Perfect Numbers

2003-12-12, 20:40

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

cheesehead · 2003-12-13, 01:56

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.)

Xyzzy · 2003-12-13, 03:29

Here is a Bittorrent of that number:

http://opteron.mersenneforum.org/perfect6.zip.torrent

cheesehead · 2003-12-13, 03:55

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"?)

2003-12-12, 20:40	#1
MajUSAFRet 7×821 Posts	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

2003-12-13, 01:56	#2
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²·3·641 Posts	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

2003-12-13, 03:55	#4
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²×3×641 Posts	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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2003-12-13, 03:29	#3
Xyzzy "Mike" Aug 2002 17410₈ Posts	Here is a Bittorrent of that number: http://opteron.mersenneforum.org/perfect6.zip.torrent