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

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

With Rep. Armstrong running for the Senate, North Dakota's At-Large Congressional District is up for grabs, and the two main contenders in the Republican primary look to be Public Service Commissioner Julie Fedorchak and former state Rep. Rick Becker. Fedorchak has a solid electoral record, having won three statewide races to retain her current office, and she earned Trump's endorsement in late May. Meanwhile, Becker has a complicated relationship with the GOP: During his legislative tenure, Becker founded a far-right caucus, and in 2022, he actually ran for Senate as an independent against Republican Sen. John Hoeven. That campaign left Becker ineligible for the state GOP endorsement vote in April, but his supporters spoiled their ballots to give the endorsement to a minor candidate instead of Fedorchak.

Meanwhile, Becker and his allies have mostly kept up with Fedorchak in the money race. Fedorchak has brought in $979,000, compared with Becker's $911,000, although Becker self-funded $550,000 of his haul. Yet outside groups have spent slightly more promoting Becker or attacking Fedorchak ($1.6 million) than on supporting Fedorchak or opposing Becker ($1.3 million). Two surveys have shown a close race, too: An early May poll from DFM Research/North Dakota United put Becker ahead 29 percent to 26 percent, while a late May survey from WPA Intelligence/North Dakota News Cooperative found Fedorchak leading 32 percent to 25 percent. However, both polls predated Trump's endorsement, and, in a possible signal that Fedorchak has the upper hand, the pro-Becker Club for Growth canceled a planned ad buy for the final week of the campaign.

—Geoffrey Skelley, 538