Can you prove that there are infinite palindromic primes that when squared give a palindromic number?



Is it true that there are infinite palindromic primes that when squared give palindromic number?
There are in fact more than those 4, and they have [their own page on OEIS](https://oeis.org/A225603). Two conjectures, then, would be:


* are they infinitely many? I suspect so.
* are $2$ and $3$ the only ones formed with *decimal* digits other than $0$ and $1$? I suspect so.


