2008 iTest Problems/Problem 4
Problem
The difference between two prime numbers is . Find their sum.
Solution
We know that any prime number, excluding , is congruent to
. Thus, if both of the primes are not
, their difference would be congruent to
. Because
, one of the primes must be
. It follows that the other prime must then be
. Therefore, the sum of the two is
.