Paul Ashwell

Sheffield, United Kingdom

Having an art college background, I've recently created a body of abstract paintings and prints. I often play with number and mathematics and work using mix media on canvas and digital print techniques.

My creative journey with prime numbers began in 2007 with a painting called Eratosthenes. A modified six across Eratosthenes sieve, this work shows how prime values beyond 2 and 3 occur as multiples of six, plus or minus 1.

I now use primes to make visually stimulating art that explores pattern, spirals, sequence and area. My aim is for my work to visually connect without any knowledge of the underlying maths.

The examples here illustrate the beauty and patterning which can be created from prime factors and the prime number series.

60 x 90 cm
Giclee print on art paper

This print is derived from an artwork comprising of 72 canvases. Here, symbols are used to depict values from 1 to 54. Each lone symbol represents a prime number. A non-prime number has a combination of symbols showing its prime factors.

For example, the primes 2 and 3 are represented by a yellow chevron and a red triangle respectively. The non-prime 6 is represented by its prime factors 2 and 3 shown as a yellow chevron and a red triangle. All 54 values are derived in the same way.

This arrangement in a 9x6 grid show how the prime and factored numbers make patterns and symmetries.

Original canvas artwork featured in American Scientist article - Ode to Prime Numbers
by Professor Sarah Glaz -

60 x 60 cm
Giclee print on art paper

In 1963 Stanislaw Ulam devised a number spiral showing prime occurrences. The primes appeared to organise into verticals, horizontals and diagonals. This has since fascinated many mathematicians.

UlamX6 is an Ulam spiral of 483 values depicted as polka dots. All the prime values are given an individual colour and all values which are multiples of 6 are depicted as dark grey. The remaining values are a lighter grey.

The multiples of 6 make an interesting grid pattern in themselves. But also, the coloured primes cling to the 6 grid with a tendency to form long lines. It therefore appears that it is the underlying pattern of sixes that control and create the assembly of primes into these straight vertical, horizontal and diagonal lines.