Doesn't take very much searching to find this pretty nifty palindrome prime:

3,212,123 (the 333rd palindrome prime)

Interestingly, there are no four digit palindrome primes because they would be divisible by 11. This is obvious in retrospect but I found this fact by giving NotebookLM a big list of palindrome primes (just to see what it could possibly say about it over a podcast).

For the curious, here's a small set of the palindrome primes: http://brainplex.net/pprimes.txt

The format is x. y. z. n signifying the x-th prime#, y-th palindrome#, z-th palindrome-prime#, and the number (n). [Starting from 2]