A deletable prime is a prime number from whose decimal digits it is possible to delete one digit at a time in some order, obtaining a prime number at every step until a single-digit prime remains. Leading zeros in intermediate strings are allowed and are ignored when interpreting the remaining digits as an integer. 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).
