What are some numbers that are can be factored by Hurwitz primes but not Gaussian primes?

Question

Since gaussian primes can factor conventional prime numbers like 5, I was wondering about the same question but for quaternions.

Answer 1

The number $11$ will do the job. It's not a sum of two squares, so it can't be a product of Gaussian primes, but it can be written $$ 11 = ( 1 + 3i + j)(1 - 3i - j). $$