In this special episode (the longest one I've created yet) let me show you an interesting pattern I recently found, and all of the cool mathematical connections I've been able to deduce about it.... Timestamps of different chapters:
0:00 - My Explorations Into Primeglitching
3:29 - Explanation of the Main Pattern
9:18 - Discoveries Among the First 50 Numbers
14:36 - Discoveries Among Larger Numbers
19:57 - Finding the Other Research About This
27:38 - What I Could Deduce About the General Pattern
32:30 - What I Could Deduce About Fixed Points
42:13 - What I Could Deduce About Two-Number Cycles
50:47 - Ideas for Larger Cycles and General Proofs
55:12 - Extending to Fractions and Square Roots
1:05:22 - Other Forms of Potential Primeglitching

I only came across this pattern about a month ago, so I'm sure I'll realize or deduce other things about it when I return to the problem later. I'll probably investigate this (and other primeglitching patterns) more on my bonus @Domotro channel so make sure you're tuned in there as well.... And if any of you find or prove anything about this concept yourself, leave a comment and/or send me an email at combouniversity@gmail.com (or just write your own paper about it and credit me somewhere!)

Corrections/clarifications:
- One of the diagrams shows 48 going to 15 and then 24, but it doesn't actually pass by 15 (48 goes directly to 24).
- In an early example, I showed 1050 going to 840 but it really goes to 672 (the general point about it shrinking overall it still true).

Next episode will be the Grade -2 finale! (Before we enter Grade -3 soon). The finale will be like a documentary about making this grade, including lots of interesting behind-the-scenes moments that didn't make it into episodes, among other things...
In the meantime, make sure you've checked out my previous Grade -1 finale/documentary: [ Ссылка ]
And here's a playlist of all of Grade -2 so far (in order) if you want to make sure you've seen them all: [ Ссылка ]

Special thanks to my current supporters on Patreon!
Max, George Carozzi, Chandler Smith, Eric Brodeur, Henry Spencer, Jon Mandarin, Mitch Harding, Tybie Fitzhugh, Joshua S, Julius 420, Peter Offutt, Quinn Moyer, Beugul, Stan Seibert, Dave Brondsema, Florian, Jan Bosenberg, Mathias Ermatinger, terry, William Hawkes, Christopher Masto, Claudio Fanelli, Craig Butz, Harry Cruse, Joost Boesburg, Kali OmegaRogue, Michael Friemann, The Green Way, Mack, cat, Stephen Davies, and Mackenzie Newman!
I WILL BE THANKING ALL PATREON SUPPORTERS (NEW AND OLD) AND WRITING YOUR NAMES ON A WHITEBOARD NEXT EPISODE.
If you want to get your name on that list and help support this channel (which helps me keep making videos without any brand advertisements) and get some bonus content, check out the Patreon here: [ Ссылка ]

In case anybody searches any of these terms, some topics that show up in this episode include: prime numbers, prime factorizations, something I call "primeglitching", the OEIS (Online Encyclopedia of Integer Sequences), squarefree numbers, powerfree parts of numbers, factors/divisors, extended prime factorizations into rational numbers like fractions as well as some irrational numbers like square roots, natural density, tree-like visualizations of numbers, and much more.

This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg. The visuals of the number trees were designed by Stick.

Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.

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