Watch Prime Number Sieve and the Ulam Spiral in New Channel | Channify

The Ulam Spril was publicized by Stanislaw Ulam in 1963. The spiral can be generated using the sieve of Eratosthenes to etch out the prime numbers. This animation depicts 123 iterations of the sieve. Initially, the Ulam Spiral is drawn and the primes are colored dark red. Those primes that have a rank, the order that the prime appears in the prime number sequence, that is also prime are colored yellow, and those that have a rank that is a prime with a rank that is also prime are colored blue. The sieve begins with 2 and 'evaporates' every other cell. When a cell is evaporated, the cells ahead of it in the spiral shift back to fill the vacant space but they retain their original value for future division tests. The next iteration evaporates those cells divisible by 3, and then 5, 7 and so on. Red cells(primes) change to black when they are less than p^2. Thus, the area of the inner square is π(x)^2 (the prime counting function). What is left after all composites have been evaporated and the newly created black cells are interperted as composites is an exact replica of what we started with, only shifted in the hierarchy of primeness so to speak. The path of a couple of prime points is traced as they move to their final destination. Music by: cloudtalk, Austin Texas.