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13177Re: Prime Number Progresions

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  • Mark Underwood
    Aug 5 9:05 AM
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      Thanks for the correction Jack, I would not have discerned that
      difference from what I read unless it was pointed out.

      I remember the Hardy-Littlewood k tuple Conjecture but I never did
      connect it to polynominals.

      Whether the k tuple conjucture is true, I guess I believe it with a
      condition, which is that the tuple does not occur if it does not
      occur early on, or something like that...

      Mark



      --- In primenumbers@yahoogroups.com, "jbrennen" <jack@b...> wrote:
      > --- Mark Underwood wrote:
      >
      > > Perhaps 2x^2 + 29 generates the longest sequence of consecutive
      > > primes of any two term equation.
      >
      > If you believe the first Hardy-Littlewood Conjecture (also known
      > as the k-tuple Conjecture), there exist arbitrarily long sequences
      > of primes from two term equations.
      >
      > > 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.
      >
      > Again, the same conjecture implies that arbitrarily long sequences
      > of primes exist of the form x^2+x+p.
      >
      > What has been shown is that p=41 is the largest prime such that
      > x^2+x+p is prime for all x, 0 <= x <= p-2.
      >
      > It has not been shown that x^2+x+p is never prime for 0 <= x <= 40.
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