素数の螺旋

This video is a translation and re-edit of a 3Blue1Brown video by Ufolium, published under official license. Please subscribe and like. Translation: Ufolium ufolium.com offers mathematics courses from middle school through college, covering a variety of topics, including linear algebra and basic analysis! https://ufolium.com    / @ufolium   Archimedean spiral This refers to a spiral represented by the polar coordinate equation r=aθ. Of course, this video only plots cases where r and θ are natural numbers, so it would be more accurate to say that this is just a portion of it. Note The Japanese version is generally a faithful translation of the original English version, but around 18:00, the Japanese version has been dubbed and corrected to reflect corrections made after the English version was released. 16:45 I say "the first person to solve this puzzle," but to avoid any misunderstanding, I should clarify that Dirichlet demonstrated that these "cosets that may contain primes" actually contain an infinite number of primes by using the divergence of the reciprocal sum. However, as for the uniform distribution, as discussed around 18:00 in the video, he only confirmed it numerically, and it was not proven until much later (if I'm not mistaken, by Vallée Poussin in (1899)). Dirichlet's paper (1837) https://arxiv.org/pdf/0808.1408.pdf Math StackExchange https://math.stackexchange.com/questi... Mathologer video (English)    • Infinite fractions and the most irrational...   There's also something called the Ulam spiral ↓ (English)    • Prime Spirals - Numberphile   19:01 https://arxiv.org/abs/math/0505300 https://annals.math.princeton.edu/201... -3/p07 Japanese Twitter   / 3b1bjp   Original Channel (English)    / 3blue1brown   Original Video (English)    • Why do prime numbers make these spirals? |...   ---------------------------------------- Support the English Translation Channel   / 3blue1brown   Animation created with manim https://github.com/3b1b/manim Official English Social Media Website: https://www.3blue1brown.com Twitter:   / 3blue1brown   Facebook:   / 3blue1brown   Reddit:   / 3blue1brown   ---------------------------------------- Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a... Stream the music on Spotify: https://open.spotify.com/album/1dVyjw...