Note: Due to changes in the Riesel prime template, most of those pages (and related) are not shown properly.
This will take some time!
Wanna help? Please move any Riesel prime page first, then edit/add the base parameter.
Topics Register • News • History • How to • Sequences statistics • Template prototypes

Proth's theorem

From Prime-Wiki
Jump to: navigation, search

This article is about Proth's theorem.

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 a Proth prime.

External links