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== Equivalent Statements ==

== Equivalent Statements ==

[[Gauss]] conjectured the equivalent statement that <math>\pi(x)</math> was asymptotic to <math>\mbox{Li}(x)</math> defined as:  

[[Carl Friedrich Gauss]] conjectured the equivalent statement that <math>\pi(x)</math> was asymptotic to <math>\mbox{Li}(x)</math> defined as:  

<math> \mbox{Li}(x) = \int_2^x \frac{dt}{\ln t}</math>.  

<math> \mbox{Li}(x) = \int_2^x \frac{dt}{\ln t}</math>.  

In fact, for large x this turns out to be a better approximation than <math>\pi(x)</math>.

In fact, for large x this turns out to be a better approximation than <math>\pi(x)</math>.