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

In a Cartesian coordinate system the counterclockwise Ulam spiral (1963) with startvalue  0  is defined by  eight  families of functions  (see above).
With these families of functions  ANY  area of the spiral can be examined, without building the spiral from the ground up.

For example: a natural number in  Q1  is member of the  East  or  North  family of functions.
On the  NE-diagonal  a natural number is member of either one of the families of functions, as well as the  NE  main diagonal function.


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The Ulam spiral: The eight families of functions that define the Ulam spiral