Primary election updates: Brad Raffensperger wins Georgia primary

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.

In the Georgia Senate Republican primary, ABC News projects Herschel Walker will win, beating out his highest-profile competitor, state agriculture commissioner Gary Black.

Walker’s nomination is a victory for former President Donald Trump, who endorsed the former football star before he even entered the race. Walker also had endorsements from Republican leader Mitch McConnell and former ambassador to the United Nations Nikki Haley despite his scandal-ridden past.

Walker will face incumbent Sen. Raphael Warnock in November’s general election.

ABC News has projected Raphael Warnock will win the Democratic nomination for Senate in Georgia.

Warnock took office last year after winning a special election against Republican Kelly Loeffler. His victory, as well as that of Sen. Jon Ossoff, secured the Democratic Party's narrow advantage in the chamber.

Warnock cruised through the primary but not without evading scandal. Earlier this year, the freshman senator became entangled in child custody battles with his ex-wife. The Atlanta Journal-Constitution reported Warnock had also been accused of running over his ex-wife's foot. Warnock said he’d “stay focused on the people of Georgia” in response to the allegations.