Decisive number
= Decisive number
A positive <integer> $n$ is decisive when every <integer> $a$ satisfying $1<a<n$ and $\gcd(a,n)=1$ is a <prime number>. There are only finitely many decisive numbers: every prime $p<\sqrt n$ must divide a decisive $n$, so the <Chebyshev theta function> gives $\log n\geq\vartheta(\sqrt n)$, which eventually contradicts the linear lower bound for $\vartheta(\sqrt n)$.