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The Ulam Spiral

… and many other spirals¬†
inspired by it …

Fig. -1.

Tetrapolar
Ulam-type spiral.
Showing only
prime adjacents.

Notes.

Even given the limited extent of this spiral
2 lenghty uninterrupted rows of prime numbers
can immediately be seen, in Fig. -1 above
emplaced on spiroid tracks.
One row has its numbers color-coded blue and
its numbers are also shown in Table -1,
the other row has its numbers color-coded red and
its numbers are also shown in Table -2.

Another row can be seen in Fig. -1a below,
its numbers are color-coded purple and
its numbers are also shown in Table -3.

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.

Fig. -1a.

Tetrapolar
Ulam-type spiral.
Showing only
prime adjacents.