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

The unraveling of the Ulam spiral is summarized in  Prime number pattern in the Ulam spiral.pdf.
The website supplies more information in detail.

The  Ulam spiral,  as discovered in  1963  by  Stanislaw Ulam,  uses the  non-negative integers  (see above on the left).
In this research the  Ulam spiral  is redefined to use the  natural numbers  0, 1, 2, 3, 4, 5, ...  (see above on the right).
The  counterclockwise  Ulam 0-spiral  is placed in a  Cartesian coordinate system,  with start value  0  in the  origin.

Comparing both spirals shows that sequences on the diagonals are interrupted by the  main diagonals,  e.g.:
The prime number  SE-set  {7, 23, 47, 79, ...}  is either  united  with the  NW-set  {7, 19, 67, ...}  or  {5, 17, 37, ...}.
The prime number  SW-set  {5, 19, 41, 71, ...}  is either  united  with the  NE-set  {5, 59, ...}  or  {3, 13, 31, ...}.




Ing. J.I.M. (Hans) Dicker MEd.
The Netherlands


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The Ulam spiral : Prime number pattern in the Ulam spiral