# Sunday Times Teaser 2679 – Palprimes

*by David Buontempo*

Myself and two friends each found a five digit palindromic prime, mine being 39293.

These three primes were all different and, among them, they used all the digits from 1 to 9.

What were the other two numbers that we found?

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Since we are looking for two 5-digit palindromic primes and as any 2-digit and higher digit prime must necessarily end with either 1,3,7 or 9 as we already have 39293 , then the two palindromic primes must take the form of :

1aba1 and 7cdc7 out of which by trial and error one can easily reach the answer.

Using Ahmet’s logic, we can find the other two palindromic primes as follows: