Left-truncatable prime
A prime number which, in a given base, contains no 0, and if the leading (“left”) digit is successively removed, then all resulting numbers are prime.
Right-truncatable prime
A prime number which remains prime when the last (“right”) digit is successively removed.
Left-and-right-truncatable prime
A prime number is a prime which remains prime if the leading (“left”) and last (“right”) digits are simultaneously successively removed down to a one- or two-digit prime.