# Proth's theorem

This article is about **Proth's theorem**.

Proth's theorem (1878) states:

Let [math]n = h*2^k+1[/math] and [math]h\lt 2^k[/math]; then [math]n[/math] is prime if (and only if) there is an integer [math]a[/math] such that

- [math]a^{(n-1)/2} \equiv -1 (mod\,n)[/math].

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