# How To Prove It – Exercise 0.4

Oct 05 2012

Solutions to Exercises in the Introduction of How To Prove It by Daniel J Velleman.

Problem (4): Find five consecutive integers that are not prime.

Solution:

First we find $x= (n-1)! + 2$

We have to find five consecutive non-prime numbers, so $n = 5$

So $x = (5+1)! + 2 = 722$

$\therefore$ Five consecutive integers that are not prime are 722, 723, 724, 725 and 726.