Conjecture on the distribution of Gaussian primes

The conjecture about Gaussian primes suggests that these special points—complex numbers with prime properties—are spread throughout the complex plane in a pattern similar to how ordinary primes are distributed along the number line. Specifically, it hypothesizes that Gaussian primes become equally common in all directions as you look farther out, following a predictable density. This idea extends the way mathematicians understand prime numbers, proposing a form of randomness and uniformity in their complex analogs, though a full proof remains an open challenge in number theory.