Kukho ubungqina obuninzi bokungabikho kwamanani aphambili- i- theorem eyaziwayo ye- Euclid evela kwiNcwadi yeZinto ayilahlekanga nakweyiphi na ikhosi yeenqobo ezisisiseko. KwiAmerican Mathematical Monthly (khupha i-122) ngo-2015 uSam Northshield wapapasha ubungqina obuphantsi obunobunkunkqele ngohlobo lomgca omnye, endingafuni ukukubamba (ngamagqabantshintshi).
$$0 < \prod_{p} \sin \underbrace{ \left( \frac{\pi}{p} \right) }_{ < \pi, \text{ da } p > 1 } = \prod_{p} \sin \left( \frac{\pi}{p} + 2 \pi \underbrace{ \frac{ \prod_{p'} p' }{p} }_{ \in \mathbb{N} } \right) = \prod_{p} \sin \left( \pi \underbrace{ \frac{ 1 + 2 \prod_{p'} p' }{p} }_{ \in \mathbb{N}, \text{ da } \left( 1 + 2 \prod_{p'} p' \right) \notin \mathbb{P} } \right) = 0$$