Businesswoman and fellow conservative Marjorie Taylor Greene clinched the primary with 40 percent of the vote.
Dr. Cowan, who practices at Harbin Clinic in Rome, Ga., received 21 percent of the vote, according to BI.
In Georgia primaries, if neither candidate receives more than 50 percent of the vote, the race goes to a runoff.
The candidates were vying for the open seat left by U.S. Rep. Tom Graves, R-Ga., who is not seeking reelection for 2020.
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