deletable prime (another Prime Pages' Glossary entries)
 Glossary: Prime Pages: Top 5000: If we can delete the digits from N one at a time from the right and still get a prime, then N is a right truncatable prime.  If we can delete the digits from N one at a time from the left and still get a prime, then N is a left truncatable prime.  Are there any primes in which we can repeatedly delete any digit and still get a prime at each step? If so, each digit would have to be prime, and no digit could occur twice, so this would be a short list: 2, 3, 5, 7, 23, 37, 53 and 73. To make the search more interesting, a deletable prime has been defined ([Caldwell87]) to be a prime that you can delete the digits one at a time in some order and get a prime at each step.  One example is 410256793, because the following are (deletable) primes: 410256793 41256793 4125673 415673 45673 4567 467 67 7 It is conjectured that there are infinitely many of these primes (and this may be one of the easiest conjectures in this glossary to prove!) References: Caldwell87 C. Caldwell, "Truncatable primes," J. Recreational Math., 19:1 (1987) 30--33. [A recreational note discussing left truncatable primes, right truncatable primes, and deletable primes.] Chris K. Caldwell © 1999-2018 (all rights reserved)