'''
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.

What is the largest n-digit pandigital prime that exists?
'''

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 isPandigital(n):
    l = len(str(n))

    digits = set(range(1, l+1))

    if digits == set(map(int, str(n))):
        return True
    return False

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

    primes = sieve(987654321)

    print("Calculated enough primes")

    r = 1

    while not isPandigital(primes[-1 * r]):
        r += 1
    
    print(primes[-1 * r])

if __name__ == "__main__":
    main()