Eleven (11) is the only even-length prime palindrome, as every even-length
palindrome is divisble by 11.
Suppose we have some number `n` written in base-10 notation,
n = sum_{k = 0}^l n_k * 10^k .
Then
n (mod 11) = sum_{k = 0}^l (n_k mod 11) * (10^k mod 11)
= sum_{k = 0}^l (n_k mod 11) * ((-1)^k mod 11)
If `n` is an palindrome of even length, then the contribution `mod 11`
of each digit on one side of the number will exactly cancel out the
contribution from the mirrored digit on the other side, so `n` is `0 (mod 11)`,
and therefore `n` is divisble by 11.