Re: [Phys-l] Prime numbers

[John Denker <jsd@av8n.com>]

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.