## Reverse Prime

#### Problem

The number 13 is prime and so too is its reverse, 31. How many two digit primes can you find for which their reverse is also prime?

#### Solution

It should be clear that the primes cannot have an even number of tens; for example, 23, as its reverse will have even units and will be divisible by 2. Similarly, we cannot have 5 tens.

By considering the list of primes with 1, 3, 7, or 9 tens, we obtain the following list of nine 2-digit primes for which their reverse is also prime:

11, 13, 17, 31, 37, 71, 73, 79, and 97.

How many 3-digit primes have this property?

Problem ID: 156 (Mar 2004) Difficulty: 1 Star