A deletable prime is a prime number which has the property that deleting digits one at a time in some order gives a prime at each step.
For example, 410256793 is a deletable prime since each member of the sequence 410256793,
41256793, 4125673, 415673, 45673, 4567, 467, 67, 7 is prime.

The first few deletable primes are 2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 103, 107, ... (OEIS A080608).
It is conjectured that there are infinitely many deletable primes (Caldwell).