Quotient sets have attracted the attention of mathe-
maticians in the past three decades. The set of quotients of primes is
dense in the positive real numbers and the set of all quotients of Gauss-
ian primes is also dense in the complex plane. Sittinger has proved that
the set of quotients of primes in an imaginary quadratic ring is dense in
the complex plane and the set of quotients of primes in a real quadratic
number ring is dense in R: An interesting open question is introduced
by Sittinger: Is the set of quotients of Hurwitz primes dense in the
quaternions? In this paper, we answer the question and prove that the
set of all quotients of Hurwitz primes is dense in the quaternions.