# deletable prime

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

**See Also:** PermutablePrime, Primeval, LeftTruncatablePrime, MinimalPrime

**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.]

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