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[PrimeNumbers] Re: The evolution of a tuple

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  • Jens Kruse Andersen
    ... The smallest admissable 168-tuplet is 1033 wide according to an exhaustive search by Thomas J. Engelsma: http://www.opertech.com/primes/k-tuples.html His
    Message 1 of 3 , Jun 2, 2005
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      Mark Underwood wrote:

      > There are exactly 168 primes from 1 to 1,000. I
      > wouldn't be surprised at all now if a prime constellation waaaay up
      > there somewhere exeeds 168 primes in an interval of 1,000.

      The smallest admissable 168-tuplet is 1033 wide according to an exhaustive
      search by Thomas J. Engelsma:
      http://www.opertech.com/primes/k-tuples.html

      His current results say that if there is a prime tuplet closer together than the
      earliest primes then it must be at least a 311-tuplet.
      From inexhaustive searching, his smallest admissable tuplet beating the earliest
      primes is a 447-tuplet of width 3159, where p(447) = 3163. Finding an occurrence
      of such a tuplet is out of the question today. However I agree with the k-tuplet
      conjecture that there are infinitely many.

      --
      Jens Kruse Andersen
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