Dr Holly Krieger discusses Merterns' Conjecture.
Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
More links & stuff in full description below ↓↓↓

More videos with Holly (playlist): http://bit.ly/HollyKrieger

Dr Holly Krieger is the Corfield Lecturer at the University of Cambridge and a Fellow at Murray Edwards College: https://www.dpmms.cam.ac.uk/~hk439/
On Twitter:   / hollykrieger  

PAPER: Disproof of the Mertens Conjecture: http://www.dtc.umn.edu/~odlyzko/doc/a...

More on Mertens Conjecture: http://mathworld.wolfram.com/MertensC...

Useful OEIS sequences:
https://oeis.org/A002321
https://oeis.org/A084237

Holly on the Numberphile Podcast:    • Champaign Mathematician (with Holly K...  

The Riemann Hypothesis:    • Riemann Hypothesis - Numberphile  

Mathematical correction from Dr Krieger: The first counterexample to Mertens conjecture must happen for some number no worse than about 10^(10^40), but the actual expectation is that the first counterexample is around 10^(10^23).

Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile

We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outr...

And support from Math For America - https://www.mathforamerica.org/

NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook:   / numberphile  
Numberphile tweets:   / numberphile  
Subscribe: http://bit.ly/Numberphile_Sub

Videos by Brady Haran
Animation by Pete McPartlan

Patreon:   / numberphile  

Numberphile T-Shirts: https://teespring.com/stores/numberphile

Brady's videos subreddit:   / bradyharan  

Brady's latest videos across all channels: http://www.bradyharanblog.com/

Sign up for (occasional) emails: http://eepurl.com/YdjL9