Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.1 Number Theory: Prime and Composite Numbers - Exercise Set 5.1 - Page 258: 113


The statement does not make sense.

Work Step by Step

Consider the given number. ${{2}^{57885162}}-1$ The number in the power has $2$ at its one place thereby making it divisible by $2$. So, it is not prime. For ${{2}^{p}}-1$ to be prime, number $p$ needs to be prime. Thus, the number ${{2}^{57885162}}-1$ is not prime as $57885162$ is composite. Thus, the given statement is not true. The statement does not make sense.
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