10111...11101 (39-digits)

This number is a prime.

                                  101112131 4151617181 9181716151 4131211101

Recipe for a palindromic prime: write down the palindrome 0123456789876543210 and separate each digit with a 1. Include a 1 on each end. Found by Bobby Jacobs (a math whiz from Virginia), who was almost 9-years-old at the time.