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 International Conference on Complex Systems (ICCS2007)

Primes Numbers are the Holes Behind Complex Composite Patterns

Jeffrey Ventrella

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     Last modified: December 7, 2007

Number theorists have been searching for patterns in the distribution of primes throughout history. But studying large composite numbers may hold greater potential – for modeling interactions of signals of varying periods, and for providing rich visuals for math education. This paper presents a visualization called the “divisor plot”, which relates chaos theory to number theory. Very small versions of this graph have been used to explain primes. But as yet there appear to be no extensions to very large numbers (i.e., in the billions range), where unexpected structures emerge. Of particular interest is the square root boundary, exhibiting symmetry and an infinite progression of nested parabolas with number-theory properties. These are compared to product curves on Sacks’ Number Spiral.

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