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From: fry@zariski.harvard.edu (David Fry)
Newsgroups: comp.sys.mac.programmer
Subject: Re: Prime numbers, Help
Message-ID: <6444@husc6.harvard.edu>
Date: 18 Apr 91 14:18:51 GMT
References: <1991Apr4.164338.329@asacsg.mh.nl> <1991Apr17.164107.28457@ni.umd.edu>
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Organization: Harvard Math Department
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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. 

Not quite.  What you're thinking of is that if p1, p2,
p3,...pn are sequentially numbered primes (with p1 = 2, p2 =
3, etc.), then p1 * p2 * p3 * ... * pn +/- 1 is either prime
OR is divisible by a prime greater than pn.  This is the basis
of Euclid's proof of the infinitude of primes. 

David Fry                               fry@math.harvard.EDU
Department of Mathematics               fry@huma1.bitnet
Harvard University                      ...!harvard!huma1!fry
Cambridge, MA  02138