If you don't mind me going all picky on you (after all I used to be an academic), it's a plurality (i.e. the most votes), even if you don't get a majority (i.e. >50%).
The real question is how much of a plurality do you have to get to avoid a run off. In the primary it was 40%.
If one Party candidate files they move to the Nov Ballot, no primary.
If two Party candidates file, they compete in the primary, winner moves to Nov Ballot.
If three or more Party candidates file, they compete in the primary and the winner moves to the Nov Ballot—MAYBE. To move directly to Nov, the winner in this case must receive a SUBSTANTIAL PLURALITY or the second place candidate can, in writing, request a second primary. Substantial Plurality is more than 40% of the total votes cast for that race.
Rules for winning or moving to the November Ballot
I don't see a similar release for the general election. I think Ken H posted the answer for the general election but I can't remember it now.
Nope, I believe it is a simple plurality wins. That is the candidate with the most votes wins and their is no run off in the general. As far as I know Louisianna were there are no primaries and everyone runs together in the general is the only state with runoff general elections. But there may be others I don't know about.