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13174Re: Prime Number Progresions

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  • Mark Underwood
    Aug 5, 2003
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      Right Gary, I guess that would be the transformation. Actually I just
      checked out the progression in the sequence starting with 29, 31,
      37 ... and it was easy to see it was of this form. I now see from

      http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html

      that Legendre is the first reported to have seen this one. Perhaps
      2x^2 + 29 generates the longest sequence of consecutive primes of any
      two term equation.

      And I see that Virginia's sequence of primes is reported in the
      Encyclopedia on Integer Sequences as sequence A060834.

      The Mathworld link above has alot of informative things to say about
      the matter. (Virginia would like to read this!) I agree with you Gary
      that there are other polynomials out there that can generate even
      longer sequences. How to cleverly find them, that is the question.

      But for expressions of the form x^2 + x + p there is no need to look
      for a longer one since it has been shown that p = 41 generates the
      longest one.

      Mark



      --- In primenumbers@yahoogroups.com, Gary Chaffey <garychaffey@y...>
      wrote:
      > > I just figured that Gary's equation can be reduced
      > > to 2x^2 + 29 to
      > > generate his 29 distinct primes from x=0 to x=28 !
      > >
      > > Mark
      > I have just spotted this too.. make y=x-22...(is this
      > the transformation you have spotted Mark???)
      > Gary
      >
      >
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