Generalized Fermat Prime search program
genefer version 20 is an OpenCL™ application.
It performs a fast probable primality test for numbers of the form b2n + 1 (Generalized Fermat Numbers) using a Fermat test.
genefer was created by Yves Gallot in 2001. It has been extensively used by PrimeGrid computing project. genefer is dedicated to the search for large primes (n ≥ 16).
genefer 20 is a highly optimised GPU application, created in 2020. It is dedicated to the search for GFN primes in the range 8 ≤ n ≤ 16. The search for b < 2,000,000,000 and n ≤ 14 is now complete thanks to the PRIVATE GFN SERVER. Statistics are available at Generalized Fermat Numbers and data at GFN Prime Search Status and History.
Efficient Modular Exponentiation Proof Scheme discovered by Darren Li is implemented and the tests are validated with Gerbicz - Li error checking.
Any number of the form b2n + 1 such that 2 ≤ b ≤ 2,000,000,000 and 8 ≤ n ≤ 17 can be tested.
genefer version 20 is deprecated. It is replaced with genefer version 26.