In one fundamental corner of mathematics, some prime numbers stop being prime.
0:00 -The Typical View of Primes
1:37 - Two-Dimensional Numbers
3:57 - Multiplying Special Conjugates
4:46 - Hidden Factorizations
6:42 - Modular Square Patterns
8:54 - Which Primes Are Which Type
9:55 - Conclusion
Thanks to my Patreon supporters (and supporters on the Youtube memberships on my @Domotro channel). See the credits at the end of this episode for all the names! Please consider supporting Combo Class here: https://www.patreon.com/comboclass
Clarification:
- Around 6-7 minutes in, I say we are allowing all complex numbers as possibilities. I meant just the Gaussian integers of those (similar to how typically only integers are considered as factors).
Catch up on the earlier episodes of Grade -3 with this chronological playlist:
https://www.youtube.com/playlist?list=PLsATqXCEHAboWuDWuwrPGA0ZsiGNPOOvd
(the "playlists" section of this channel also has playlists for Grade -1 and Grade -2).
Bonus channel:
https://www.youtube.com/@Domotro
Discord: https://discord.gg/nMxjCEhhFn
Subreddit: https://www.reddit.com/r/comboClass
This episode of Combo Class was created, directed and edited by me (Domotro) and I also made all of the music in it. It was mostly filmed by Evan Clark, with some clips filmed by Carlo Trappenberg, and some filmed by me.
Mathematical topics in this video include: prime numbers, factor pairs, integers, real numbers, imaginary numbers, the complex plane, complex conjugates, multiplying complex numbers and getting real numbers, Gaussian integers, Gaussian primes, modular arithmetic, quadratic residues, square numbers in mod 4, patterns with which numbers can be expressed as the sum of two squares, surprising hidden factorizations of prime numbers, and other interesting mathematical subtopics and fun facts.
Disclaimer: Do not copy any potentially dangerous actions you may see in these videos, such as any actions related to fire, glass, or tools.