Florida will hold a statewide primary for the Libertarian Party on August 30, for U.S. Senate. The candidates are Augustus Invictus and Paul Stanton. Here is a link to the list of primary candidates so far. The list may grow, because the filing deadline is June 24. Thanks to Rich Moroney for the link.
Florida has not held a statewide primary for any party, other than the Democratic and Republican Parties, since 1920. Although technically all parties nominate by primary in Florida (if they qualify in time for the primary), no primary is actually held unless at least two candidates for the same office file. A few years ago Florida held a Libertarian primary, but it was just for one state house district.