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Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations

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Further reading 1

When does a pattern in a picture become a proof? →A tiling suggests a conjecture, a new encoding turns rectangles into collisions, and a plotting rule creates spirals before primes even enter the picture. What work does each picture actually do?This video helps answer · Does the spiral survive when every integer is plotted?

Caption notes

Using each integer as its polar angle creates near returns after certain step sizes. The spiral geometry begins with the plotting rule; which arms survive a prime filter is a separate arithmetic question.

Video or transcript source ↗
Original passages · 2
taking 44 steps is very close to a whole number of turns
Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations · ▶ 7:13–7:21
each of these spiral arms corresponds to a residue class mod 6
Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations · ▶ 6:49–7:00

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