Robin Houston
Fri, 02 Mar 2001 10:37:30 -0800
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."