Ulam Spiral with
origin at 1.
Ulam Spiral with
origin at 0.
The spirals above are distinct as follows:
the top spiral has “1” as its origin and
the bottom spiral has “0” as its origin.
Along each of the
8 cardinal directions on both spirals
starting at the origin of the spiral
a series of 4 numbers are shown.
Also shown: the respective
formulations generating these numbers.
The formulations in the bottom spiral
are simpler as follows:
a)
In the case of the numbers
along the diagonal directions:
In the top spiral their respective formulations
contain “1” as a 2nd. term,
in the bottom spiral their respective formulations
contain no 2nd. term.
b)
In the case of the numbers
along the horizontal- & vertical directions:
in both spirals their respective formulations
contain a 2nd. term,
but in the bottom spiral it is less by “1”,
-even to the point of vanishing by becoming “0”.
thus greater simplicity and clarity is obtained by
having “0” as the spiral origin.
Other benefit are the following:
with “0” as the spiral origin:
a)
none of the prime numbers are
located along the diagonal directions.
(Except “2”.)
b)
none of the prime numbers are
located along the horizontal- & vertical directions.
(Except: “1”, “3”, “5”, “7”.)