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.]


constant ltp = $[2, 3, 5, 7], -> @ltp {
    $[ grep { .&is-prime }, ((1..9) X~ @ltp) ]
} ... *;
 
constant rtp = $[2, 3, 5, 7], -> @rtp {
    $[ grep { .&is-prime }, (@rtp X~ (1..9)) ]
} ... *;
 
say "Highest ltp = ", ltp[5][*-1];
say "Highest rtp = ", rtp[5][*-1];