Yves Gallot's Proth.exe: an implementation of Proth's Theorem for Windows  (Another of the Prime Pages' resources)
 New record prime: 277,232,917-1 with 23,249,425 digits by Pace, Woltman, Kurowski, Blosser & GIMPS (26 Dec 2017).
 [ Download | Submit Primes | Ranges & Projects | Related Programs | Search Database ] Current version: 7.1 last modified: May 2004

### Introduction

Originally, Yves Gallot wrote a program to implement the following theorem from 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...

### Related pages

• Paul Jobling's NewPGen which can be used to pre-sieve candidates for Prothe.exe searches.
• George Woltman's PRP can be used to take the output of NewPGen, apply a prp test, then create a file for  Proth.exe to prove.  Get prp.zip for Windows and prp.tgz for Linux on an Intel *86 processor.
• Chris Nash's PrimeForm - built with the same arithmetic library as Proth.exe, PrimeForm allows much move variety in the form of the prime numbers sought.
• Andy Penrose's Proth benchmarks for various machines

### When you find a new prime:

At this site we keep database of the 5000 Largest Known Primes, plus the top twenty of certain special forms (Cullen, twin,...) If you find any primes that would fit on this list, please let me know! To see what is already on the list, you can use the search engine below.

### Search the list for primes of these forms

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 Another prime page by Chris K. Caldwell