# Yves Gallot's Proth.exe

#### An implementation of Proth's Theorem for Windows

### Introduction

Originally, Yves Gallot wrote a program to implement the following theorem found on our pages on primality proving (page three):

Proth's Theorem(1878): LetN=k^{.}2+1 with 2^{n}>^{n}k. If there is an integerasuch that thenNis prime.

This test is so simple that in practice the difficulty is *quickly*
multiplying the large numbers involved. It is also a very useful test:
it applies to Cullen
primes, Fermat
factors, the primes in the Sierpinski
conjecture... (See Ray Ballinger's Range Pages for additional information.)

Yves Gallot
has now expanded this program to also cover prime of the form *k*^{.}2* ^{n}*-1!
His "Proth.exe" program makes finding all these types of primes
as easy as selecting the form you desire from a menu, choosing the starting
values (here Ray Ballinger's Proth
Range page's are especially helpful) and then letting the machine
go. Big primes take awhile to find, so Yves programs tracks where it is
and can automatically continue each time you start your machine. You can
adjust the priority of the program so it only runs when your machines
is doing nothing else...

Other features include the ability to set a range for the starting *k*
(odd) and *n*, to set certain algebraic forms for the multiplier,
and to test (automatically) if any prime you find is part of a twin
prime or Sophie
Germain prime pair...

### To download, choose one of the following:

- Download Program (size 380k, last updated: May 2004)
- (or download pkzipped version 181K)