Prime Spiral

 I just learned about something called prime spirals or Ulam’s spiral. Ulam’s spiral is named after Stanslaw Ulam who was born in Poland in 1909 but moved to the United States in 1936, becoming an American Citizen in 1943, during World War II.  He worked at Los Alamos from 1943 to 1965 when he began lecturing at various Universities.  Over his lifetime, he published multiple papers on a variety of different mathematical topics. In addition, he contributed to the creation of thermonuclear reactions.

Ulam’s spiral is a grid with prime numbers written in beginning with 1 at the center, and continuing in a spiral around it so one is in the center, two is next to it, three is above the two, four is to the left of three, five is to the left of four, six is right below five and the spiral continues.

The prime spiral is  named after mathematician Stanislaw Ulam.  Back in 1963, while he sat through a boring lecture at a scientific meeting, he doodled.  He created a numerical spiral out of integers beginning with one and spiraling outwards. One he finished creating his spiral, he decided to circle only the prime numbers.

In the end, he noticed a pattern.  All of  the prime numbers appeared on diagonal lines. These diagonal lines are made up of both prime and composite numbers but the primes only appear on the diagonal lines. Since he’d used a small sample, he expanded the grid to 200 by 200 and the same pattern appeared. Mathematicians are not sure why this happens but they do know it is significant. 

During his tenure at Los Alamos, he worked with many of the early computers and he even tried this using a computer.  He is credited with being one of the first people to develop mathematical computer graphics.  Eventually, he produced a short paper with two other mathematicians and published it with computer graphics. 

It is possible to find grids on the internet that you can print out and have the students do the same thing so they see how he made the discovery.   I found the whole topic illuminating and quite interesting.  I’d never realized this before and I think it’s cool.  Let me know what you think, I’d love to hear. Have a great day.