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RE: [PrimeNumbers] Re: Easy formula for next prime... cant make it any easier.

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  • Peter Kosinar
    Matteo, ... An expression (e.g. 2n+1) represents a set S if every number from set S can be written in the form prescribed by the expression. It s not necessary
    Message 1 of 16 , Aug 3 3:08 PM
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      Matteo,

      > > Wrong. 6n+/-1 represents all -odd- integers not divisible by 3 and,
      > > consequently, it represents all primes with the exception of 2 and 3. This
      > > is where it differs from your form 3n+2+4, which guarantees the "not
      > > divisible by 3" condition, but not the "is odd" one.
      >
      > I don't thing i understand very well what you're saying about 6n+/-1 that
      > should represent all primes.

      An expression (e.g. 2n+1) represents a set S if every number from set S
      can be written in the form prescribed by the expression. It's not
      necessary for all the numbers of that form to belong to set S.

      For example, the form 2n+1 represents all odd integers. Thus, it can also
      be used to represent each and every odd prime, odd square or odd perfect
      number -- since all of these are just subsets of the set of odd numbers.

      Peter
    • Martin Aaronson
      Peter Thanks for your comment. I admit I am wrong technically in that since 2 is the only even prime, I usually skirt around that issue by always prefacing
      Message 2 of 16 , Aug 3 4:00 PM
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        Peter Thanks for your comment. I admit I am wrong technically in that since
        2 is the only even prime, I usually skirt around that issue by always
        prefacing my remarks by stating ³in the set of odd numbers only,² which I
        neglected to do in this case. I do that because prime 2 always obfuscates
        the issue, as it is doing in this very instance. Thanks for your interest.
        Marty



        From: Matteo Mattsteel Vitturi <mattsteel@...>
        Date: Tue, 3 Aug 2010 23:25:54 +0200
        To: <primenumbers@yahoogroups.com>
        Subject: RE: [PrimeNumbers] Re: Easy formula for next prime... cant make it
        any easier.







        Peter,

        > > Folks out there including yourself and Lelio don't seem to understand

        > > that 6n+/-1 represents ALL integers that are not multiples of 3, so of

        > > course every single prime to infinity is either 6n+1, or 6n-1,

        >

        > Wrong. 6n+/-1 represents all -odd- integers not divisible by 3 and,

        > consequently, it represents all primes with the exception of 2 and 3. This

        > is where it differs from your form 3n+2+4, which guarantees the "not

        > divisible by 3" condition, but not the "is odd" one.

        >

        I don't thing i understand very well what you're saying about 6n+/-1 that
        should represent all primes.
        When n=20 then 6n-1=119 and 6n+1=121 and both aren't primes since 121 is
        11x11 and 119 is 7x17.

        Matteo.



        [Non-text portions of this message have been removed]








        [Non-text portions of this message have been removed]
      • Martin Aaronson
        Peter Thanks for your comment. I admit I am technically wrong in that since 2 is the only even prime, I usually skirt around that special case by always
        Message 3 of 16 , Aug 3 9:39 PM
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          Peter Thanks for your comment. I admit I am technically wrong in that
          since 2 is the only even prime, I usually skirt around that special case by
          always prefacing my remarks with ³in the set of odd numbers only,² which
          I neglected to do, much to my regret since I am getting flak from around
          the world. I do that because prime 2 always obfuscates the issue, as it is
          doing in this very instance.
          So, to correct, the locus for ALL primes except 2 is 6n+1 or 6n-1,
          which of course is not to say that all 6n+-1 are prime. Another way to
          define 6n+-1 is 3n+2+4, where both are one and the same. The distinction I
          am making is that 3n+2+4 is descriptive (to me) of all non-multiples >3 to
          infinty, while 6n+-1, makes it appear that there is something profound and
          revealing about this infinite set when in fact it has been staring us in the
          face from the very outset as 3n+2+4. If you look at in this light, it will
          all come together. Thus, the search for a pattern in 6n+1-1 is all in vain.
          A list of prime numbers (go primes.utm.edu ) has provided this information
          forever. Thanks for your interest. Regards. Marty



          From: Peter Kosinar <goober@...>
          Date: Wed, 4 Aug 2010 00:08:38 +0200 (CEST)
          To: Matteo Mattsteel Vitturi <mattsteel@...>
          Cc: <primenumbers@yahoogroups.com>
          Subject: RE: [PrimeNumbers] Re: Easy formula for next prime... cant make it
          any easier.






          Matteo,

          > > Wrong. 6n+/-1 represents all -odd- integers not divisible by 3 and,
          > > consequently, it represents all primes with the exception of 2 and 3. This
          > > is where it differs from your form 3n+2+4, which guarantees the "not
          > > divisible by 3" condition, but not the "is odd" one.
          >
          > I don't thing i understand very well what you're saying about 6n+/-1 that
          > should represent all primes.

          An expression (e.g. 2n+1) represents a set S if every number from set S
          can be written in the form prescribed by the expression. It's not
          necessary for all the numbers of that form to belong to set S.

          For example, the form 2n+1 represents all odd integers. Thus, it can also
          be used to represent each and every odd prime, odd square or odd perfect
          number -- since all of these are just subsets of the set of odd numbers.

          Peter







          [Non-text portions of this message have been removed]
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