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# Proth's theorem

Proth's theorem (1878) states:

Let $\displaystyle{ n = h*2^k+1 }$ and $\displaystyle{ h\lt 2^k }$; then $\displaystyle{ n }$ is prime if (and only if) there is an integer $\displaystyle{ a }$ such that

$\displaystyle{ a^{(n-1)/2} \equiv -1 (mod\,n) }$.

A prime of this form is known as a Proth prime.