# Are 2, 3 the only prime numbers that don't have the digit 1 and are palindromes whose squares are also palindromes?

While thinking about prime numbers, I noticed that:

$$(1)$$ Very few prime numbers have squares that are palindromes.

Ex: $$2$$, $$3$$, $$11$$, $$101$$, $$307$$

$$(2)$$ Even rarer are prime numbers that are palindromes whose square are palindromes.

Ex. $$2$$, $$3$$, $$11$$

This inspired me to ask the following questions:

$$(1)$$ Are $$2, 3$$ the only prime numbers that don't have the digit $$1$$ and are palindromes whose squares are also palindromes?

$$(2)$$ If not, then are there a finite number of these types of these prime numbers.

• OEIS entry for primes $p$ such that both $p$ and $p^2$ are palindromes. It is apparently a conjecture that all such primes $>3$ consist only of zeros and ones. – Wojowu Apr 22 at 14:31