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 2003-12-12, 20:40 #1 MajUSAFRet   25·34 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 1E0C16 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, 03:29 #3 Xyzzy     "Mike" Aug 2002 2·4,073 Posts Here is a Bittorrent of that number: http://opteron.mersenneforum.org/perfect6.zip.torrent
 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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