I've been fascinated with the visual properties and potential of the prime number series for many years. One aspect that has struck me is that apart from the first two primes (2 and 3), every further prime will potentially occur only as a multiple of 6 plus or minus 1 (e.g. 5,7,11,13,17,19,23,29 and so on).
Back in 1963 the physicist and mathematician Stanislaw Ulam devised a simple rectangular spiral of numbers accentuating all the occurrences of primes. Within this spiral the primes tended to organise into vertical, horizontal and diagonal lines. This phenomenon has fascinated many mathematicians ever since.
UlamX6 is an Ulam spiral of 483 values depicted as polka dots. All the prime values are given a 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.
I have also created other artworks based on hexagonal spirals that also show this interesting relationship and patterning in different ways – e.g. Prime spiral honeycomb