Sunt testimonia primi numeri in infinitum per - the well-known Euclides Restitutus conclusio ex Libro Elementa, non defuit utique ullo basic doctrina numerus. In American Vestibulum Mathematica (issue CXXII) in MMXV Sam Northshield published in contradictio Non minus venusta forma una-probationem in liner, quo non vis prohibere poterit quin (with brief comments).
$$0 < \prod_{p} \sin \underbrace{ \left( \frac{\pi}{p} \right) }_{ < \pi, \text{ da } p > 1 } = \prod_{p} \sin \left( \frac{\pi}{p} + 2 \pi \underbrace{ \frac{ \prod_{p'} p' }{p} }_{ \in \mathbb{N} } \right) = \prod_{p} \sin \left( \pi \underbrace{ \frac{ 1 + 2 \prod_{p'} p' }{p} }_{ \in \mathbb{N}, \text{ da } \left( 1 + 2 \prod_{p'} p' \right) \notin \mathbb{P} } \right) = 0$$