Abstract
Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work, we give parametrizations of Arf numerical semigroups with multiplicity $11$ and $13$, and combining these results with previous results about the number of Arf numerical semigroups with multiplicity $2, 3, 5, 7$, we share some observations about the set of Arf numerical semigroups with prime multiplicity.
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