Computational search for Gaussian perfect integers

This paper is primarily concerned with the definition of perfect integers in the Gaussian plane and then testing their existence with the help of number theoretic algorithms and other computational tools. Here, we deal with Gaussian primes, their primary counterparts (which are essentially developments on primes), and the identification of Gaussian perfect integer, if any. Experimental results show that there is no definite indication of any Gaussian perfect integer up to a very large norm.