Derek's 60

p60.py

# 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.

def primes(n):
  ret = list()
  multiples = set()
  for i in xrange(2, n+1):
    if i not in multiples:
      ret.append(i)
      multiples.update(xrange(i*i, n+1, i))
  return ret
 
PRIMES = primes(10**8)
PRIMES_set = set(PRIMES)
group_list = list()

def check(a,b):
  return (int(str(a)+str(b)) in PRIMES_set) and (int(str(b)+str(a)) in PRIMES_set)

def solve():
  for p in PRIMES:
    for group in group_list:
      if all([check(prime, p) for prime in group]):
        g = list(group) # DAMN PYTHON
        g.append(p)
        group_list.append(g)
        if len(g) == 5:
          return g, sum(g)
    group_list.append([p])

print solve()