  For any field $F$ (of characteristic not equal to 2), we determine the
Zariski spectrum of homogeneous prime ideals in $K^{MW}_*(F)$, the Milnor-Witt
$K$-theory ring of $F$. As a corollary, we recover Lorenz and Leicht's
classical result on prime ideals in the Witt ring of $F$. Our computation can
be seen as a first step in Balmer's program for studying the tensor triangular
geometry of the stable motivic homotopy category.
