View Submission - COMPSTAT

A0491
**Title: **A computational statistics approach for estimating the smallest natural number $x$ for which $\pi(x) > li(x)$
**Authors: **Ryuichi Sawae - Okayama University of Science (Japan) **[presenting]**

**Abstract: **In number theory, there may be an extremely large number, which is defined by the smallest natural number $x$ such that $\pi(x) > li(x)$, where $\pi(x)$ is the prime counting function and $li(x)$ is the logarithmic integral function. The smallest natural number is known as the so-called Skewes' number, and has been proved to be between the 19th power of 10 and about $6.6587 \times 10^{152}$ by many recent researches. We will try to improve the lower bound of the Skewes' number to the 27th power of 10 with a computational statistics approach, in which the number of prime number is statistically counted with the estimated errors by use of the sieve of Eratosthenes.