On the linearity of ω-primality in numerical monoids

In an atomic, cancellative, commutative monoid, the ω-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 ω-function for a general numerical monoid and give an explicit formula when the monoid has embedding dimension 2.