What is...the infinitude of prime knots?

Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.

This time.
What is...the infinitude of prime knots? Or: Euclid's theorem for knots.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.
http://www.dtubbenhauer.com/youtube.html

Thumbnail.
https://mathcurve.com/courbes3d.gb/no...

Main discussion.
https://en.wikipedia.org/wiki/Connect...
https://en.wikipedia.org/wiki/Prime_knot
https://mathworld.wolfram.com/PrimeKn...
https://en.wikipedia.org/wiki/List_of...
https://en.wikipedia.org/wiki/Torus_knot
https://oeis.org/A051764
https://en.wikipedia.org/wiki/Pretzel...
https://mathoverflow.net/questions/81...
https://mathoverflow.net/questions/41...
https://www.sciencedirect.com/science...
https://en.wikipedia.org/wiki/Euclid%...

Background.
https://www.math.cuhk.edu.hk/course_b...
https://en.wikipedia.org/wiki/Knot_(m...)
https://en.wikipedia.org/wiki/Knot_in...
https://en.wikipedia.org/wiki/Braid_g...
https://en.wikipedia.org/wiki/Reideme...

KnotAtlas.
http://katlas.math.toronto.edu/wiki/T...

SnapPy.
https://snappy.math.uic.edu/

Mathematica.
https://www.wolfram.com/language/12/m...
https://demonstrations.wolfram.com/To...
http://katlas.org/wiki/The_Mathematic...

Pictures used.
https://www.biographyonline.net/wp-co...
Pictures from    • What are...torus knots?  
Pictures from    • What are...prime knots?  
Picture from https://en.wikipedia.org/wiki/Prime_knot
https://en.wikipedia.org/wiki/Pretzel...
https://en.wikipedia.org/wiki/(%E2%88...

YouTube and co.
   • Prime Knots - Numberphile  
   • What are...prime knots?   (shameful self-promotion)
   • What are...torus knots?   (shameful self-promotion)
   • 596.4d Prime and Composite Knots  

#knottheory
#topology
#mathematics