Edit made on January 13, 2013 by ColinWright at 17:25:13

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~~WW~~ WM

HEADERS_END

The function ~~EQN:\text{Li}(x)=\int_2^x~\frac{dx}{\log~x}~~ EQN:\text{Li}(x)=\int_2^x\frac{dx}{\log~x} is called the "logarithmic integral".

According to the Prime Number Theorem, it is approximately equal to the number of primes below /x./

The function ~~EQN:\text{li}(x)=\int_0^x~\frac{dx}{\log~x}~~ EQN:\text{li}(x)=\int_0^x\frac{dx}{\log~x} is also called the logarithmic integral;

the two functions differ by a constant.

(Since the definition of EQN:\text{li}(x) involves integrating through a singularity,

some care is needed in interpreting the definition.)