'''
The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.

Find the sum of the only eleven primes that are both truncatable from left to right and right to left.

Note: 2, 3, 5, and 7 are not considered to be truncatable primes.
'''

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 isTruncable(n, primes):
    s = str(n)
    for i in range(len(s)):
        if int(s[:i+1]) not in primes or int(s[i:]) not in primes:
            return False
    
    return True

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

    primes = set(sieve(10000000))

    truncs = []

    i = 11
    while len(truncs) < 11:
        if isTruncable(i, primes):
            truncs.append(i)
            print(truncs)
        i += 2

    print(f"Trunc sum: {sum(truncs)}")


if __name__ == "__main__":
    main()