Eulerian Logarithmic Integral is Asymptotic to Prime-Counting Function/Examples/10^6

Examples of Use of Eulerian Logarithmic Integral is Asymptotic to Prime-Counting Function

Let $\map \Li x$ denote the Eulerian logarithmic integral of $x$.

Let $\map \pi x$ denote the prime-counting function of $x$.

Then:

\(\ds \map \Li {10^6}\)

\(\approx\)

\(\ds 78 \, 628\)

\(\ds \map \pi {10^6}\)

\(=\)

\(\ds 78 \, 498\)

\(\ds \leadsto \ \ \)

\(\ds \dfrac {\map \Li {10^6} } {\map \pi {10^6} }\)

\(\approx\)

\(\ds 1 \cdotp 00166\)

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logarithmic integral