  In an atomic, cancellative, commutative monoid, the \omega-value measures how
far an element is from being prime. In numerical monoids, we show that this
invariant exhibits eventual quasilinearity (i.e., periodic linearity). We apply
this result to describe the asymptotic behavior of the \omega-function for a
general numerical monoid and give an explicit formula when the monoid has
embedding dimension 2.
