Thread 'There are only finitely many primes' I just saw this one. If there are finitely many primes, then ##0<\prod_{p}\sin(\frac\pi p)=\prod_p\sin\left(\frac{\pi(1+2\prod_q q)}p\right)=0## Of course it is in a way just a variation of Euclid's idea, but it is a one liner. View full post »
I just saw this one. If there are finitely many primes, then ##0<\prod_{p}\sin(\frac\pi p)=\prod_p\sin\left(\frac{\pi(1+2\prod_q q)}p\right)=0## Of course it is in a way just a variation of Euclid's idea, but it is a one liner.