A new bound for the smallest $x$ with $π(x) > li(x)$

Mathematics – Number Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Final version, to be published in the International Journal of Number Theory [copyright World Scientific Publishing Company]

Scientific paper

We reduce the leading term in Lehman's theorem. This improved estimate allows us to refine the main theorem of Bays and Hudson. Entering $2,000,000$ Riemann zeros, we prove that there exists $x$ in the interval $[exp(727.951858), exp(727.952178)]$ for which $\pi(x)-\li(x) > 3.2 \times 10^{151}$. There are at least $10^{154}$ successive integers $x$ in this interval for which $\pi(x)>\li(x)$. This interval is strictly a sub-interval of the interval in Bays and Hudson, and is narrower by a factor of about 12.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

A new bound for the smallest $x$ with $π(x) > li(x)$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A new bound for the smallest $x$ with $π(x) > li(x)$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A new bound for the smallest $x$ with $π(x) > li(x)$ will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-680518

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.