A second primary, when necessary, must be held two weeks after the first and is subject to the rules governing the first primary. At the second primary the two candidates among those who do not withdraw their candidacies and who received more votes in the first primary than any other remaining candidate alone shall run for any one office and if only one candidate remains, he is considered nominated, except that if there are two or more vacancies for any particular office, the number of candidates must be double the number of vacancies to be filled if so many candidates remain. In all second primaries the candidate receiving the largest number of votes cast for a given office must be declared the nominee for the office whether or not he has received a majority of the votes cast for that office, and when there are several candidates for several different offices, then the several candidates receiving the largest number of votes for the several positions are considered as nominated for the offices whether or not they received a majority of the votes cast. Other primaries, if necessary, must be ordered in a similar manner by the county board of voter registration and elections or the State Election Commission, as appropriate.