#Find prime factors in python
from math import sqrt

def primality_testing(n):
    """test if the given number is prime or not"""
    if type(n) != int:
        print("the given number is not a positive integer")
    elif n == 1:
        return False
    elif n == 2:
        return True
    elif n == 3: #exception occurs when n == 3
        return True
    elif n > 2:
        if int(sqrt(n)) > 2:
            for i in range(2, int(sqrt(n))):
                b = n % i #Check if the modulo of n against a trial division number i is 0
                if b == 0:
                    return False #if modulo is zero, then the given number is a factor, so n is not a prime number
            return True #if modulo is not zero, then the given number is not a factor, so n is a prime number
        elif int(sqrt(n)) == 2: #taking out the exceptional case when sqrt(n) = 2
            b = n % 2 #the trial division number here is 2
            if b == 0:
                return False
            return True

is_prime = primality_testing(13)
print(is_prime)