Omar holds off well-funded primary challenger

8:50 p.m. Vermont Gov. Phil Scott has won the Republican nomination to seek his third, two-year term as the state's top elected official. Scott defeated four little-known Republican challengers on Tuesday to win his party's nomination to run in the November election. He didn't hire staff or actively campaign during the primary, citing the coronavirus.

The Latest on Tuesday's elections (all times local): 10:25 p.m. Rep. Ilhan Omar of Minnesota has survived a stiff Democratic primary challenge from a well-funded opponent who tried to make an issue of her national celebrity.

Omar defeated Antone Melton-Meaux, an attorney and mediator who raised millions of dollars. The victory means Omar is nearly certain to easily win a second term in November in her solidly liberal 5th Congressional District. Omar in 2018 became one of the first two Muslim women elected to Congress, building on a national profile that started when the onetime refugee from Somalia was elected to the Minnesota Legislature just two years earlier.

Her aggressive advocacy on liberal issues, and her eagerness to take on Donald Trump, made her even more prominent. She is known as one of the four “squad” members of progressive first-term congresswomen of colour. 9:45 p.m.

Marjorie Taylor Greene has won the Republican nomination for Georgia's 14th Congressional District. She's a businesswoman who has expressed support for the far-right conspiracy theory QAnon and has been criticized for a series of racist comments.

Greene beat neurosurgeon John Cowan in a primary runoff for the open seat on Tuesday. That's despite several GOP officials denouncing her campaign after videos surfaced in which she expresses racist, anti-Semitic and anti-Muslim views. She has responded to the criticism by blasting “the fake news media” and “the DC swamp.” Her victory comes in a deep-red area in northwest Georgia.

9:37 p.m. Former Rep. Jason Lewis has won Minnesota's five-way Republican primary for Senate.

Lewis, a one-term congressman and former conservative radio host, had the name recognition and money to easily beat several challengers on Tuesday. Lewis has spent months on a mostly virtual campaign aimed at taking down Democratic Sen. Tina Smith. He has been an outspoken critic of the state's coronavirus restrictions, and he has worked to tie Smith to what he calls “heavy-handed lockdown measures.” Smith is seeking election to her first full term since being appointed to replace Al Franken after Franken was caught up in sexual misconduct allegations. She won the Democratic primary Tuesday.

9:34 p.m. Democratic Sen. Tina Smith has won the Democratic primary in Minnesota as she seeks to win her first full term in the seat once held by Al Franken.

Smith faced four little-known opponents on Tuesday. She was appointed to the seat in early 2018 after Franken resigned amid sexual misconduct allegations. She won an election later that year to finish the remainder of his term. Smith is a former lieutenant governor. Jason Lewis, a one-term congressman and a former syndicated radio talk show host, was the favorite among Republicans seeking to challenge her in November. He is a staunch Trump supporter.

The fall campaign is shaping up as a referendum on President Donald Trump, who came close to carrying Minnesota in 2016 and is making an extra push to win the state this time. 9:15 p.m.

Vermont Lt. Gov. David Zuckerman has won the state's Democratic gubernatorial primary. Zuckerman will go up against incumbent Republican Gov. Phil Scott in the November general election. On Tuesday, Zuckerman defeated former Vermont Education Secretary Rebecca Holcombe and two lesser-known candidates to win the party's gubernatorial nomination.

The 48-year-old Zuckerman, a Hinesburg farmer, says he was motivated to run by what he calls “the imperative nature of the climate crisis.” Zuckerman says he thinks Scott is “a really admirable person,” but he hasn't been really visionary on how to address these issues. 8:50 p.m.

Vermont Gov. Phil Scott has won the Republican nomination to seek his third, two-year term as the state's top elected official. Scott defeated four little-known Republican challengers on Tuesday to win his party's nomination to run in the November election.

He didn't hire staff or actively campaign during the primary, citing the coronavirus. When announcing his reelection plans in May, Scott said, “Facing, fighting and defeating this virus — and rebuilding a stronger, more resilient economy — are my top priorities.” 8:20 p.m.

Joe Biden has won Connecticut's Democratic presidential primary. Biden defeated Vermont Sen. Bernie Sanders and Hawaii Rep. Tulsi Gabbard on Tuesday's ballot. Sanders and Gabbard dropped out of the race months ago but didn't ask the secretary of the state's office to remove their names from the ballot.

Biden visited Connecticut in October, when he appeared at a fundraiser hosted by Democratic Gov. Ned Lamont and his wife, Annie, at their home in Greenwich. Biden was expected to visit the state in March for another fundraising event at a private home, but that was scrapped because of the COVID-19 pandemic.

Biden is set to be formally nominated as the Democratic presidential nominee at next week's Democratic National Convention. 8:15 p.m.

President Donald Trump has won Connecticut's Republican presidential primary. Trump on Tuesday defeated California real estate developer and perennial candidate Rocky De La Fuente. Former Massachusetts Gov. William Weld and former Illinois congressman Joe Walsh were also in the race at one point but later withdrew.

Connecticut Republican Party chair J.R. Romano had criticised Secretary of the State Denise Merrill for holding a GOP primary, saying it was a waste of money for communities because Trump faced no viable competition. Merrill argued that she was following state law. De La Fuente was endorsed by the Alliance and Reform parties and has appeared on the ballot in at least a half dozen states as a Republican. He is the onetime owner of more than two dozen car dealerships.