Factoring large numbers into primes | Famous Math Problems 1 | NJ Wildberger

This is the first video of a new series, which will discuss a wide variety of famous (and perhaps not so famous) mathematical problems, ranging from antiquity to modern times. I am N J Wildberger, a pure mathematician at UNSW, the discoverer of Rational Trigonometry and Universal Geometry, and a big fan of YouTube, the future of free on-line education!

After introducing the series, we begin with FMP #1: how to factor a particular number z (10 to the 10 to the 10...altogether ten times, plus 23) into primes. We remind viewers about primes and the Fundamental theorem of Arithmetic, and have a look at explicit factorizations related to our basic problem.

Then we introduce briefly modular arithmetic and the theorems of Fermat and Euler. This is used to show that 7 does not divide z. Some comments on difficulties with arithmetic with big numbers follows, and then some exercises give some challenges for the viewer.

Thanks to Professor Saad El-Zanati from Illinois State University for suggesting this series. Thanks also to Steve Sexton from Exchange for giving permission to use their music track Highlights.

Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of each lecture. Great for review, study and summary.

A screenshot PDF which includes FamousMathProbs1 to 12 can be found at my WildEgg website here: http://www.wildegg.com/store/p111/product-FamousMathProblems-screenshot-pdf

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .

Видео Factoring large numbers into primes | Famous Math Problems 1 | NJ Wildberger канала Insights into Mathematics