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15711Re: [PrimeNumbers] Re: another way to calculate primes

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  • Paul Leyland
    Dec 8, 2004
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      On Tue, 2004-12-07 at 20:52, D├ęcio Luiz Gazzoni Filho wrote:
      > On Tuesday 07 December 2004 18:20, you wrote:
      > > --- In primenumbers@yahoogroups.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.

      Thanks Decio.

      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?


      Paul
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