Pythagorean prime

A Pythagorean prime is a special type of prime number that can be expressed in the form \(4k + 1\) for some integer \(k\), or the prime number 2. In other words, Pythagorean primes are the primes that can be represented as the sum of two squares, specifically in the form \(a^2 + b^2\) where \(a\) and \(b\) are integers.