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 table below gives per  family of functions  the special factorable members.
The  NE  and  SW  families of functions  have no special factorable family members, since their special factorable family members are also divisible by  2.


The Ulam spiral: Definition of the special factorable functions