observation 1) It can't be a single digit, because the resulting sum is divisible by 2

observation 2) It can't have an even number of digits, because the resulting sum is divisible by 11. Using a mod 11 test, the number and its reverse necessarily have opposing signs. For instance, consider 1019. The odd digits minus the even ones = 7. Its reverse is 9101, for which the odd digits minus the even ones = -7 . So the sum, 10120, is necessarily divisible by 11.

observation 3) It can't have an initial odd digit, because the resulting sum is necessarily divisible by 2.

Using a prime number table, that makes the first 4 candidates 211 223 227 229 .

211 + 112 = 323, which is a multiple of 17

223 + 322 = 545, which is a multiple of 5

227 + 722 = 949, which is a multiple of 13

229 + 922 = 1151, which is prime number, so our answer is 229

*Edited on ***January 15, 2013, 6:09 pm**