  A (positive definite and integral) quadratic form $f$ is said to be
$\textit{universal}$ if it represents all positive integers, and is said to be
$\textit{primitively universal}$ if it represents all positive integers
primitively. We also say $f$ is $\textit{primitively almost universal}$ if it
represents almost all positive integers primitively. Conway and Schneeberger
proved (see [1]) that there are exactly $204$ equivalence classes of universal
quaternary quadratic forms. Recently, Earnest and Gunawardana proved in [4]
that among $204$ equivalence classes of universal quaternary quadratic forms,
there are exactly $152$ equivalence classes of primitively almost universal
quaternary quadratic forms. In this article, we prove that there are exactly
$107$ equivalence classes of primitively universal quaternary quadratic forms.
We also determine the set of all positive integers that are not primitively
represented by each of the remaining $152-107=45$ equivalence classes of
primitively almost universal quaternary quadratic forms.
