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Explore A Prime Surprise (Mertens Conjecture) - Numberphile with 879,832 views, 22,555 likes, and 1,534 comments. Experience the impact of this video content that has captured audience attention.

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: 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

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