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The Ulam Spiral

… and many other spirals¬†
inspired by it …

Fig. -1.

Ulam-type spiral.
Showing only
prime adjacents.


Even given the limited extent of this spiral
3 lenghty uninterrupted rows of prime numbers
can immediately be seen in
Fig. -1 emplaced on spiroid tracks.

These rows are distinguishable according as
their constituent numbers are
color-coded blue, red & purple respectively,
their numbers are also listed in
Tables -#1, -#2 & -#3 respectively.

These tables clearly show the respective
generating methods by which
these rows are created algebraically.

Close to the center of the spiral
these spiroid tracks become severely deformed and
locating the numbers visually becomes impossible.
I had to consult the tables to locate them.
This problem is particular to only these 3 rows,
all other rows that may populate this spiral are
far away enough from the spiral center to
escape from their spiroid tracks being deformed.