Editing Fermat primality test (section)

==Applications==

As mentioned above, most applications use a [[Miller–Rabin primality test|Miller–Rabin]] or [[Baillie–PSW primality test|Baillie–PSW]] test for primality.  Sometimes a Fermat test (along with some trial division by small primes) is performed first to improve performance.  [[GNU Multiple Precision Arithmetic Library|GMP]] since version 3.0 uses a base-210 Fermat test after trial division and before running Miller–Rabin tests.  [[Libgcrypt]] uses a similar process with base 2 for the Fermat test, but [[OpenSSL]] does not.

In practice with most big number libraries such as GMP, the Fermat test is not noticeably faster than a Miller–Rabin test, and can be slower for many inputs.<ref>{{citation|author=Joe Hurd|date=2003|title=Verification of the Miller–Rabin Probabilistic Primality Test|page=2|citeseerx=10.1.1.105.3196}}</ref>

As an exception, OpenPFGW uses only the Fermat test for probable prime testing.  The program is typically used with multi-thousand digit inputs with a goal of maximum speed with very large inputs.  Another well known program that relies only on the Fermat test is [[Pretty Good Privacy|PGP]] where it is only used for testing of self-generated large random values (an open source counterpart, [[GNU Privacy Guard]], uses a Fermat pretest followed by Miller–Rabin tests).