Proth Search Page

Yves Gallot wrote an excellent Windows program which makes it easy for anyone to find record size or otherwise interesting primes, but this creates a problem: without a coordinated effort, many of us were be searching the same ranges of numbers for primes! Some spent hundreds of hours checking ranges that were already known to be barren. So I have begun this page in order to reduce this unnecessary duplication. Please join us in the search!

News Flash! February 29, 2008

I am pleased to announce an agreement with the PrimeGrid project for the searching of Proth primes.

Here is how it will work. PrimeGrid will reserve large ranges of k and n. It will perform both a first test and a double-check of all candidates. When it is within weeks of completing this reservation, it will place another reservation for a smaller range of k and n. Of note, some of these ranges will overlap ranges currently reserved to other searchers. PrimeGrid will NOT SEARCH those ranges. The standard ProthSearch policy is that each searcher has two months to complete any reservation. That policy will not be changed. If you have a reservation that is not completed within two months, that range will be available for PrimeGrid to search.

If you are concerned about any of this, please contact Mark Rodenkirch immediately.

News Flash! June 26, 2011

PrimeGrid has finished its double-check for all k < 1200 and n < 1,000,000.

News Flash! August 25, 2011

PrimeGrid has finished its double-check for all k < 100 and n < 2,000,000. PrimeGrid will continue on k < 32 to n < 2,5000,000.

News Flash! February 14, 2012

PrimeGrid has finished its double-check for all k < 1200 and n < 1,500,000.

News Flash! January 16, 2014

PrimeGrid has finished its double-check for all k < 1200 and n < 2,000,000.

Proth primes Definition and status
Recently reserved ranges
Reserve or submit a range email me at logon {at} for the username and password from a valid email address.
List of primes for k < 300
List of primes for 300 < k < 600 
List of primes for 600 < k < 900 
List of primes for 900 < k < 1200 
Primes k.2n - 1  List of primes for k < 300
Cullen primes  Definition and status
Woodall primes  Definition and status
The Sierpinski problem Definition and status
The Riesel problem Definition and status
Fermat numbers Standard factoring status
Factors of generalized Fermat numbers

You might want to check out the following pages for more information on primes!

Here are a few links to programs to aid in the search for primes:

  • Geoff Reynold's sieving suite. His sieves are faster than NewPGen and MultiSieve and can be used for any numbers in the form k*b^n+/-1 and for Cullens/Woodalls. They also run on multiple platforms.
  • NewPGen for rapid sieving of ranges for various searches
  • LLR to prove primality of numbers of the form k*b^n+/-1 (x86 only)
  • PFGW to prove primality of general mathematical expressions (x86 only)
  • phrot to perform primality tests on Proth numbers or PRP tests on other numbers of the form k*b^n+/-1 (any CPU)
  • PRPNet, a client/server application that runs on multiple platforms which can be used to easily distribute PRP testing of a list of numbers
  • The Proth software

Here are some links to other prime searches:

Thanks to Chris K. Caldwell, Yves Gallot, Wilfrid Keller, and Mark Rodenkirch for their help and encouragement in developing this web site. Sincere gratitude is extended to Leonid Durman for suggesting and writing macros to greatly reduce the size of the search range pages!

If you have any questions about this web-site, you can e-mail Ray Ballinger or Mark Rodenkirch.

Last Modified: January 14, 2014