Number of Primes up to n Approximates to Eulerian Logarithmic Integral/Mistake

Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary

$10^{10^{10^{34}}}$

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$10^{10^{10^{34}}}$

Mistake

The number of primes less than or equal to $n$ is approximately $\ds \int_0^n \frac {\d x} {\log x}$.

Correction

That should be $\ds \int_2^n \frac {\d x} {\log x}$.

$\log x$ in this instance denotes the natural logarithm function.

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): $10^{10^{10^{34}}}$