In base ten, the two-digit prime n is 45 more than the number formed by reversing the digits of n, find all the possible values of n.

Let , so that is the digits in the tens place and is the digit in the ones place. (Clearly .)



There are five possible two digits integers that satisfy this relation:







But the first, third, and fifth candidates are even, so they are not prime. The remaining are prime, however, so or .

Top right since it passes vertical line test