Graeme Taylor

Research Fellow
University of Bristol

'The smoothness spiral' is an interactive applet (see that plots the first 10,000 integers on an Archimedean spiral. Each point has a brightness depending on its number-theoretic smoothness (its largest prime divisor), controlled by a user-selected threshold. Curves of smooth numbers emerge (for instance, the square numbers are necessarily present for any threshold beyond 101), whilst large primes are conspicuous by their absence, causing 'missing' curves.

101-smooth numbers
Print from digital

Print from 'the smoothness spiral'- the threshold is set to show values which are at most 101-smooth, with brightness proportional to smoothness.