Former Alaska Attorney General GOP candidate Dan Sullivan, after winning Tuesday's primary, will now challenge incumbent Senate Democrat, Mark Begich in the November election.

"Now is the time to focus on the real issues that matter the most to Alaskans," Sullivan said in a statement early Wednesday. "I look forward to painting a clear contrast between Mark Begich's inability to move our state forward and my vision for a brighter and better Alaska."

With 80 percent of precincts reporting, Sullivan had 40 percent of the vote to 25 percent for Alaska Lieutenant Governor Mead Treadwell and 32 percent for Tea Party favorite Joe Miller, according to the Associated Press.

With an endorsement by former Alaska Governor and vice presidential candidate Sarah Palin over the weekend, Miller received nearly twice the support he got in a recent Huffington Post poll before the election. In that poll, Sullivan led at 37 percent, with Treadwell at 26.5 percent and Miller at 16.6 percent

The Alaska Senate race is one of less than a dozen key fights for seats in the battle for the control of the chamber this November. Republicans need six seats to upset the Democratic majority, currently 55-45.

Begich was first elected in 2008 and spent $8 million to win the election by 4,000 votes against veteran incumbent Republican Senator Ted Stevens. A few weeks before the election, Stevens had been found guilty of seven charges of corruption in a federal trial. Those charges were later overturned.

Sullivan served in the President George W. Bush administration, including three years as an assistant secretary of state. "He counts among his backers Bush political adviser Karl Rove and former Secretary of State Condoleezza Rice, according to Bloomberg. Such Republican big hitters will provide Sullivan with access to big donors in this campaign against Begich.

A CBS News/New York Times poll conducted July 5-24 showed Begich with a 12 percent lead over Sullivan.

Alaska is a big state with a small population. Because of the state's size, people can vote by mail and absentee ballot. There were 300,000 registered voters in 2010, and native peoples represented 14 percent of the vote.

In the Wyoming primary, Governor Matt Mead beat his two challengers, claiming a victory in the Republican majority state for his second term. Mead faces Pete Gosar, a Democrat, in the November election. Mead has opposed the Obama Administration's Affordable Care act, and mounted lawsuits against federal air quality regulations which he argues threatens the state's coal industry.

U.S. Senator Mike Enzi, (R), 70, beat four Republican challengers and faces Democrat Charlie Hardy, a 75-year-old former Roman Catholic priest.

Primary elections in Arizona, Florida and Vermont are on Tuesday.