A161623


Greatest n for which the Andricalike conjectural inequalities, Prime[n+1]Prime[n](1/k)*Sqrt[Prime[n] < 0, appear to fail to hold, for k = 1,2,3,4,..., based on empirical evidence.


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%I
%S 30,430,3644,4612
%N Greatest n for which the Andricalike conjectural inequalities, Prime[n+1]Prime[n](1/k)*Sqrt[Prime[n] < 0, appear to fail to hold, for k = 1,2,3,4,..., based on empirical evidence.
%C This is a family of increasingly restrictive Andricalike conjectures that all imply Legendre's conjecture.
%e Example: For k = 1, one needs n > 30 for the inequality to obtain, and it is conjectured that it holds for all n > 30. In words, the first such inequality says that we expect to see a new prime p(n+1) between p(n) and p(n)+ Sqrt(p(n)).
%K nonn
%O 1,1
%A _Daniel Tisdale_, Jun 15 2009
