Prime Number Problem 16

Model Answer

p=5 and q=2 is one obvious solution. Now suppose both p, q>3. p and q can only be of the forms 6k+1 or 6k+5. Since p-q=3, both must be of the same forms. But then difference will be divisible by 6. Therefore, p-q cannot be equal to 3. Thus, p=5, q=2 is the only possible solution.