What is gauss prime?

Gaussian prime is a type of prime number in the complex plane. It is defined as a complex number of the form a+bi, where a and b are integers, and i is the imaginary unit. A Gaussian prime is said to be a prime number if it is a natural number that cannot be written as the product of two Gaussian integers other than 1 and itself.

Gaussian primes can be plotted in a similar way to real primes but in a two-dimensional grid, where the horizontal axis represents the real part of a complex number and the vertical axis represents the imaginary part. By this representation, interesting geometrical pattern of Gaussian primes is found.

The study of Gaussian primes is essential in number theory and algebraic geometry. It also has applications in cryptography and computer science. The Gaussian primes are essential for solving Diophantine equations. Also, they are used in algebraic number theory, where they play a crucial role in the study of algebraic number fields.