A truncatable prime is a prime number that when you successively remove digits from one end of the prime, you are left with a new prime number.



Examples

The number 997 is called a left-truncatable prime as the numbers 997, 97, and 7 are all prime.

The number 7393 is a right-truncatable prime as the numbers 7393, 739, 73, and 7 formed by removing digits from its right are also prime.

No zeroes are allowed in truncatable primes.



Task

The task is to find the largest left-truncatable and right-truncatable primes less than one million (base 10 is implied).



Related tasks
 
 Find largest left truncatable prime in a given base
 Sieve of Eratosthenes


See also

 Truncatable Prime from MathWorld.]


( 1000001:?i
&   whl
  ' ( !i+-2:>0:?i
    & !i:?L
    & whl'(!L^1/2:#?^1/2&@(!L:% ?L))
    & !L:~
    )
& out$("left:" !i)
& 1000001:?i
&   whl
  ' ( !i+-2:>0:?i
    & !i:?R
    & whl'(!R^1/2:#?^1/2&@(!R:?R %@))
    & !R:~
    )
& out$("right:" !i)
)