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What are...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 are...prime knots? Or: The prime numbers of knot theory!? 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 Knot theory. https://en.wikipedia.org/wiki/Knot_th... https://bookstore.ams.org/KNOT https://people.math.harvard.edu/~ctm/... https://en.wikipedia.org/wiki/Reideme... https://en.wikipedia.org/wiki/Unknott... Prime knots. https://en.wikipedia.org/wiki/Prime_knot https://mathworld.wolfram.com/PrimeKn... https://en.wikipedia.org/wiki/List_of... https://en.wikipedia.org/wiki/Connect... https://mathworld.wolfram.com/KnotSum... https://mathoverflow.net/questions/81... https://math.stackexchange.com/questi... Granny knot. https://en.wikipedia.org/wiki/Granny_...) https://mathworld.wolfram.com/GrannyK... Knot atlas. http://katlas.math.toronto.edu/wiki/M... http://katlas.math.toronto.edu/wiki/T... Number of knots. https://oeis.org/A086825 https://oeis.org/A002863 https://codegolf.stackexchange.com/qu... SnapPy. https://www.math.uic.edu/t3m/SnapPy/ Mathematica. https://demonstrations.wolfram.com/to... Pictures used. https://www.researchgate.net/figure/T... https://upload.wikimedia.org/wikipedi... https://en.wikipedia.org/wiki/Connect... Pictures from https://arxiv.org/abs/2001.01472 Pictures from https://people.math.harvard.edu/~ctm/... https://en.wikipedia.org/wiki/Prime_k... https://en.wikipedia.org/wiki/Granny_... YouTube and co.    • Knotty Problems - Marc Lackenby      • Prime Knots - Numberphile      • 596.4d Prime and Composite Knots