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Fourth Highest Perfect Number


Date: 08/21/97 at 21:39:42
From: Daryl Livasy
Subject: Fourth highest perfect number

What is the fourth (4th) highest perfect number?


Date: 08/22/97 at 15:21:39
From: Doctor Wilkinson
Subject: Re: Fourth highest perfect number

The even perfect numbers are all of the form 2^(p-1) * (2^p - 1), 
where p is a prime.  It is not known whether there are any odd perfect 
numbers, but there are certainly no small ones.  So the fourth perfect 
number is obtained by substituting the fourth prime for p in the above 
formula.  The fourth prime is 7, so the fourth perfect number is

 2^6 * (2^7 - 1) = 64 * 127 = 8128

-Doctor Wilkinson,  The Math Forum
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Associated Topics:
Middle School Number Sense/About Numbers

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