The (double) Primorial sieve  &  Prime spirals E-mail

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.


The Ulam spiral: Special factorable functions  in the  Ulam spiral