The (double) Primorial sieve & Prime spirals |
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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