Are prime fractals, or have a fractal geometry ?

In summary, the question being discussed is whether prime numbers exhibit a fractal geometry. The idea is that if we represent all the primes using a computer, it will give us a fractal pattern. A paper suggests that the zeta function, which is a product of primes, could be a fractal. However, it is unclear if prime numbers themselves exhibit fractal characteristics. The use of prime numbers in PGP and Gnupg also raises the possibility of a connection between prime numbers and fractals.
  • #1
zetafunction
391
0
are prime fractals, or have a fractal geometry ??

my idea is, if we consider the geometry of primes could we conclude they form a fractal ? , for example if we represent all the primes using a computer, it will give us a fractal pattern.

according to a paper http://arxiv.org/PS_cache/chao-dyn/pdf/9406/9406003v1.pdf

zeta function (which is just a product of primes for s >1) could be a fractal, but how about primes ?¿?
 
Physics news on Phys.org
  • #2


In what sense are you saying the primes are (or may be) fractals? Are they self-similar? Do they have non-integer dimension?
 
  • #3


my question is, if we use the Sieve of Eratosthenes.. for big scales (let us say 1000000000000000000000000 primes or similar) then the picture drawn is a fractal, for example.
 
  • #4


If I interpret your question correctly: no, they don't, because of the prime number theorem.
 
  • #5


zetafunction said:
my idea is, if we consider the geometry of primes could we conclude they form a fractal ? , for example if we represent all the primes using a computer, it will give us a fractal pattern.

according to a paper http://arxiv.org/PS_cache/chao-dyn/pdf/9406/9406003v1.pdf

zeta function (which is just a product of primes for s >1) could be a fractal, but how about primes ?¿?

This is an amazing question, was thinking about it last night. PGP and Gnupg both use prime numbers to generate the keys. If the Mandelbrot fractal pattern that Mandelbrot saw in the noise in the network lines is the same as the fractal's chaotic patterns we see then hummmmmmmmm...this is a good very good question, did you get an answer yet?
 

Related to Are prime fractals, or have a fractal geometry ?

1. What are prime fractals?

Prime fractals are geometric patterns that possess self-similarity and complexity, and they are made up of only prime numbers. Prime numbers are numbers that are only divisible by 1 and themselves.

2. How are prime fractals different from regular fractals?

Prime fractals are different from regular fractals because they are made up of only prime numbers. Regular fractals can be made up of any number, including non-prime numbers.

3. Do prime fractals have a specific geometric shape?

No, prime fractals do not have a specific geometric shape. They can take on various shapes and forms depending on the specific formula or algorithm used to generate them.

4. Are prime fractals found in nature?

There is no evidence to suggest that prime fractals are found in nature. However, fractal patterns can be observed in natural phenomena such as coastlines, trees, and clouds.

5. What is the significance of prime fractals?

The significance of prime fractals lies in their complexity and self-similarity, which can be applied in various fields such as mathematics, computer science, and art. They also provide a deeper understanding of the distribution and patterns of prime numbers.

Similar threads

Replies
11
Views
2K
Replies
1
Views
856
Replies
4
Views
1K
  • General Math
Replies
4
Views
3K
  • Beyond the Standard Models
Replies
7
Views
808
  • Linear and Abstract Algebra
Replies
1
Views
3K
  • Linear and Abstract Algebra
Replies
2
Views
1K
  • Topology and Analysis
Replies
3
Views
1K
  • General Discussion
Replies
4
Views
2K
  • Beyond the Standard Models
Replies
5
Views
5K
Back
Top