How to contribute to the search ?

All you need is a personal computer, patience, and ... luck.

First steps...

This section indicates how to search for generalized Fermat primes if you are not yet familiar with the prime number search and the Proth program. However if the prime number search have no secrets for you, go directly to the Participate to the search section.

First of all, go to the download page and install "Proth" on your computer(s).

Select a small range that you would like to test, for exemple N = 256, 1000 <= k <= 2000.

Run the Proth program and select form "Gen. Fermat Num. k^n+1" and mode "Standard" and  (default modes).

Enter the value of N in the outer loop and the range of b (or k) in the inner loop: for example, if you choosed the range 1,000-2,000 for N=256, you should have:

Then "Start". If a prime is found, it is printed to the screen of the program and to the log file. At the end of the computation, the message "Done." is printed to the screen. Here we have:

You found four primes! Now you are ready for contributing to the search: the method is not more difficult, except that the numbers are larger and then more time and patience will be needed to see a prime on your screen...

Participate to the search...

First go to the status  and reserve pages and reserve a range of numbers to test.

Before testing the primality of a number, we first test if this number has a small factor: it speeds up the test because it removes quickly several candidates. With GFN it's even possible to do better because the divisibility of all the GFN of a fixed exponent can be checked simultaneouly. This method is called a sieve and sieving can be carry to a higher limit and the search is quickened. Today all the GFN are sieving (or sieved). The candidates that left can be downloaded as a file and Proth can check this file rather than testing fixed bounds. Try to use this mode and pick up the file that contains your range here and your search will be optimal.

Run the Proth program and select form "Gen. Fermat Num. k^n+1" and mode "File".

Set the Options->Preferences option "Manual PMax" to 0.

Check that "Verbose mode" is on for File (default) such that all results (prime and composite numbers) are printed to the log file:

You can select "Verbose mode" on for Screen if you want to print also all results to your screen. 

Enter the filename of the file that contains numbers to test, reset line counter to 0 and start...

When a prime is found, it is printed to the screen and to the log file. At the end of the computation, the message "Done." is printed to the screen. Go to the submit page and send the log file to us. Your range will be added to the tested ranges and your name added to the list of the producers.

Other search...

If you really want to sieve the GFN yourself, you can download David Underbakke's program. But before duplicating the work, don't forgot that ranges were already sieved by this program thanks to Phil Carmody coordinated effort.