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-   -   Perfect Numbers (https://www.mersenneforum.org/showthread.php?t=1672)

MajUSAFRet 2003-12-12 20:40

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

cheesehead 2003-12-13 01:56

Yep, and its 13-million-digit decimal representation is at [I]([U]Think[/U] before entering this URL -- it's a 13 megabyte download!)[/I] http://mersenne.org/gimps/perfect6.txt.

(Why perfect[B]6[/B].txt?

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

Xyzzy 2003-12-13 03:29

Here is a Bittorrent of that number:

[url]http://opteron.mersenneforum.org/perfect6.zip.torrent[/url]

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"?)


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