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From: hansz@ruuinf.cs.ruu.nl (Hans Zantema)
Newsgroups: comp.edu,sci.math,sci.misc
Subject: Re: Subtle Math Questions
Summary: 1 is no prime
Message-ID: <4988@ruuinf.cs.ruu.nl>
Date: 24 Apr 91 07:59:46 GMT
References: <1991Apr22.165415.9843@contact.uucp> <1991Apr23.144230.14500@mailer.cc.fsu.edu>
Followup-To: sci.math
Organization: Utrecht University, Dept. of CS
Lines: 25

In article <1991Apr23.144230.14500@mailer.cc.fsu.edu>, mayne@delta.cs.fsu.edu (William Mayne) writes:
> 
> Why isn't 1 considered a prime number?
> 
> As far as I know (I am not a mathematician) this really is somewhat
> arbitrary. It makes the definition of a prime arguably easier, or
> at least the question of the least prime factor of a number more
> useful, but is this a good reason? Here is a problem, copied from

A main theorem of number theory is the unique factorization: every natural
number can be written as a product of prime numbers. This prime number
decomposition is unique up to the order.

If 1 is considered as a prime number then this uniqueness is not true any
more. This is a very good reason for not considering 1 a prime number.

Every math teacher should know this.

				with kind regards,
				Dr Hans Zantema
				Department of Computer Science
				University of Utrecht
				P.O. Box 80.089 
				3508 TB  Utrecht
				The Netherlands.