| Abstract: |
| This work concerns the fractal-like behavior of prime subsets. Numerical simulations indicate that some prime subsets (e.g., Chen primes, Gaussian primes) resemble a fractal-like behavior. Our simulations are based on the construction of binary images based on prime numbers. Indeed, two-integer sequences can easily be converted into a two-color image. In particular, the Cantor set seems to cover a relevant role in our analysis. It seems that the Cantor set has a sort of relevant role in prime number theory. In addition, our results have potential applications in chaotic dynamical systems and cryptography. |
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