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From: jws@hpcllf.HP.COM (John Stafford x75743)
Newsgroups: comp.lang.pascal
Subject: Re: Perfect number program
Message-ID: <4450002@hpcllf.HP.COM>
Date: Wed, 7-Oct-87 16:14:55 EDT
Article-I.D.: hpcllf.4450002
Posted: Wed Oct  7 16:14:55 1987
Date-Received: Sun, 11-Oct-87 08:52:28 EDT
References: <9652@brl-adm.ARPA>
Organization: Hewlett-Packard CLL
Lines: 28

Well it is bound to be slow; perfect numbers are rather scarce.
The first four are 6, 28, 496, and 8128.

It has been a while since I played with them, but I seem to recall
(although I may well be wrong) that:

   1. That they have a tendency, for a while, to end alternately with
      the digits 6 and 28, but not forever.

   2. There is a formula involving two raised to prime powers that will
      generate them for a while, but not forever.  I discovered this
      formula myself only to later discover I was several hundred years
      too late.  For a clue, look at the binary representation of the
      first four perfect numbers (110, 11100, 111110000, 1111111000000).

   3. You might look into Marsienne (spelling?)  primes.  I believe that
      each one of them has a related perfect number that is relatively
      easy to compute (assuming you have an easy way to compute the
      primes :-{)}).

   4. The greeks decided that some numbers are perfect.  Numbers whose
      prime factors add to less than themselves are 'insufficient' and
      those whose add to more than themselves are 'oversufficient', only
      a relative few are 'perfect' (or something to that effect).

John Stafford -- Hewlett Packard Computer Language Lab
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