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13176Re: [PrimeNumbers] Re: Prime Number Progresions

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  • Gary Chaffey
    Aug 5, 2003
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      > > 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.

      If we restrict to two term equations then it can't be
      of the form 2x^2+p since of a proof (referred to on
      Wolfram site) which shows that this type of sequence
      can only yield 29 primes.
      This implies we must look at ax^2+p for a>2. What
      would be interesting is to rule out some more values
      for a. I might look at this if I get some spare time.
      Gary

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