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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

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