Primorial sieve

The segmented prime spirals are an offspring of the counterclockwise Ulam spiral with startvalue  0,  and are described in detail in the  segmented prime spirals.pdf.

The Ulam spiral can be seen as an Ulam four-quarter spiral, and thus as a prime spiral with four segments.
There are infinitely many segmented prime spirals.
The mathematical properties of the segmented prime spirals are listed below.
The full description is found in the document   segmented prime spirals.pdf.

The  Ulam spiral (1963)  is named after the Polish mathematician  Stanislaw Ulam.
The graphical display shows that prime numbers have the tendency to appear on certain diagonals within the spiral.

The unraveling of the Ulam spiral.pdf  is an offspring of the  (double) primorial sieve.pdf   project.
The mystery of the Ulam spiral is solved by the find of the  eight  families of functions  that fully capture all natural numbers in the spiral. The unraveled Ulam spiral offers a wide range of elegant features to further analyze prime numbers.