WalterChristian
My artistic and mathematical work deals with the distribution of the
prime numbers.
It is the prevailing opinion that the prime numbers are distributed in
a way that does not allow any rule to be found, there seems to be no
system to make a prediction for a next prime number´s position.
What was missing so far is a structural pattern of their
distribution.
I have found it: It is a beautiful symmetry-pattern:
The numbers betweenn the twins are the key to this pattern: here two
examples:
1 7 13 17 19 23 29 30 31 37 41 43 47 53 59 and 1 5 11 13 17 23 31 37
41 42 43 47 53 61 67 71 73 79 83
I treat 1 as a prime.
Not only the twins stand symmetrically to the number between them but
many more primes.
I visualize this symmetry-pattern.
In the circle of the 360 degrees there are all the prime numbers
that are standing symmetrically towards 180. All the corners of 46
triangles standing in opposite positions with same colors on each
half -left and right- add up to 360.
Beginning at the bottom center.
179 + 181= 360
goin up
167 + 193= 360
163 + 197= 360
149 + 211= 360
137 + 223= 360
131 + 229= 360
127 + 233=360
109 + 251=360
103 + 257=360
97 + 263=360
89 + 271=360
83 + 277 =360
79 + 281= 360
67 + 293=360
53 + 307=360
43 + 317=360
29 + 331=360
23 + 337=360
13 + 347=360
11+ 349=360
7 + 353=360
1 + 359=360
You can take any number from between two twins, follow up the
primes backwards and find those standing mirrorlike upwards.
A grey circle of 360 degrees is framed by all the prime numbers
between 2 and 359.
The numbers 2,4,6,12,18,30,42,60,72,102,108 138,150 180 (no prime
numbers) are arranged clockwise in rainbow colors along the right,
first half of the circle. These numbers are standing between the
twins and function as symmetry numbers not only between and for
the twin-prime numbers but also many more primes. They can be
found in symmetrical positions where concentric circular arches
(that have their centers in the points of the symmetry-numbers)
cut the circle of 360 degrees.
The prime numbers beyond the twin-pairs (siblings) I call
"sib-pairs" and all together including the symmetry-number a
"prime number family" named after the number in the center.