As we all know, it's turtles all the way down. But is it primes all the way down too?
A number is considered a "turtle-prime" if it satisfies the following conditions:
1) It is prime. 2) It is possible to remove a single digit leaving a prime number. 3) Step 2 can be repeated until left with a single digit prime.
239 is a "turtle-prime", as it can be reduced to
23 then either
3, both of which are prime. It also can be reduced to
151 is not a turtle prime, as it reduces to
15 (not prime),
51 (not prime), or
11 is prime, but can only reduce to
1, which is not.
Given a positive integer, determine if it is a "turtle-prime". Your output can be in any form so long as it gives the same output for any truthy or falsey value.
input -> output 1 -> false 2 -> true 17 -> true 19 -> false 239 -> true 389 -> false
This is code-golf, so the shortest answer in each language wins!