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Is there a notion of an octonion prime? A Gaussian integer $a + bi$ with $a$ and $b$ nonzero is prime if $a^2 + b^2$ is prime. A quaternion $a + bi + cj + dk$ is prime iff $a^2 + b^2 +c^2 + d^2$ is prime. I know there is an eight-square identity that underlies the octonions. Is there a parallel statement, something like: an octonion is prime if its norm is prime?