Except as provided by Section 23-15-1081, the first primary election for Congressmen shall be held on the first Tuesday in June of the years in which congressmen are elected, and a second primary, if necessary, shall be held three (3) weeks thereafter. Each year in which a presidential election is held, the congressional primary shall be held as provided in Section 23-15-1081. The election shall be held in all districts of the state on the same day. Candidates for United States Senator shall be nominated at the congressional primary next preceding the general election at which a senator is to be elected and in the same manner that congressmen are nominated. The chair and secretary of the state executive committee shall certify the vote for United States Senator to the Secretary of State in the same manner that county executive committees certify the returns of counties in general state and county primary elections.