I was doing a proof to prove that there exists arbitrarily long strings of composite numbers.

In more technical language, for every , there exists a n such that

is composite

to do so, I let ,(for m>3) then we get the sequence:

Every element of this sequence is obviously divisible by some integer, except

Now I must prove that m!+1 is always an composite. I have no idea how to do this. I tried induction and contradiction.

Help please