- 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
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
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.