Euler Problem 37

The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.

Find the sum of the only eleven primes that are both truncatable from left to right and right to left.

NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.



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from sympy import isprime 

def right_truncatable(p = 0):
    if p == 0:
        for p in [2, 3, 5, 7]:
            for q in right_truncatable(p):
                yield q
    elif isprime(p):
        yield p
        p *= 10
        for d in (1, 3, 7, 9):
            for q in right_truncatable(p+d):
                yield q

def left_truncatable(p):
    N = 10 ** (len(str(p))-1)
    while p > 9:
        p %= N
        if not isprime(p):
            return False
        N //= 10
    return True

print(sum([p for p in right_truncatable() if p > 9 and left_truncatable(p)]))



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