'''
The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.

There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.

What 12-digit number do you form by concatenating the three terms in this sequence?
'''

import math
import numpy as np
from itertools import permutations

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 digitToList(n):
    return [int(c) for c in str(n)]

def listToDigit(l):
    res = 0
    for i in l:
        res = 10 * res + i
    return res

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

    primeSet = set(sieve(10000)) - set(sieve(1000))
    primeList = list(primeSet)

    for p in primeList:
        perms = list(set(map(listToDigit, list(permutations(digitToList(p))))))

        for perm in perms:
            if p != perm and perm in primeSet:
                if max(p, perm) + abs(p - perm) in primeSet and max(p, perm) + abs(p - perm) in perms:
                    print(min(p, perm), max(p, perm), max(p, perm) + abs(p - perm))

    

if __name__ == "__main__":
    main()