  The Gaussian Moat problem asks whether one can walk to infinity in the
Gaussian integers using the Gaussian primes as stepping stones and taking
bounded length steps or not. In this paper, we have analyzed the Gaussian
primes and also developed an algorithm to find the primes on the $\mathbb{R}^2$
plane which will help us to calculate the moat for higher value. We have also
reduced a lot of computation with this algorithm to find the Gaussian prime
though their distribution on the $\mathbb{R}^2$ plane is not so regular. A moat
of value $\sqrt{26}$ is already an existing result done by Genther et.al. The
focus of the problem is to show that primes are getting lesser as we are
approaching infinity. We have shown this result with the help of our algorithm.
We have calculated the moat and also calculated the time complexity of our
algorithm and compared it with Genther-Wagon-Wick's algorithm. As a new
ingredient, we have defined the notion of primality for the plane
$\mathbb{R}^3$ and proposed a problem on it.
