Euler #357

def primes_sieve(limit):
    a = [True] * limit
    a[0] = a[1] = False

    for (i, isprime) in enumerate(a):
        if isprime:
            yield i
            for n in range(i*i, limit, i):
                a[n] = False


def prime(n):
    if n == 2 or n == 3: return True
    if n < 2 or n%2 == 0: return False
    if n < 9: return True
    if n%3 == 0: return False
    r = int(n**0.5)
    f = 5
    while f <= r:
        if n%f == 0: return False
        if n%(f+2) == 0: return False
        f += 6
    return True


def factorize(n):
    factors = []
    for x in range(1, int(n**0.5)+1):
        if n % x == 0:
            factors.append(x)
    return set(factors)

answer = 0
for b in [x - 1 for x in primes_sieve(10**8)]:
    if b == 6:
        answer += b
        continue
    if str(b)[-1] == "6":
        continue
    if str(b)[-2:] in ["08", "12", "20", "28", "32", "40", "48", "52", "60", "68", "72", "80", "88", "92", "00"]:
        continue
    for c in factorize(b):
        if not prime(c + int(b/c)):
            break
        if c == list(factorize(b))[-1]:
            answer += b
print(answer)