15711Re: [PrimeNumbers] Re: another way to calculate primes
- Dec 8, 2004On Tue, 2004-12-07 at 20:52, Décio Luiz Gazzoni Filho wrote:
> On Tuesday 07 December 2004 18:20, you wrote:Thanks Decio.
> > --- In email@example.com, Paul Leyland <pcl@w...> wrote:
> > > The set of prime numbers is all numbers that are not composite, by
> > > definition.
> > Whoa there! That leaves a mighty narrow definition of "numbers".
> > Units? Rationals?
> Let's not be pedantic here. From the context it's pretty clear that we're
> talking about integers, so the only gap in Paul's declaration relates to
> units. Furthermore, even if his definition was not 100% mathematically
> correct, I think his point was well communicated, and that's what matters
> here -- he's not trying to write a book, but rather point out the flaw in the
> previous poster's definiton.
Two people, including Rick and another by personal email, have told me I
omitted the unit. Nobody told me I omitted zero. I freely admit that I
should have included them. As for rationals, irrationals, algebraics,
transcendentals, gaussian integers, complex numbers, quaternions and all
the rest of the zoo, I think it pretty obvious from context that the
area of discourse was N or Z. Otherwise, I may have been tempted to
point out that 3 is prime but that 2 is (1+i)(1-i) and 5 is (2+i)(2-i)
in the Gaussians.
After that clarification, can someone please tell me why in Z or N that
2, 3 and 5 need singling as special cases?
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