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This is a video message from me and a deleted scene from my video "What is the biggest tangent of a prime?"

Original video here: https://www.youtube.com/watch?v=A7eJb8n8zAw

Two more primes have been found which are bigger than the one mentioned in my video. Here is a great write-up from someone who has found both of them:https://samuelj.li/blog/2020-08-20-prime-tangents/

Thanks for your support everyone!

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PATREON BONUS: tan(prime) greater than prime

Main video here: https://www.youtube.com/watch?v=A7eJb8n8zAw This is a video message from me and a deleted scene from my video "What is the biggest tangent of a prime?" which was uploaded as bonus footage for my Patreon supporters. Here is the post on Patreon: Support me and I can make more/better videos!

Comments

Edith Dubiner

It's not about north-pole and south-pole, is it... but rather close to any of the poles but in quadrant I,III (sin,cos have the same sign) as opposed to II and IV (opposite signs). :)

Matt Parker

I think we’re saying the same thing? I was using ‘north/south pole’ as a shorthand for the top and bottom of the diagram circle (I was planning to add arrows to the diagram as I was talking).

Florian Linscheid

You really make us work for it. But I appreciate the joke, Matt.

Keith Moser

My eyes (and/or my monitor resolution) were not cut out for that! But I finally figured it out... :-) Looking forward to 2023!

Edith Dubiner

tan(pi/2-0.000001) > 0 but tan(pi/2+0.000001) ~ -1000000 < 0

Vincent Zalzal

Oh wow, ok, do I need a 4k monitor for this?

Greg Jensen

In the circular model, where each integer can be considered to deposit a "point" along the circumference of the circle, and given that the irrationality of π guarantees that no two such points will occur at the same coordinates, is the expectation that the circular distribution of points should tend toward a uniform distribution as n approaches infinity (as described by a von Mises distribution where kappa = 0.0), or is a particular angle favored (perhaps by a von Mises w/ kappa > 0), or does some multi-modal distribution eventually emerge? My intuition is that the distribution must converge on uniform, but even if that intuition is correct, how about in the near term (e.g. on all integers up to tan(prime)>prime)?

James Coutie

I've been going through frame-by-frame on a 4k monitor and I still can't work out the characters after the /

Samuel Gélineau

Even after downloading the video in 2160p and zooming in, I still only managed to read a few words. I guess we need some kind of magic de-blurring algorithm...