I just got a set of these pencils, from Mathsgear. The number printed on it is prime, and will remain so as you sharpen the pencil from the left, all the way down to the last digit, 7. Here is a recursive construction of all such truncatable primes. TruncatablePrimes[p_Integer?PrimeQ] := With[{digits = IntegerDigits[p]}, {p, TruncatablePrimes /@ (FromDigits /@ (Prepend[digits, #] & /@ Range[9]))}