bancaldo™

The primes 3, 7, 109, and 673, are quite remarkable.
By taking any two primes and concatenating them in any order
the result will always be prime.
For example, taking 7 and 109, both 7109 and 1097 are prime.
The sum of these four primes, 792, represents the lowest sum
for a set of four primes with this property.

Find the lowest sum for a set of five primes for which any
two primes concatenate to produce another prime.

python:

import time
import itertools as it

ts = time.time()

def is_prime(num):
    if num <= 1: return False
    elif num == 2: return True
    elif num % 2 == 0: return False
    else:
        d = 3
        r = int(num**0.5)
        while d <= r:
            if num % d == 0: return False
            d += 2
        return True


def conc_primes(n, m):
    return is_prime(int(str(n) + str(m))) and is_prime(int(str(m) + str(n)))

def prime_pairs(iterable):
    for n, m in it.combinations(iterable, 2):
        if not conc_primes(n, m): return False
    return True

primes = [n for n in xrange(3,10000,2) if is_prime(n)] + [2]

def get_five():
    for n in primes:
        for m in primes[primes.index(n):]:
            if conc_primes(n ,m):
                for x in primes[primes.index(m):]:
                    if prime_pairs([x, n, m]):
                        for y in primes[primes.index(x):]:
                            if prime_pairs([y, x, n, m]):
                                for z in primes[primes.index(y):]:
                                    if prime_pairs([z, y, x, n, m]):
                                        return sum([z, y, x, n, m])

res = get_five() 
print "euler 60: {}\nelapsed time: {}sec".format(res, time.time() - ts)