A

prime is called

left-truncatable (or just truncatable) if deleting any string of

digits from its left always leaves behind another prime. For example, 317 is a left-truncatable prime because both 17 and 7 are also prime. To exclude trivial cases, the digit zero must not appear in the original number.

The largest left-truncatable prime in base 10 is 357686312646216567629137.