Prove It by Velleman, Introduction, Problem 2

Problem

Make some conjectures about the value of n for which is a prime or the value of n for which is a prime. (You might start by making a table similar to Figure 1.)

Solution

 

n	Prime		Prime		Prime
2	Yes	8	No	7	Yes
3	Yes	26	No	25	No
4	No	80	No	79	Yes
5	Yes	242	No	241	Yes
6	No	728	No	727	Yes
7	Yes	2186	No	2185	No
8	No	6560	No	6559	No
9	No	19682	No	19681	Yes
10	No	59048	No	59047	No

 

Conjecture: is never prime.

Conjecture: may be prime.