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From: neeri@iis.ethz.ch (Matthias Ulrich Neeracher)
Newsgroups: comp.sys.mac.programmer
Subject: Re: Prime numbers, Help
Message-ID: <1991Apr18.072620.6448@bernina.ethz.ch>
Date: 18 Apr 91 07:26:20 GMT
References: <1991Apr4.164338.329@asacsg.mh.nl> <1991Apr17.164107.28457@ni.umd.edu>
Sender: neeri@iis (Matthias Ulrich Neeracher)
Reply-To: neeri@iis.ethz.ch (Matthias Ulrich Neeracher)
Organization: Integrated Systems Laboratory, ETH, Zurich
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In article <1991Apr17.164107.28457@ni.umd.edu>, zben@ni.umd.edu (Ben Cranston) writes:
>I seem to remember a theorum that if p1, p2, etc are sequential prime numbers
>starting at 2 then numbers of the form
>
>   p1 * p2 * p3 ...  - 1
>
>are prime, the proof concerns the fact that if p1 or p2 or any of the pn are
>a factor of the big number then there is a second unique factorization, and
>since prime factorizations are unique it must be prime.  Or something.  Or
>maybe it was + rather than - -- any mathematicians out there?

2*3*5*7-1       =   209 = 11*19
2*3*5*7*11*13+1 = 30031 = 59*509

All the theoreme you mentioned (Euclid, I think) proves is that a number of
the form 

   p1 * p2 * p3 ... * pn - 1

isn't divisible by any of the pi for i=1...n.

Matthias

-- 
Matthias Neeracher                                      neeri@iis.ethz.ch
   "These days, though, you have to be pretty technical before you can 
    even aspire to crudeness." -- William Gibson, _Johnny Mnemonic_