I was doing this question when I came upon the fact that the number of left- or right-truncatable primes is finite. What's the proof behind this being true?
closed as off-topic by Shailesh, Watson, user91500, choco_addicted, user223391 Oct 1 '16 at 19:53
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A tedious but valid proof is to take the left/right truncatable primes of greatest length and appending the numbers from 1 to 9 left/right of them, then checking that the resulting numbers are not prime.
Since left/right truncatable primes are such that if you remove the leftmost/rightmost digit the result is a truncatable prime, this proves that there are no more left/right truncatable primes.