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

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  • 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 1 of 16 , Aug 3, 2010
      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







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