Infinitude of Primes
A one-line proof

$\displaystyle0\lt\prod_{p}\sin \left(\frac{\pi}{p}\right)=\prod_{p}\sin \left(\pi\frac{1+2\displaystyle\prod_{p'}p'}{p}\right)=0.$

(There is a great video, explaining the above formula.)

Reference

  1. S. Northshield, A One-Line Proof of the Infinitude of Primes, Am Math Monthly Volume 122, Number 5, May 2015, pp. 466-466(1)
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