Truncatable Primes

A left-truncatable prime is a prime number that contains no 0 digits and, when the first digit is successively removed, the result is always prime.

A right-truncatable prime is a prime number that contains no 0 digits and, when the last digit is successively removed, the result is always prime.

Create a function that takes an integer as an argument and:

• If the integer is only a left-truncatable prime, return "left".
• If the integer is only a right-truncatable prime, return "right".
• If the integer is both, return "both".
• Otherwise, return False.

Examples

truncatable(9137) ➞ "left"
# Because 9137, 137, 37 and 7 are all prime.

truncatable(5939) ➞ "right"
# Because 5939, 593, 59 and 5 are all prime.

truncatable(317) ➞ "both"
# Because 317, 17 and 7 are all prime and 317, 31 and 3 are all prime.

truncatable(5) ➞ "both"
# The trivial case of single-digit primes is treated as truncatable from both directions.

truncatable(139) ➞ False
# 1 and 9 are non-prime, so 139 cannot be truncatable from either direction.

truncatable(103) ➞ False
# Because it contains a 0 digit (even though 103 and 3 are primes).

Notes

The input integers will not exceed 10^6.