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	A Gaussian integer is a [[wp:Gaussian_integer#Gaussian_primes\|Gaussian prime]] if and only if either its '''norm''' is a prime number, or it is the product of a unit '''(±1, ±i)''' and a prime ~~number~~ of the form '''4n + 3'''.		A Gaussian integer is a [[wp:Gaussian_integer#Gaussian_primes\|Gaussian prime]] if and only if either its '''norm''' is a prime number, or it is the product of a unit '''(±1, ±i)''' and a prime integer of the form '''4n + 3'''.

	Prime integers that are ''not'' of the form '''4n + 3''' can be factored into a Gaussian integer and its complex conjugate so are not a Gaussian prime.		Prime integers that are ''not'' of the form '''4n + 3''' can be factored into a Gaussian integer and its complex conjugate so are not a Gaussian prime.