Proth's theorem

This article is about Proth's theorem.

The Proth's theorem (1878) states:

Let $n=h\ast 2^k+1$ and $h<2^k$; then $n$ is prime if (and only if) there is an integer $a$ such that

$a^{(n-1)/2}\equiv -1(modn)$.

A prime of this form is known as Proth prime.

See also

• Proth's theorem