Inflation

I programmed to count prime numbers by PC, so I can see the same pattern from "Prime Obsession". There is the function about prime numbers.

π means the function of prime numbers up to x.
For example, you can put 100 to x.
10 is the square root of 100, 4.6415・・is the cube root of 100, 3.1622・・is the fourth root of 100・・,2.1544・・is the sixth root of 100,and 1.9306・・is the seventh root of 100. 2 is the first prime number,so you can ignore the seventh root of 100.

Therefore
J(100)=π(100)+1/2π(10)+1/3π(4.64・・)+1/4π(3.16・・)+1/5π(2.51・・)+1/6π(2.15・・)+0+0・・・

You can count prime numbers by 100, so you see π(100)=25, π(10)=4, π(4.64・・)=2, π(3.16・・）=2, π(2.51・・)=1, π(2.15・・)=1.

J(100)=25+(1/2×4)+(1/3×2)+(1/4×2)+(1/5×1)+(1/6×1)

This is the graph.

X is a prime number.
When x is 2, J(2)=1. When x is 3, J(3) jump to 2. When x is 5, J(5) jump to 3.5.

This graph would go up infinitely.