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.
Artworks
Symmetry of primes towards 180
69 x 69 cm
Acrylic on canvas
2019
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.
prime number-symmetry
60 x 60 cm
acrylic on canvas
2018
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.
