artofproblemsolving  on 22 May 2004, and  has been solved in a french math forum. The solution used tools as Fourier analysis, Vinogradov’s theorem, Erdos-Turan inequality and many others things.

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