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UKMT Intermediate Mathematical Challenge, 2015

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

You are asked to choose two positive integers, $m$ and $n$ with $m > n$ , so that as many as possible of the expressions $m + n$ , $m - n$ , $m \times n$ and $m \div n$ have values that are prime. When you do this correctly, how many of these four expressions have values that are prime?

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $4$

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