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
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.
I apologize for the typos. I also apologize for posting this in the wrong forum but I did not expect the problem to involve Number Theory, as it is a topic I had not yet covered.
And as for proving that is always composite, I had stated it was over the range