from tools import primes_sieve2, is_prime


def check_ab_ba_is_prime(a, b):
    if a == b:
        return False
    ab = int('%d%d' % (a, b))
    ba = int('%d%d' % (b, a))
    return is_prime(ab) and is_prime(ba)


def prime_pairs():
    """
    Using cached dict with prime numbers for keys and possible sets as values of primes that had been discovered so far.
    For every new prime, it generates a list of primes that are created by concatenating them with the new prime.
    For every prime in the list of positives, it checks all the contained sets for being a subset of the set of positives.
    If it is a subset, then the set containing the union of the set and the current prime is added to the set of sets for the index and for the new prime.
    Result is the first generated set with a length of five.
    """
    cache = {}
    p_gen = primes_sieve2(10000)
    # discard 2
    p = p_gen.next()

    p = p_gen.next()
    cache[p] = set([frozenset([p])])

    # discard 5
    p = p_gen.next()
    while True:
        p = p_gen.next()
        possibles = set([i for i in cache.keys() if check_ab_ba_is_prime(p, i)])
        p_set = frozenset([p])
        gen_sets = set([p_set])
        for i in cache.keys():
            if i in possibles:
                new_sets = set()
                for s in cache[i]:
                    if s <= possibles:
                        sp = s | p_set
                        if len(sp) == 5:
                            return sp
                        new_sets.add(sp)
                        gen_sets.add(sp)
                cache[i] |= new_sets
        cache[p] = gen_sets


def run():
    result = prime_pairs()
    return sum(result)