Formulas for pi(n) and the n-th prime

Details Formulas for pi(n) and the n-th prime Formulas for pi(n) and the n-th prime

2002-10-21

arxiv.org/abs/math/0210312v2

Mathematics

Number Theory

4 pages, simplified formula for p_n, how to implement it in time O((n.log(n))^(3/2)), other optimizations

Scientific paper

Using inequalities of Rosser and Schoenfeld, we prove formulas for pi(n) and
the n-th prime that involve only the elementary operations +,-,/ on integers,
together with the floor function. P. Sebah has pointed out that the formula for
pi(n) operates in O(n^(3/2)) time.

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