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Definition: Gaussian primes are Gaussian integers z=a+bi satisfying one of the following properties. 1. If both a and b are nonzero then, a+bi is a Gaussian prime if and only if a^2+b^2 is an ordinary prime. 2. If a=0, then bi is a Gaussian prime if and only if |b| is an ordinary prime and |b|=3 (mod 4). 3. If b=0, then a is a Gaussian prime if and only if |a| is an ordinary prime and |a|=3 (mod 4).