'''
The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.

There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.

How many circular primes are there below one million?
'''
import math
import numpy as np

def sieve(n):
    assert n > 1

    ns = [True] * n

    for i in range(2, math.ceil(np.sqrt(n))):
        if ns[i]:
            j = pow(i, 2)

            while j < n:
                ns[j] = False
                j = j + i

    return [i for i,val in enumerate(ns) if val][2:]

def rotate(n):
    if n < 10:
        return n
    else:
        l = n % 10
        return l * 10**(len(str(n)) - 1) + n // 10

def isCircular(p, primes):
    result = True

    cur = rotate(p)
    while cur != p:
        if cur not in primes:
            result = False
            break
        cur = rotate(cur)

    return result

def main():
    print("Hello this is Patrick")

    primes = sieve(1000000)
    res = 0

    for p in primes:
        if isCircular(p, primes):
            print(p)
            res += 1
    print("Number of circular primes:", res)

if __name__ == "__main__":
    main()