truncatable prime numbers

[Sam Benry]

I have this question from euler

The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.

Find the sum of the only eleven primes that are both truncatable from left to right and right to left.

NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.

I can't figure out the eleven prime numbers, why are these prime numbers wrong:
11
13
17
23
31
37
53
71
73
113
131

aren't they all truncatable from both left and right? and if they are, there are still many more truncatable prime numbers from both left and right... what am I doing wrong?

[Paul Clapham]

1 isn't a prime number, so that rules out many of the numbers in your list.