The City And The Stars by Arthur C. Clarke

He could find how numbers behaved, but he could not explain why. Relationships and rules which more talented men might incorporate in general laws. All he could do was to search among the infinite array of primes for special Jeserac was no mathematician, though sometimes he liked to believe 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).Ĭlarke wrote, 'Jeserac sat motionless within a whirlpool of numbers. March 1964 cover of Scientific American magazine. Lines or, in Ulam's slightly more formal prose, it 'appears to exhibit a strongly Surprisingly, the circled primes appeared to fall along a number of diagonal straight While drawing a grid of lines, he decided to number the intersections according toĪ spiral pattern, and then began circling the numbers in the spiral that were primes. Ulam (1909-1986) in 1963 while doodling during a boring talk at a scientific meeting. This construction was first made by Polish-American mathematician Stanislaw Unexpected patterns of diagonal lines are apparent in such a plot, as illustrated in the above

The plot above shows a larger part of the spiral in which the primes are shown as dots. In red and composites are indicated in yellow. In the right plot above, primes are indicated The prime spiral, also known as Ulam's spiral, is a plot in which the positive integers are arranged in a spiral (left figure), with primes

The City And The Stars by Arthur C. Clarke