Primorial sieve

The counterclockwise  Ulam spiral (1963)  with startvalue  0  is defined by  eight  families of functions.
Within these families of functions there are special factorable functions that contain no prime numbers > p4
(with p4 = 7),   see the unraveling of the Ulam spiral.pdf.

In the Cartesian coordinate system these special factorable functions appear as exclusion lines.
The straight lines all start at one of the  | y | = | x |  functions.
Downwards for smaller natural values of  n  all lines spiral inwards, faster at each crossing of a  | y | = | x |  line.
Note: the  main diagonals  are added, since these functions are also factorable.

The picture shows an  Ulam spiral  with  startvalue  0,  in a  [-90, 90] x [-70, 70]  window.
In  red  are the straight lines of the  special factorable family members.

The picture below is the same as above, but without the red lines of the special factorable functions.