Question

If $m$ and $n$ are prime numbers greater than $2$, which of the following could also be a prime number?

• A. $m-n$
• B. $m+n+1$
• C. $m+n+2$
• D. $mn$
• E. $mn+1$

Answer 1

The correct option is B $m+n+1$

From the given statement we can conclude that $m$ and $n$ are odd positive integers.

(A) Difference between any two odd numbers is always even hence it can be prime number $2$ but not greater than $2.$

(B) Sum of two odd numbers is even and then $1$ is added to it means expression $m+n+1$ is odd hence, it can be a prime number greater than $2.$ For example - If $m$ is equal to $5$ and $n$ equal to $7$,

$m+n+1=5+7+1$

$=13$ [Which is prime number greater than $2$]

(C) From the previous option $m+n+1$ is odd so, $m+n+2$ will be even hence cannot be a prime.

(D) Expression $mn$ represent a composite number hence cannot be prime.

(E) Product od odd number is odd as well so, $mn$ will be odd and $mn+1$ will be even hence cannot be prime.

Hence, option $B$ is correct.