This video is an attempt to explain the Prime Number Theorem in a way that gives you a tactile intuition regarding the density of primes. It’s an idea Gauss is famous for having at the age of 16 while studying tables of prime numbers < size (x). The idea for this video came to me while walking in the forest and noting the gradual shift in leaf density as I moved away from the trees. I thought it could be a nice way to introduce density gradient.

More importantly, check out the amazing visualization that Khan Academy user Peter Collingridge made to follow up the video:

http://www.khanacademy.org/cs/spiral-sieve-of-eratosthenes/1125572884