Generalization of Bertrand's Postulate for Gaussian Primes

Abstract

Bertrand's Postulate states about the prime distribution for the real numbers. The generalization of Bertrand's Postulate was proved by Das et al. [Arxiv 2018]. In this paper, we have formalized this idea for the Gaussian primes (or the primes on the complex plane). This result gives information about the prime distribution on the complex plane.

The claim of Main Theorem 1 is wrong. The prime counting function on the complex plan does not satisfy the inequality. The prime number Theorem contradicts the claim