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): Let N = k.2n+1 with 2n > k.   If there is an integer a such that
a(N-1)/2 = -1 (mod N),
then N is 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 Proth Range Page for additional information.)

Yves Gallot has now expanded this program to also cover prime of the form k.2n-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...

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