Farhan's problem of prime numbers

For $m^{3} - n^{3} = (m - n)(m^{2} + mn + n^{2})$ to be prime it must be the case that $m - n = 1$ , for otherwise it could be expressed as the product of two integers greater than $1$ . The only primes that differ by $1$ are $2$ and $3$ , so $m = 3, n = 2$ and $m^{3} - n^{3} = 3^{3} - 2^{3} = 19$ , which is indeed prime.

Thus $(m^{3} + n^{3})(m + n) = (3^{3} + 2^{3})(3 + 2) = 35 \times 5 = \boxed{175}$ .

We know that, $m^3 - n^3 = (m-n)(m^2 + mn + n^2)$ .

Since prime numbers are only divisible by 1 and itself. $m - n$ have to 1. Which can be accomplished by $m = 3$ and $n = 2$ .

Hence $(3^3 + 2^3)(3+2) = 35 \times 5 = \boxed{175}$

If m=3,n=2, then m^3-n^3=3^3-2^3=19 which is a prime. Therefore, (m^3+n^3)(m+n)=(3^3+2^3)(3+2)=175