Filing for Utah presidential primaries closed December 12. Any qualified party is eligible to have a presidential primary, but each party had to affirmatively tell the state elections office if it wanted a presidential primary. The parties that did so are the Democratic, Republican, and Constitution Parties.
Candidates needed a filing fee of $500. No one filed in the Constitution Party presidential primary. The Democratic presidential primary will have 16 candidates; the Republican ballot will have seven. See the list here.