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

To shed some light on the conundrum of the diagonals in  the Ulam spiral,  the eight families of functions are combined with the fourth  primorial sieve. The sieve has  48  struts relative prime to the  fourth  primorial, the product of the first  four  prime numbers. For details abouth the sieve, see the  (double) Primorial sieve.pdf.  
Each function (mod 210)  of  the Ulam spiral  has a residue class of  24  elements, see the pictures above with the frequency for  f(n) < 10^9.

Diagonals may have a high ratio of prime numbers when the residue class solely alines with struts,  
see  the Ulam spiral functions (mod 210).pdf.


The Ulam spiral: The eight families of functions (mod 210)