In this chapter you will examine integers of specific forms. There are several questions which apply in all cases:

1. Under what conditions is an integer of this form always prime?

2. Under what conditions is an integer of this form always composite?

3. Are there infinitely many primes of this form?Sometimes these questions are easy and sometimes they are quite difficult (e.g., currently unsolved after hundreds of years). Of the questions listed above, often question 2 is the easiest to answer. With that in mind, work on making good conjectures for all of the questions first. Then go back and see how much you can prove.

Section 6.1 | Section 6.2 | Section 6.3 | Section 6.4

Copyright © 2001 by W. H. Freeman and Company