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From: halle1@houxz.UUCP
Newsgroups: net.math
Subject: Re: Mersenne primes and perfect numbers
Message-ID: <550@houxz.UUCP>
Date: Tue, 18-Oct-83 16:37:25 EDT
Article-I.D.: houxz.550
Posted: Tue Oct 18 16:37:25 1983
Date-Received: Thu, 20-Oct-83 06:23:05 EDT
References: <230@ihlts.UUCP>
Organization: Bell Labs, Holmdel NJ
Lines: 11

Roger's statement concerning the relationship between Mersenne primes and
perfect numbers is not quite correct.  Not all Mersenne primes produce
perfect numbers.  (This should be obvious just from counting the known number
of each.)  However, you have to go a ways before you come to the counter
example, so he should be forgiven.  It has been shown that
all EVEN perfect numbers must be of the form Roger gave:

	(2^n - 1)*(2^(n-1)), where the first term is a Mersenne prime.

It has not yet been shown that all perfect numbers are even, although
no odd ones have been discovered yet.  (Dr. Matrix notwithstanding.  :-)  )