What is the smallest prime remaining prime when added to its reverse?

Analytical solution preferred.

As no prime ends in an even digit but the trivial prime 2,
which is its own reverse, the reverse of the prime must be even,
and, thus the prime must begin with an even number.
This means the number of digits must be greater than 1.
And, as numbers with an even number of digits added to their reverse are divisible by 11, the number of digits required must be odd. Thus the smallest possible prime sought is at least 3 digits in length.

If leading zeroes are permissible in the representation of a
number, the smallest prime remaining prime is 041 {041 + 140 = 181}. Otherwise, the prime must begin with at least the digit 2. Iterating through the 3-digit primes beginning with 2, the smallest prime remaining prime is 229 {229 + 922 = 1151}.

Posted by Dej Mar on 2013-01-16 06:28:28