This repository contains some of my research projects and scripts that I work on just for fun. The initial focus here is cousin primes, but I’m fascinated by prime constellations in general..
One project I'm diving into is looking at the asymptotic density of cousin primes. Cousin primes are pairs of primes that differ by 4 (for example, 3 and 7). I recently wrote a Python script that plots how the density of these primes changes as we go higher and higher in the prime number sequence.
Here's a quick visual of the asymptotic density of cousin primes up to 1000:
Note that the asymptotic density of the cousin primes is expected to be the same as that of the twin primes, according to the Hardy-Littlewood conjecture.
Clone this repo and check out the Python scripts. You’ll need sympy and matplotlib to run most of them. Here’s how to set it up:
git clone https://github.com/your-username/mathing.git
cd mathing
pip install -r requirements.txt