I need help proving that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite. The hint that came with the problem is: Consider the numbers $$(n+1)!+2,(n+1)!+3,...,(n+1)!+n,(n+1)!+n+1$$
I honestly have no idea how to begin here. I am specifically confused about what it means when it says "there exist $n$ consecutive positive integers". Does this mean that if $n = 5$, for example, then somewhere in the positive integers there are 5 consecutive composite integers? And that we want to prove that?
I get that composite means that they are not prime, hence they have more factors than 1 and themselves.
Any help would be greatly appreciated.