In order for the name of a person as a candidate for nomination by a political party for the office of United States senator to appear under a particular party heading on the official primary ballot, a nominating petition shall be filed with the secretary of state. The nominating petition shall have been signed by a number of qualified and registered electors residing within this state as determined under section 544f. The nominating petition shall be signed by at least 100 qualified and registered electors in each of at least 1/2 of the congressional districts of this state. Nominating petitions shall be in the form as prescribed in section 544c. Until December 31, 2013, the nominating petition shall be filed with the secretary of state no later than 4 p.m. of the twelfth Tuesday before the August primary. Beginning January 1, 2014, the nominating petition shall be filed with the secretary of state no later than 4 p.m. of the fifteenth Tuesday before the August primary.