PROBLEM LINK:

Contest
Practice

Author:Roshan Choudhary

DIFFICULTY:

Easy

PREREQUISITES:

Number Theory , Fermat primality test

PROBLEM:

Given a number find wheter it is prime or not.

EXPLANATION:

If we want to test whether p is prime, then we can pick random a's in the interval and see whether the equality holds. If the equality does not hold for a value of a, then p is composite. If the equality does hold for many values of a, then we can say that p is probably prime.The complexity is O(log(N)) because we need to compute a^N and that takes O(log(N)) time.

Python Code:

from random import randint
def fun(N):
    if N > 1 :
        for _ in xrange(5):
            Num=randint(1,N-1)
            if pow(Num,N-1,N)!=1:
                return False
        return True
    return False
for _ in xrange(input()):
    if(fun(input())):
        print "PRIME"
    else:
        print "COMPOSITE"