prime_fermat, a Python code which applies Fermat's primality test to an integer n, which always correctly identifies primes, but sometimes also accepts nonprimes. Nonetheless, the test is useful for weeding out most nonprimes. The accuracy of the test can be improved by running it for several bases.
The test is based on Fermat's little theorem. If n is prime, and a is any number not divisible by n, then
a^(n-1) = 1 mod n.
To test whether n is prime, we can pick a random value a and see
if the congruence holds. If it does not, then n is definitely not
prime. If it holds, we are not sure. We can repeat the test for
several values of a to improve our confidence.
The information on this web page is distributed under the MIT license.
prime_fermat is available in a C++ version and a MATLAB version and an Octave version and a Python version.
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