def solve():
sieve = Sieve()
sieve.compute_upto(100000) # prime the sieve
# we're starting with 23 to make life easy
found_soln = False
primes = (i for i in count(23) if sieve.is_prime(i))
digits = ''.join(str(d) for d in range(0,10)) # 0-9
for p in primes:
p_str = str(p)
for i in xrange(1,len(p_str)):
# combinations of indices into p_str of length i where every value index in
# p_str has the same character
idx_combs = (j for j in combinations(xrange(0,len(p_str)), i)
if all(imap(lambda x: p_str[x] == p_str[j[0]], j)) and len(j) > 0)
for comb in idx_combs:
group_members = set([])
# we've got all the possible index combinations, so let's try swapping them
for new_char in digits:
test_str = set_val_at_idxs(p_str, comb, new_char)
val = int(test_str)
if not test_str.startswith('0') and sieve.is_prime(val):
group_members.add(val)
if len(group_members) >= 7:
print sorted(group_members)
if len(group_members) == 8:
found_soln = True
break;
if found_soln:
break
if found_soln:
break
