Skewes number

The Skewes Number, written $Sk_{1}$, is the largest number $n$ where $\pi (n)<li(n)$ is true, assuming the Riemann hypothesis is true. Here, $\pi(n)$ is the prime counting function and $li(n)$ is the logarithmic integral.

The original upper bound for the number was $e^{e^{e^{79}}} \approx 10^{10^{10^{34}}}$, in the vicinity of the googolduplex.

The second Skewes Number, $Sk_{2}$, is the largest number $n$ where $\pi (n)<li(n)$ is true, assuming the Riemann hypothesis is false. It is larger than the original Skewes Number, $10^{10^{10^{1000}}}$.

See also

• googolduplex