Mertens Conjecture
Additional information
Dr Holly Krieger discusses Merterns' Conjecture.
Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
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: https://twitter.com/hollykrieger
PAPER: Disproof of the Mertens Conjecture: http://www.dtc.umn.edu/~odlyzko/doc/arch/mertens.disproof.pdf
More on Mertens Conjecture: http://mathworld.wolfram.com/MertensConjecture.html
Useful OEIS sequences:
https://oeis.org/A002321
https://oeis.org/A084237
Holly on the Numberphile Podcast: https://youtu.be/QmfQQzjpdpM
The Riemann Hypothesis: https://youtu.be/d6c6uIyieoo
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).
