Pólya conjecture

10=2*5 There are 2 prime numbers which are called prime factorization.

This is n=50.

4=2^2 is 2 prime numbers.

12=2^2*3 is 3 prime numbers.

I put even numbers in 1. There are 21 in 50. According to Pólya conjecture, there are more odd numbers in prime factorization.

Prime numbers are chaotic, so this conjecture isn't fractal like piling squares.

906,150,257 ≤ n ≤ 906,488,079

There are more even numbers in n.

It is hard to put circles in the square. I think that you need to adjust the range of the square to extinguish the circle, such as 906000000≦n≦906500000.

For example, there are 7 even numbers in 4≦n≦16. This is contradictory.

Wolstenholme's theorem

p is a prime number (p≧5).

When p is 5, p^3=125.

2376 is one more than a multiple of 125. 2376=125*19+1

When p is 7, p^3=343.

1716 is one more than a multiple of 343.

This is chaotic, but you can find it by your spreadsheet.

Moreover, this is Binomial coefficient. Pascal's triangle is well known as fractal.

This is harmonic numbers.

You see that this is almost zeta function.

Riemann's zeta function is ζ(s)=0.