The Figure at left represents the right sector of

the spiral shown on the previous page,

facts discussed on this page are typical for all the sectors.

The Figure shows the 6-folds and all the adjacents,

prime- & composite-.

In the Figure,

a checkerboard pattern is delineated and

that checkerboard pattern is shown again

by itself in Fig’s. -2 & -3.

In Fig. -2 the checkerboard squares are

shown with only the 6-folds,

in Fig. -3 the adjacents, both prime- & composite-

have been added to the 6-folds.

The squares in Fig. -2 each contain an

identically shaped triad of numbers,

for convenience they can be called “triads”.

Each of these triads is configured as a

sharp 90° angle, and can be visualized as an

arrowhead pointing to the direction of larger numbers.

From seeing Fig’s. -2 & -3 one can deduce the following:

the 90° angle configuration of each triad enforces that

5 of its adjacents are located in a

corner-to-corner x-shaped array within the square and with

1 remaining adjacent abutted against

the outside of the square, isolated from the others.

For convenience, adjacents such as the latter

can be called the “isolates”.

Also to be deduced:

the squares are corner-contiguous, therefore

the corner-to-corner x-shaped arrays of adjacents within them

are also corner-contiguous.

Thus the endless-, uninterrupted rows of adjacents

oriented in both diagonal directions are formed,

as seen in Fig. -4.

From the foregoing it becomes obvious that:

- The diagonal orientation of the rows of adjacents

is caused by the 90° angular shape of the triads,

and caused by that only. - The endless, uninterupted extent of these lines is

caused by the corner-contiguous arrangement of

all these checkerboard squares

-squares filling out the sector towards infinity-

and caused by that only.

These rows start at the sector-lines,

or adjacent to these lines,

or nearby these sector lines, at their far side.

Fig. -4 shows that the array of adjacents is

regularly sprinkled with

“crossings”, circled in blue &

isolates, circled in red.

These items are paired in such manner that

in each pair

the isolate-number is larger by 2

then the crossing-number.

Note that in the figure above

the typical periphery of the void spaces is

identical to the

typical periphery of the fillled spaces.