Number of Primes up to n Approximates to Eulerian Logarithmic Integral

Theorem

The prime-counting function approximates to the Eulerian logarithmic integral:

$\map \pi n \approx \ds \int_2^n \frac {\d x} {\ln x}$

Proof

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Also see

• Prime Number Theorem

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $10^{10^{10^{34}}}$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $10^{10^{10^{34}}}$