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Politics : Just the Facts, Ma'am: A Compendium of Liberal Fiction -- Ignore unavailable to you. Want to Upgrade?

To: The Philosopher who wrote (42416)	12/3/2005 2:59:12 PM
From: Lazarus_Long	Read Replies (1) \| Respond to of 90947

Book IX proposition 36 "If as many numbers as we please beginning from an unit be set out continuously in double proportion until the sum of all becomes prime, and if the sum of all becomes prime, and if the sum multiplied into the last some number, the number will be perfect." Considering you're a lawyer, we'll keep things as simple as possible. (BTW, St. John's or whatever hick school you went to may still use Euclid; the rest of the world has progressed something over 2,000 years beyond that. And WTH is geometry doing being taught at a college level, anyway? You ought to know it by then!) In proposition 36, Euclid proves that if 1 + 2 + 4 + 8 + 16 ... + 2n = S be prime, then S × 2n will be a perfect number. [Note to those in need of help (hey, I didn't say "lawyer"!): A perfect number is one that is the sum of its factors.] This is still the only known method for finding perfect numbers. Now the actual proof gets a bit complicated (GOOD LUCK!). It can be found here: aleph0.clarku.edu plus a guide and some info on Mersenne primes. Now an ambulance just went by! Go get it!