South Carolina, Nevada primaries and Ohio special election: Nancy Mace, Sam Brown win

One of the races I'm watching tonight is the Republican primary for North Dakota's governor, and, as Geoffrey noted earlier, that race has been increasingly heated. Of course, the Republican nominee is seeking to replace Burgum, who is retiring after a brief run for the Republican nomination for president, and amid chatter that he could be Trump's vice presidential pick. So I'd just like to take a moment to remember this cinematic video Burgum used to launch his presidential campaign, with a voiceover that praised small-town values over scenic images of hills and livestock. Maybe we can look forward to such a video one day from his successor.

—Monica Potts, 538

Maine's 2nd District is host to a GOP primary in which two first-term state representatives, Austin Theriault and Mike Soboleski, are contending for the right to take on three-term Democratic Rep. Jared Golden. The incumbent has managed to hold onto this seat, which takes in most of Maine north of its southern coastal area, despite its slight Republican lean: Trump would have carried it 51 percent to 45 percent in 2020, according to Daily Kos Elections, making it the second-most Republican-leaning seat (by presidential vote) that a Democratic incumbent is defending in 2024, trailing only Rep. Mary Peltola's at-large seat in Alaska.

Theriault, a former NASCAR driver, looks to be favored. He has Trump's endorsement, which he's naturally emphasized in his ads, and he's congressional Republicans' top choice, having earned the backing of Speaker Mike Johnson and the Congressional Leadership Fund. Moreover, Theriault has raised $1.2 million to Soboleski's $117,000. The only somewhat recent poll was an early April survey from Public Opinion Strategies on behalf of Theriault's campaign that found him leading Soboleski 30 percent to 7 percent. But while Theriault has Trump's backing, Soboleski aligns with the former president — and around two-thirds of Republicans nationally — on the question of the 2020 election's legitimacy. Unlike Theriault, Soboleski has echoed Trump's unsupported claim that Biden didn't legitimately win.

—Geoffrey Skelley, 538

It's 7 p.m. Eastern, and polls are now closed in South Carolina. Stay tuned for results from key races there!

—Tia Yang, 538

According to our recent analysis of primaries this cycle through May 21, 41 percent of Democrats' nominees (that is, primary winners) for House, Senate and governor are women, compared to just 16 percent of Republicans'. That's a big difference. To date, no non-incumbent Republican women have won a nomination for a safe Republican seat in November — and there were certainly plenty of opportunities, given a high number of GOP (and overall) retirements this year. In short, Democrats are nominating many more women than Republicans thus far, and doing so in places where their chances are better in November.

Tonight there is at least one Republican woman with a good shot at bucking that trend and effectively claiming a safe red seat in November: North Dakota Public Service Commissioner Julie Fedorchak, who's running for the state's open at-large House seat. In addition to endorsements from several of the women's groups we're tracking (E-PAC, VIEW PAC and Winning for Women), she has Trump's endorsement, too.

Another Republican primary of note features two women, and GOP women's groups, going head-to-head: In South Carolina's 1st District, incumbent Rep. Nancy Mace faces several challengers, but her most notable opponent is former state cabinet official Catherine Templeton. Templeton is endorsed by Winning for Women, while Mace is endorsed by VIEW PAC (and notably, Trump). It's the first race we've seen so far in this season where two of the women's groups we're tracking are actively endorsing against each other.

On the Democratic side, three incumbent Democratic women in Nevada — Sen. Jacky Rosen, Rep. Susie Lee and Rep. Dina Titus — should cruise to victory with no serious competition in their primaries today, but they'll be watching today's GOP primaries to see which Republicans they'll face in November, when their races could be close, as Geoffrey wrote in 538's primary preview.

—Meredith Conroy, 538 contributor