P^2+Σ2P

This paper introduces a geometric framework that defines numbers not as dimensionless points, but as the areas of squares, emphasizing dimension and spatial extension. By modeling the interaction between the infinity of the integer space and the self-similar (fractal) expansion of squares . This is my formula which generate prime numbers. In geometric terms, this formula is rigorously illustrated as follows: 1. Core Formation: A closed square domain of area p^2 , with a side length equal to the prime p. 2. Asymmetric Expansion (Gnomon): Two rectangular domains of width (d−1) and length p, structurally appended to the horizontal and vertical boundaries, denoted by 2p(d−1). This process represents an infinite expansion algorithm wherein the square consumes the external integer space while strictly preserving its own self-similarity. Squares possess the highest structural affinity for fractals due to their capacity for infinite grid-like division and consolidation. As d progr...

This is Erdős–Straus conjecture. n is prime number. This is Diophantine equation . You can write this. Y=nX Therefore, you need to know prime numbers in my blog. n=p(p+2d−2) Ex. p≡1 (mod4) p=5

This is four kissing circles . The bigger is the smaller curvature. -10 is the outer circle. You put the numbers on it. This is religion in my country.

The kissing number has no overlapping spheres. A kissing number is defined as the independent sphere which is touched. In lattice packing , the kissing number is the same, but arbitrary sphere packing is different because of the random shape of spheres. It is the maximum possible kissing number for n-dimensional spheres in (n + 1)-dimensional Euclidean space. In one dimension, the kissing number is 2 . In two dimensions, the kissing number is 6. This is isosceles. D=1　⇒ 2 D=2　⇒ 6 D=3　⇒ 12 D=4　⇒ 24 D=5　⇒ 40 This is like exponential function.