Fermat Primality Test - Algorithm and Running Time

Algorithm and Running Time

The algorithm can be written as follows:

Inputs: n: a value to test for primality; k: a parameter that determines the number of times to test for primality Output: composite if n is composite, otherwise probably prime repeat k times: pick a randomly in the range if, then return composite return probably prime

Using fast algorithms for modular exponentiation, the running time of this algorithm is O(k × log2n × log log n × log log log n), where k is the number of times we test a random a, and n is the value we want to test for primality.