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?


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    $\begingroup$ If you allow $0$s inside the number, there are an infinite number of left truncatable primes, including $13,103, 100003, 1000003, 100000000003, 100000000000000003, 1000000000000000003,\ldots$ $\endgroup$ – Henry Oct 1 '16 at 10:02

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.


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