Wolfram Demonstrations Project

The natural numbers are arranged along an Archimedean spiral so that the squares 1, 4, 9, … are on the

axis, with the primes drawn in blue, up to a circle of radius

. The spiral is parametrized in polar coordinates by

. Also shown is the curve given by

(red), and its intersections with the spiral (purple boxes).

References

[1] R. Sacks. Number Spiral. (2007) www.numberspiral.com.

[2] H. Hahn. "The Distribution of Prime Numbers on the Square Root Spiral." arXiv. (Jan 9, 2008) arxiv.org/abs/0801.1441.

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Spiral of Primes