Explore the fascinating world of prime numbers and their unexpected spiral patterns in this 22-minute video by 3Blue1Brown. Delve into the curious phenomenon of prime number spirals, uncover approximations for pi, and investigate prime distributions. Learn about residue classes, Euler's totient function, and Dirichlet's theorem as you journey through the mathematical landscape. Discover the connections between these concepts and their broader implications in number theory. Gain insights into the historical development of these ideas, including corrections to common misconceptions about Dirichlet's work on prime distribution. Engage with complex mathematical concepts through clear explanations and stunning visualizations, making abstract ideas more accessible and intriguing.