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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). 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/outreach/science-sandbox/ And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Animation by Pete McPartlan Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9