Siji baris kanggo tanpa wates nomer prima

Ana akeh bukti babagan tanpa wates nomer prima - teorema Euclid sing kondhang saka Book of Elemen ora ilang ing kursus teori nomer dhasar. Ing Bulanan Matematika Amerika (Masalah 122) ing taun 2015, Sam Northshield nerbitake bukti kontradiksi sing ora kalah apik kanthi wujud garis siji, sing ora pengin ditahan saka sampeyan (kanthi komentar ringkes).


$$0 < \prod_{p} \sin \underbrace{ \left( \frac{\pi}{p} \right) }_{ < \pi, \text{ da } p > 1 } = \prod_{p} \sin \left( \frac{\pi}{p} + 2 \pi \underbrace{ \frac{ \prod_{p'} p' }{p} }_{ \in \mathbb{N} } \right) = \prod_{p} \sin \left( \pi \underbrace{ \frac{ 1 + 2 \prod_{p'} p' }{p} }_{ \in \mathbb{N}, \text{ da } \left( 1 + 2 \prod_{p'} p' \right) \notin \mathbb{P} } \right) = 0$$

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