So just for fun, I decided to look for a list of palindromic primes, that is, primes that when in base 10 representation are the same whether backward or forward. 1003001, just to give an example. I quickly noticed something striking: Other than 11, every palindromic prime out of the first 100,000 primes had an odd number of digits! Naturally, I wondered just why this was, but not being a number theorist, I cannot for the life of me figure out why without help. So with that, I must ask: Can you help me understand just why 4 and 6 digit palindromic numbers, as a rule, are composite? Does a reason even exist in the first place? And finally, can a proof be made to show that 11 is the only even-digited palindromic prime?