Candidates for the elective state executive and state and national legislative offices shall be nominated in a primary election by direct vote of the people in the manner prescribed by this chapter. The primary election does not serve to determine the nominee of a political party or political group but serves only to narrow the number of candidates whose names will appear on the ballot at the general election. Except as provided in AS 15.25.100(d), only the four candidates who receive the greatest number of votes for any office shall advance to the general election.