I Have been given this question and cannot get an answer so here goes if anyone can help within the next hour would be great.

Explore the divisors of m! + k for various m and k. Hence explain how to find a run of n consecutive integers which are composite.

Example:

m=5

5! = 120  Composite
5! + 1 = 121  Composite
5! + 2 = 122  Composite
5! + 3 = 123  Composite
5! + 4 = 124  Composite
5! + 5 = 125  Composite
5! + 6 = 126  Composite
5! + 7 = 127  Not Composite

The ? are suppose to be arrows.