Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!wuarchive!sdd.hp.com!spool.mu.edu!munnari.oz.au!uniwa!cc.curtin.edu.au!nlewispn
From: nlewispn@cc.curtin.edu.au (Peter N Lewis)
Newsgroups: comp.sys.mac.programmer
Subject: Re: Prime numbers, Help
Message-ID: <1991Apr19.102652.7840@cc.curtin.edu.au>
Date: 19 Apr 91 02:26:52 GMT
References: <1991Apr4.164338.329@asacsg.mh.nl> <1991Apr17.164107.28457@ni.umd.edu>
Organization: NCRPDA, Curtin University
Lines: 41

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?
> 
Ummm, well except for the fact the 2*3*5*7-1=209=11*19....
Actually, 2*3*5*...*pn-1 does not have a factor of 2,3,5,...,pn in it.
BUT it can have a factor of pn+1,pn+2,...,sqrt(2*3*5*...*pn-1).  +'s wont
work either since 2+3-1=4, 2+3+5-1=9, 2+3+5+7-1=16 (see a trend here?)
2+3+5+7+11-1=27, 2+3+5+7+11+13-1=40 (ooops, there goes that nice trend).

> Anyway, if you use the table to get the p1, p2, etc you could generate some
> incredibly big primes.  The main failure is that they will not be particularly
> dense, in fact, the ones at the end of the list will be about 16,000 times
> each other.  I don't know *how close* the original requirement was.

It isnt that easy :-(.  There are lots of fancy algorithms for finding
really huge primes, but they mostly take huge amounts of processing
time as well.  I don't know much about them so if you are interested
go to a maths library and look them up.

Have fun,
   Peter.
PS: Now what on earth does all this have to do with mac programming? :-)

-- 
Disclaimer:Curtin & I have an agreement:Neither of us listen to either of us.
*-------+---------+---------+---------+---------+---------+---------+-------*
Internet: Lewis_P@cc.curtin.edu.au              I Peter Lewis
Bitnet: Lewis_P%cc.curtin.edu.au@cunyvm.bitnet  I NCRPDA, Curtin University
UUCP: uunet!munnari.oz!cc.curtin.edu.au!Lewis_P I GPO Box U1987
PSImail: psi%050529452300070::Lewis_P           I Perth, WA, 6001, AUSTRALIA
Has anyone ever found someone who used a Mac and then Changed To a PC?