The (double) Primorial sieve & Prime spirals |
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The segmented prime spirals are an offspring of the Ulam spiral (see the segmented prime spirals.pdf)

The counterclockwise Ulam spiral with startvalue 0 is a four-quarter spiral, and thus a prime spiral with four segments. There are infinitely many segmented prime spirals.

The unraveling of the Ulam spiral.pdf is an offspring of the (double) primorial sieve.pdf project.

The counterclockwise Ulam spiral with startvalue 0 is completely defined by eight families of quadratic functions.

When the Ulam four-quarter spiral is presented as a prime spiral with four segments, the prime spiral is defined

by (2*m* + 1) families of functions, with *m* = 4.

Below the first segment is seperated from the other segments to clarify the concept of the segmented prime spirals.

Clearly visible is the translation *n * to *n* - 1 when crossing the SE main diagonal, due to the different functions.

Prime spirals: The Ulam four-quarter spiral as prime spiral with four segments.