The Ulam Spiral


Back again with some more interesting concept! Today we are going to talk about one of the most unusual discoveries unleashed during a casual ‘simultaneous’ activity. (Nope, not about doing your homework while playing Battlefield).

Ever had that encouraging feeling of grabbing a piece of paper and randomly doodling any possible sketches that come to your mind while talking through the phone? Well, that tends to happen quite often!

So had it been for Polish-American mathematician – Stanislaw Ulam.

Stanislaw Ulam

Yep, that’s him

In 1963 while doodling during a boring talk at a scientific meeting, Ulam started writing down all the prime numbers he knew in a circular direction:


While drawing a grid of lines, he decided to number the intersections according to a spiral pattern, and then began circling the numbers in the spiral that were primes. Surprisingly, the circled primes appeared to fall along a number of diagonal straight lines or, in Ulam’s slightly more formal prose, it “appears to exhibit a strongly nonrandom appearance” (Stein et al. 1964). The spiral appeared on the March 1964 cover of Scientific American magazine.

Image result for scientific american magazine march 1964

Remarkably, noted science fiction author Arthur C. Clarke described the prime spiral in his novel The City and the Stars (1956, Ch. 6, p. 54). Clarke wrote,

“Jeserac sat motionless within a whirlpool of numbers. The first thousand primes…. Jeserac was no mathematician, though sometimes he liked to believe he was. All he could do was to search among the infinite array of primes for special relationships and rules which more talented men might incorporate in general laws. He could find how numbers behaved, but he could not explain why. It was his pleasure to hack his way through the arithmetical jungle, and sometimes he discovered wonders that more skillful explorers had missed. He set up the matrix of all possible integers, and started his computer stringing the primes across its surface as beads might be arranged at the intersections of a mesh.”

Image result for The City and the Stars arthur

However, Clarke never actually performed this thought experiment, thus leaving discovery of the unexpected properties of the prime spiral to Ulam seven years later.




That it is it for today dear readers! This is my first minor article I have published here, thus, please leave a comment mentioning whether you’d prefer the ‘longer’ or ‘shorter’ versions of my publications.

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Written by Shohruh Artaman
A typical writer illustrating typical principles
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