Palindromic Primes Quiz Puzzle

There is a conjecture that there are an infinite number of palindromic prime numbers, but this has not been proved.

However, all the palindromic prime numbers discovered so far have an odd number of digits, except 11.

Could there be another even-numbered palindromic prime number lurking among the (probably) infinite number of palindromic prime numbers? Or is that impossible, and if so, why?