For well-known presidential candidates seeking a place on a major party presidential primary, Virginia has the toughest rules.  The state requires 5,000 signatures.

On November 18, Pete Buttigieg became the first Democratic presidential candidate to submit a petition.  His petition has approximately 12,000 signatures.

The Arizona Libertarian Party is ballot-qualified in Arizona, and could have a presidential primary if it wished.  But the party has informed the Secretary of State that it doesn’t want a presidential primary.

In 1996, the Arizona Democratic Party and the Arizona Libertarian Party jointly won a lawsuit in state court, establishing that if they don’t want a presidential primary, they can prevent such a primary.  Later the legislature codified that any party is free to cancel a presidential primary.  In 2020, the Arizona Republican Party has also cancelled its presidential primary.

Candidates get on an Arizona presidential primary ballot by showing that they are on in at least two other states’ presidential primaries.  So far Pete Buttigieg is the only Democratic presidential primary candidate who has filed in Arizona.

The California Green Party has told the California Secretary of State that the party has approved Howie Hawkins and Dario Hunter for the March 2020 presidential primary ballot.

Although candidates can get on a California presidential primary ballot without party approval, it is not easy, in the case of California’s minor parties.  An alternate method to get on a California minor party presidential primary is to show that the candidate is already on the presidential primary ballot of some other state.  But the other states that have minor party presidential primaries tend to have later filing periods.  The California requirement must be satisfied by November 26.  The other states with Green Party presidential primaries don’t even let candidates file that early.