Ok, my question is: prove that all of the following numbers are composite: 1000! +2, 1000! +3, 1000+4, ....., 1000! + 1002

Now, I assume I have to start with proving that 1000! is composite or not and then prove the other numbers being added to the factorial?

Also, our class definition of composite is: A positive integer a is called composite provided there is an integer b such that 1< b < a and b|a.

Help is much appreciated!