Back in 1963 the physicist and mathematician Stanislaw Ulam . Within this spiral the primes tended 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 further prime potentially occurs only as a multiple of 6 plus or minus 1 (e.g. 5,7,11,13,17,19,23,29 and so on).
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 6 multiples 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 6 multiples that control and create the assembly of primes into these straight vertical, horizontal and diagonal lines.