Gaussian primes are Gaussian integers z = a + b i satisfying one of the following properties. 1. If both a and b are nonzero then, a + b i is a Gaussian prime iff a^2 + b^2 is an ordinary prime. 2. If a = 0, then b i is a Gaussian prime iff left bracketing bar b right bracketing bar is an ordinary prime and left bracketing bar b right bracketing bar congruent 3 (mod 4). 3. If b = 0, then a is a Gaussian prime iff left bracketing bar a right bracketing bar is an ordinary prime and left bracketing bar a right bracketing bar congruent 3 (mod 4). The above plot of the complex plane shows the Gaussian primes as filled squares.
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