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^{.}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:
Tuesday, 04-May-2010 11:10:11 CDT
)

Ray Ballinger's Proth
Range Page's contains pages for coordinating the searches for Cullen
primes, Woodall primes, "Proth" primes and the Sierpinski
problem.

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.