In both spirals above:

Along each of the 8 cardinal directions starting at the origin of the spiral

a series of 4 numbers are shown.

Also Shown:

the formulas generating these numbers.

The number-formulas in the bottom spiral are simpler as follows:

a)

In case of the numbers along the diagonal directions:

In the top spiral their formulas each contain “1” as a 2nd. term,

in the bottom spiral these formulas contain no such term.

b)

In case of the numbers along the horizontal- & vertical directions:

In the top spiral their formulas each contain 2nd. term,

in the bottom spiral these 2nd. terms are reduced by “1”.

For these reasons the bottom spiral presents itself as a

more “fortuitous” arrangement with which to investigate

various properties of the Ulam spiral.

Another unique benefit of the bottom spiral is the following:

none of the prime numbers are

located on any of the 4 diagonal sector-lines.