1. The problem statement, all variables and given/known data Given: For all n > 2, there exists a prime p : n < p < n! (given hint: Since n>2, one has n!-1>2 and therefore n!-1 has a prime divisor p.) 3. The attempt at a solution I made an attempt at doing the proof by induction, as the previous question was by induction. However, I am not very good at induction at all. Here is what I have: Start: n=3 => 3< 5 < 6 Hypothesis: Let P(n) be true for some n >= 3 Step: Show P(n+1) true: n+1 < (n+1)! -1 < (n+1)! n+1 < n!*(n+1)-1 < n!*(n+1) ... and then I don't know where to go. I tried throwing around some numbers, but I don't understand what I'm supposed to be looking for really.