I was given the following problem:
Generate a sequence of n consecutive composite numbers.
The answer was $$(n+1)!+2,(n+1)!+3,(n+1)!+4,...,(n+1)!+n+1$$
However I was thinking if we could simplify the answer a bit by knowing for which numbers $n!+1$ is prime or composite.
By putting values I got that it is prime for $n=1,2,3,11$
How do I proceed?