Jun 202012

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.