Primary election updates: Brad Raffensperger wins Georgia primary

ABC News projects that Rep. Marjorie Taylor Greene is the winner of the Republican primary in Georgia's 14th Congressional District.

Greene edged out five Republican competitors and overcame a legal challenge to her reelection despite her turbulent tenure in Congress.

As ABC’s Hannah Demissie reported, a group of Georgia voters said that Greene was not eligible to run for reelection due to her alleged involvement in the Jan. 6 attacks on the Capitol, citing the 14th Amendment. Georgia Secretary of State Brad Raffensperger agreed in early May with the court’s recommendation that Greene is allowed to stay on the ballot.

The final polls of the night have closed in Arkansas and Montana.

In Arkansas, voters are picking their party's nominees for governor and Senate. In Minnesota, there is a special election to choose a replacement for Rep. Jim Hagedorn, who died in February.

ABC News has projected that sitting Gov. Brian Kemp will win the Republican nomination in Georgia, defeating former President Donald Trump's pick David Perdue.

Trump personally courted Perdue to challenge Kemp after the governor refused to indulge his baseless claims about the 2020 election. Despite the former president’s backing, Perdue consistently lagged in polling and fundraising against Kemp.

Kemp’s presumptive victory sets up a rematch between him and Stacey Abrams, who ABC News has projected to win the Democratic nomination. Their bitter 2018 race for the governorship was decided by less than 55,000 votes. Abrams admitted defeat but said she refused to call it a “concession,” citing tactics she said were used to suppress the vote.

Polls are now closed in Alabama and most of Texas.

In Texas, all eyes are on a runoff election between Democrat Rep. Henry Cuellar and immigration attorney Jessica Cisneros in the state’s 28th Congressional District. Cisneros is backed by the progressive wing of the party, while Cuellar has maintained support from the Democratic establishment despite his anti-abortion stance.

In Alabama, Sen. Richard Shelby’s retirement has resulted in a competitive Republican primary between Rep. Mo Brooks, attorney Katie Britt and former Army helicopter pilot Mike Durant. Brooks initially won former President Donald Trump’s endorsement in the race, but later lost it after suggesting it was time to move on from the 2020 election. Trump has not made another endorsement in the contest.