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truncatable primes
A prime    is called truncatable if all its prefixes or all its suffixes are primes. More precisely, they are respectively called right-truncatable primes, and left-truncatable primes.

In both cases only zeroless numbers are considered.

For example, the prime 23399 is a (right) truncatable prime because all the numbers 2, 23, 233, and 2339 are primes. Similarly, 26947 is a (left) truncatable prime because 7, 47, 947, and 6947 are primes.

There are 83, right-truncatable primes, the largest being 73939133, while the largest of the 4260 left-truncatable primes is the 24-digit prime 357686312646216567629137.

Clearly the concept of truncatability depends on the base in which the numbers are represented. For example, in base 100 (in which each single digit can be represented with two base 10 digits), there are exactly 9823399067 right-truncatable primes, the largest being 7 01 23 91 63 63 51 51 99 41 61 99 51 83 01 69 83 21 19 53 39 01 27 27 99 47 99 19 03 71 99 21 51 27 97 29 97 47 57 39 79 09 99 23 27 93 69 43 87 71 27 37 57 81 09 11 43.

The first left or right truncatable primes are 2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 113, 137, 167, 173, 197, 223, 233, 239, 283 more terms

Truncatable primes can also be... (you may click on names or numbers and on + to get more values)