Truncatable Primes -- Project Euler 37?
There's no need to convert lists to ints every time. Truncation from the right is an integer division by 10. Truncation from the left is modulo certain power of ten; you can keep track of the modulo as the loop progresses.

There's no need to run a very expensive primality every time. Keep track of the primes you already found.

PS: The biggest hint in the problem is that there's only 11 numbers of interest. There must be a way to prove that fact, and the proof is most likely constructive.