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A161623

Greatest n for which the Andrica-like 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.

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)).