What to consider in the primaries in Maine, South Carolina, Nevada and North Dakota

The presidential primary is over, but lower-district primaries are still taking place across the country. On Tuesday, candidates will be on the ballot in five states: South Carolina, Nevada, Maine, North Dakota and Ohio, where there is a special race for a House seat.

Representative Bill Johnson retired from Ohio's Sixth Congressional District in January, and State Senator Michael Rulli, the Republican nominee for that seat, will face Democratic candidate Michael L. Kripchak. Former President Donald J. Trump won that district in 2020 by a margin of 29 percentage points.

Here are the area codes to keep an eye on:

Republican Rep. Nancy Mace of South Carolina, considered a candidate for Trump's running mate, faces an opponent in the primary backed by former Speaker Kevin McCarthy. McCarthy opposes her because she voted to oust him from the speaker's office last year. The primary in the state's 1st Congressional District comes just days after the House Ethics Committee began investigating Ms. Mace's use of a congressional compensation program.

Ms. Mace's opponent, Catherine Templeton, worked for Nikki Haley when she was governor of South Carolina, and Ms. Templeton ran for that office in 2018. Ms. Mace was once a moderate ally of Ms. Haley, but switched to the MAGA wing of the Republican Party when her district was redrawn in 2022, making it more conservative.

The third and fourth congressional districts also have hotly contested Republican primaries. Representative Jeff Duncan has given up his seat in the deeply conservative third district, and in the fourth district, Representative William R. Timmons IV, who defeated Republican challengers in the 2022 primary, is being challenged by Representative Adam Morgan, the leader of the far-right Freedom Caucus, which serves as a counterpart in their chamber.

Republicans in Nevada will select their candidate for a seat in the U.S. Senate from a large field of candidates.

The leading candidate, Sam Brown, a former Army captain, received a last-minute boost from Trump, who spoke out about the race on Sunday night, but only after early voting had ended.

Still, the support has cemented Brown's position as the clear favorite for November's election against Democratic Senator Jacky Rosen. Brown is also backed by the state's Republican governor, Joe Lombardo, and has raised the most money of any candidate in the race.

Brown will have to contend with Jeff Gunter, a wealthy dermatologist who was Trump's ambassador to Iceland, as well as Jim Marchant, who supports Trump's lie that the 2020 election was stolen from him, and a number of other minor candidates.

Gov. Doug Burgum, a North Dakota Republican who self-financed his failed presidential campaign and is now one of Trump's leading vice presidential contenders, is not seeking a third term as governor. Two Republicans will face off on Tuesday to succeed him.

One of them, Representative Kelly Armstrong, has held North Dakota's only seat in the House since 2019 and helped lead the investigation into President Biden's son, Hunter. He will face Lieutenant Governor Tammy Miller, who was appointed to the post by Mr. Burgum last year and has the support of the governor.

The winner will face Democratic Senator Merrill Piepkorn in November. In 2020, Mr. Burgum defeated his Democratic opponent by 42 points.

Rep. Jared Golden, Democrat of Maine, has waged a tough re-election battle in the state's rural 2nd Congressional District, and Republicans will have to choose between two candidates vying to give him another seat in this year's general election.

State Rep. Austin Theriault, a former NASCAR driver, will face state Rep. Michael Soboleski. Mr. Theriault is endorsed by Mr. Trump, who urged his supporters to support him on the eve of the election.

Anna Harden

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