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Prime Number Theorem (view source)
Revision as of 03:18, September 13, 2008
, 03:18, September 13, 2008history - who proved it, etc.
In fact, for large x this turns out to be a better approximation than <math>\pi(x)</math>. The size of the error <math>\mbox{Li}(x) - \pi(x) </math> is closely related to the behavior of the [[Riemann Zeta function]]
In fact, for large x this turns out to be a better approximation than <math>\pi(x)</math>. The size of the error <math>\mbox{Li}(x) - \pi(x) </math> is closely related to the behavior of the [[Riemann Zeta function]]
== History of the Theorem ==
The theorem was first conjectured by [[Legendre]] and [[Gauss]] (independently) circa 1796. In 1848 and 1850, [[Chebyshev]] made significant progress towards proving the theorem using the [[Riemann zeta function]] and other [[elementary techniques|non-elementary techniques]]. His non-elementary proof was completed in 1896 by [[Hadamard]] and Charles de la Vallee-Poussin.
The grand culmination of these efforts occured in 1949 and 1950 when [[Paul Erdos]] and [[Atle Selberg]] presented an elementary proof of the theorem. This proof earned Selberg the highest prize in math, the [[Fields Medal]].
[[Category:Mathematics]]
[[Category:Mathematics]]