For another question I just found an answer on Chris Caldwell's

PrimeGlossary: do all palindromic primes have a p^n number of digits? - No!

For base-10, I tested it up to 2^31 - 1, which gave 1, 2, 3, 5 and 7 digits.

For twin palindromic primes (BTW, I think 'palindromic prime pair' could be a better name to avoid confusion with palindromic primes that are also prime twins, besides it's a nice anaphora.:)) this isn't the case, either. Counter example: 1009 and 9001.

Benjamin

P.S.: If I got it right, in Chris Caldwell's

PrimeGlossary, they are called 'invertable primes'.