Back in 1963 the physicist and mathematician devised a simple accentuating all the occurrences of primes. Within this spiral the prime numbers tend to organise into vertical, horizontal and diagonal lines. This phenomenon has fascinated many mathematicians ever since.
Apart from the first two primes (2 and 3), every other prime number potentially occurs only as a multiple of 6 plus or minus 1 (e.g. 5,7,11,13,17,19,23,29,31, and so on).
My artwork is an Ulam spiral of 484 values from 0 to 483 all represented as polka dots. The prime numbers are given a colour and numbers which are multiples of 6 are dark grey. The remaining values are light grey.
UlamX6 structureWithin my UlamX6 print
and its structure diagram shown here the dark grey 6-multiples create a facinating organised pattern. The primes (mid grey in the diagram) cling to this structure of 6-multiples. So you can see that it is the close relationship with the 6-multiples that organises the primes into these vertical, horizontal and diagonal lines.
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Compare the patterning here with my hexagonal spiral prints, and , where the 6-multiples are rendered white and the set of primes a single colour.