Why only 11 ?
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.
There are only eleven primes that are both truncatable from left to right and right to left.
Edit:
The original answer below is wrong, as so clearly explained by sundar below. However the method remains correct if one applies the same answer to the left truncatable primes, the right truncatable primes, and then intersects the two computed lists.
Original Answer:
If there are no $n$ digit primes with this property, then there are also no $n+1$ digit primes which this property. One can thus do an exhaustive search, and as soon as you search through all the $n$ digit primes and don't find a number with this property, you know you are done. Presumably your list will have 15 numbers on it, although I haven't checked.