Proth's theorem

This article is about Proth's theorem.

The Proth's theorem (1878) states:

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

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

A prime of this form is known as Proth prime.

See also

• Proth's theorem