Re: [Phys-l] Prime numbers

["David Bowman" <David_Bowman@georgetowncollege.edu>]

Very nicely put, John.  Keeping the definition of 'prime' to refer to whatever class makes for a *unique* factorization of natural numbers (and a host of other results) makes the most sense in terms of the nomenclature of convenience.
 
David Bowman

________________________________

From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of John Denker
Sent: Mon 5/21/2007 1:44 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Prime numbers



On 05/21/2007 01:33 PM, Kilmer, Skip wrote:
> We're getting a bit off track, here, but I've always been curious as to why primes are defined in
> such a way (exactly two factors) as exclude 1.

That's a deep question, but the answer is shallow:  Things were
defined that way for convenience, pure and simple.

I hereby define "primoid integer" to be any positive integer that
has no factors other than itself and unity.  I emphasize that 1 is
primoid.

It turns out that almost all the interesting results (such as the
unique factorization theorems) are more conveniently expressed in
terms of primes rather than primoids.

You most certainly could restate things in terms of "primoids greater
than 1" but you would probably get tired of it.

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