Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!uwm.edu!psuvax1!hsdndev!cmcl2!lanl!cochiti.lanl.gov!jlg
From: jlg@cochiti.lanl.gov (Jim Giles)
Newsgroups: comp.edu
Subject: Re: 1 is not prime (Was Re: Subtle Math ...)
Message-ID: <22652@lanl.gov>
Date: 25 Apr 91 23:35:33 GMT
References: <1991Apr23.144230.14500@mailer.cc.fsu.edu> <51667@nigel.ee.udel.edu> <1991Apr23.175350.29941@kuhub.cc.ukans.edu> <1991Apr24.114444.16145@zaphod.mps.ohio-state.edu>
Sender: news@lanl.gov
Organization: Los Alamos National Laboratory
Lines: 14

One (1) is not considered a prime because of the fundamental 
theorem of arithmetic (or should it be capilalized?).  The
theorem states that all integers greater than one (1) can
be factored into primes in only one (1) way (independent of
rearrangement).  But, if one (1) were treated as a prime,
then there would be an infinite number of factorizations
of any integer greater than one (1) (or of one (1) itself
for that matter).  To be sure, these different factorizations 
would differ only in the number of one (1) factors given, but 
they'd differ.  It's easier to just define one (1) as non-prime 
than it is to rewrite the theorem with a special case for one (1) 
as a factor.

J. Giles