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[ Download | Submit Primes | Ranges
& Projects | Related Programs | Search
Database ] |
Current version:
7.1
Program last modified:
Tuesday, 04-May-2010 11:10:11 CDT |
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...
To download, choose one of the following:
- Download
Program (size
380K
, last updated:
Tuesday, 04-May-2010 11:10:11 CDT
)
- (or download
pkzipped version,
181K
last updated:
Tuesday, 04-May-2010 11:10:12 CDT
)
Ranges to search & Projects to join
- Joe DeMaio's Generalized
Woodall number search.
- Ray Ballinger's Proth
Range Page's contains pages for coordinating the searches for Cullen
primes, Woodall primes, "Proth" primes and the Sierpinski
problem.
- Yves Gallot's Generalized
Fermat Prime Search--Proth.exe is faster when used on this type
of prime.
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
- See also the Prime Links++ programs
directory.
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
Search Database of the Largest Known Primes
for primes of the form: k.bn+/-1
Limit on multiplier k
(leave blank for no limit) |
minimum
maximum
|
Limit on exponent n
(leave blank for no limit) |
minimum
maximum
|
| Base b |
base
|
| Which sign(s)? |
plus
minus
|
| Find at most |
number
|
|
(other
searches) |
Click here for other ways to
search at this site and in this database. |