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Old 2003-12-12, 20:40   #1
MajUSAFRet
 

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Default Perfect Numbers

There is a theorem that states that if
2^N - 1 is prime, then (2^N - 1) * 2^(N-1)
is perfect. A perfect number is, by definition, a number that is the sum of all its divisors, excluding itself. The numbers 6 and 28 are the first two perfect numbers. By finding the 40th Mersenne prime, GIMPS also has found what must be the largest known perfect number, namely:
(2^20,996,011 - 1 ) * 2^20,996,010
 
Old 2003-12-13, 01:56   #2
cheesehead
 
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"Richard B. Woods"
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Yep, and its 13-million-digit decimal representation is at (Think before entering this URL -- it's a 13 megabyte download!) http://mersenne.org/gimps/perfect6.txt.

(Why perfect6.txt?

A: It's GIMPS's 6th discovery.)

Last fiddled with by cheesehead on 2003-12-13 at 02:00
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Old 2003-12-13, 03:29   #3
Xyzzy
 
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Here is a Bittorrent of that number:

http://opteron.mersenneforum.org/perfect6.zip.torrent
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Old 2003-12-13, 03:55   #4
cheesehead
 
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"Richard B. Woods"
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Oh, yeah, Bittorrent - the latest newfangled thing I haven't gotten used to thinking of yet. Bittorrent. Bittorrent.

Next we'll have Byterapids and Wordgushers.

Hey - Byterapids - see, there's a "tera" in the middle of it. "Tera" sounds like you're tearin' along at great speed.

Say, where do I trademark this?

(But what's an "ordgu"?)

Last fiddled with by cheesehead on 2003-12-13 at 04:00
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