# Project Euler Problem 37
#

# Gen a prime list
from math import sqrt
UBound = 100000
primes = range(2, UBound)
for x in primes:
    if x > 0:
        for n in xrange(2*x, UBound, x):
            primes[n-2] = 0

# change to a set to make "not in" faster
primes = set([x for x in primes if x > 0])

# Check each prime
for x in primes:
    if x > 10:
        s = str(x)
        flag = True
        for i in xrange(1, len(s)):
            # if any truncated number is not
            # a prime, break and set fail
            if int(s[i:]) not in primes or int(s[:len(s)-i]) not in primes:
                flag = False
                break
        if flag:
            print x

11 748317
[23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397]
Elapsed time: 1.97395228 seconds

#! /usr/bin/env python

from mytictoc import tic, toc

tic()

# produce prime list
stop = 1000000
pmlist = range(stop+1)
pmlist[:2] = [0,0]
i = 2
while i*i<=stop:
    if pmlist[i]>0:
        for j in xrange(2*i,stop+1,i):
            pmlist[j] = 0
    i += 1

nums = []
for i in xrange(23,stop+1):
    if pmlist[i]>0 and '0' not in str(i): # isprime and don't contain 0
        # get all sub number
        allnum = []
        for j in xrange(1,len(str(i))):
            allnum.extend([int(str(i)[:j]),int(str(i)[-j:])])
        # check all sub number
        if all([pmlist[x]>0 for x in allnum]):
            nums.append(i)

# print result
print len(nums),sum(nums)
print nums
        
toc()