On Fri, Mar 02, 2001 at 06:59:10PM +0000, Greg McCarroll wrote:
>
> No, definetly not. The partial set of prime numbers increases over
> the journey through integers. 1 is the logical starting point,
> and so it is added. This is the very spirit of primality. However
> this may be the rantings of a madman, it's just i feel like a jockey
> sometimes as i ride the sequence of prime numbers, jumping each
> new one and then feeling their occurence decrease.
Debates about definition tend to become dogmatic, and I don't think
you're being serious anyway :-) Still...
There is one excellent pragmatic reason for not considering 1 to be
prime, which is that by ordinary definitions every integer >1 has
a unique prime factorisation. 12=2*2*3, 100=2*2*5*5 etc.
If you allow 1 as a prime, then you lose that because 100 is also
1*2*2*5*5, 1*1*2*2*5*5, etc ad infinitum.
I'll resist the temptation to go into Ring Theory, the difference
between prime and irreducible etc. But even though it seems obvious
that 1 should be prime, there are good reasons to say that it's not,
(the best of which I've just mentioned).
[The reason for the confusion, I think, is that we tend to assume
that whole numbers are either prime or composite (ie can be made
by multiplying smaller numbers together). But 1 is neither -- it's
what ring theorists would call a unit.]
There's no reason you can't say that 1 is prime if you like though.
(What do you think about -1?)
.robin.
--
"do not assume that you are in control of your own actions,
but take responsibility for them anyway."
