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prime humongo-tuplets

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  • WarrenS
    Let pi(N) = number of primes p with p
    Message 1 of 1 , Dec 2, 2012
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      Let pi(N) = number of primes p with p<=N.

      A well known question is whether
      pi(A)+pi(B) <= pi(A+B)
      always. Usually this is true, but
      Hensley & Richards suspect answer is "not always"
      and a way to find a counterexample A,B is:

      find a set of more than pi(3159)=446
      primes within an interval of cardinality 3159.

      There are constellations of 447 possible-primes that would allow this
      in principle to happen -- a fact detected by Thomas J. Engelsma
      http://www.opertech.com/primes/k-tuples.html
      http://www.opertech.com/primes/w3159.html
      hence it presumably happens.

      However, finding an actual example of such a prime 447-tuple,
      seems like an almost impossible computation way beyond the
      prime-tuplets records that the likes of J.Wroblewski have recently been
      posting here.
      Englema guestimates the first example might be
      around 2.23 x 10^343.

      There is no way you are going to find something that rare by random trial.
      You need a way-better search technique.
      I have no idea what that technique could be.
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