Wednesday, February 07, 2018

Sack's and Ulam Spiral

Numbers on the marked curve are of the form

x2 + x + 41,

the famous prime-generating formula discovered by Euler in 1772.

 Riemann discovered a geometric landscape, the contours of which held the secret to the way primes are distributed through the universe of numbers.

It seemed the patterns Montgomery was predicting for the way zeros were distributed on Riemann’s critical line were the same as those predicted by quantum physicists for energy levels in the nucleus of heavy atoms. The implications of a connection were immense: If one could understand the mathematics describing the structure of the atomic nucleus in quantum physics, maybe the same math could solve the Riemann Hypothesis.

Sack's spiral-a version of the Ulam spiral

 Sift the Two's and Sift the Three's,
The Sieve of Eratosthenes.
When the multiples sublime,
The numbers that remain are Prime.