## prime humongo-tuplets

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• 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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