Q:

Find all positive integers $n$ such that $n$,$n + 2$, and $n + 4$ are all primes...

Find all positive integers $n$ such that $n$,$n + 2$, and $n + 4$ are all primes.

Having a tough time with this problem, I feel that brute force is a possibility especially considering that my professor said that there are only a small amount of numbers that fit this category, but there has to be a better way. Any help or suggestions are greatly appreciated. I did see a similar post to this question but it did not help me solve this nor did it look to find the same thing, please do not mark this as a duplicate. 

A:

Note that one of the three numbers must be a multiple of $3$. So the only possible choice is that one of them is $3$ itself. So $3,5,7$

