But as of Monday evening, Grand Canyon University instructor Bob Branch was trailing Riggs by just 295 votes. A recount will automatically occur if the margin of victory drops to 200 votes or fewer, according to Arizona law.
The incumbent superintendent, Diane Douglas, has been stuck in third place. She was about 3,000 votes behind Branch, according to the ballots counted as of Monday.
Also competing in the Republican primary are Tracy Livingston and Jonathan Gelbart, who fell behind Douglas with 20 percent and 15 percent of the vote, respectively.
These four Republicans, as well as apparent Democratic nominee Kathy Hoffman, are jockeying to replace Douglas, who was widely viewed as a vulnerable candidate in her bid for re-election.
Douglas was elected by a slim margin in 2014 over David Garcia, now the Democratic nominee for governor. She also was criticized during the teachers' strike for her menacing statements about investigating educators who walked out of classrooms in April.
Another weak Republican incumbent toppled in Tuesday's primary was Secretary of State Michele Reagan – she lost in a landslide to first-time candidate Steve Gaynor.
A conservative who advocates increased parental involvement at the Department of Education, Riggs has been heavily involved in charter schools ever since the system was developed in 1990s.
Riggs represented California's First District from 1991 to 1993, and later from 1995 to 1999. As a congressman, he authored the 1998 Charter School Expansion Act, which outlined increased federal financial support for charter schools.
He declined to run for re-election in 1998, opting to run for Senate instead. However, Riggs lost in the Republican primary to challenge incumbent Barbara Boxer.
Riggs served as the CEO of the nonprofit Charter Schools Development Corporation, which helps newly established charter schools finance and manage their growth. He was also the founding board president of Arizona Connections Academy, an online charter school.
This is not his first foray into Arizona politics. Riggs ran in the 2014 Republican gubernatorial primary, finishing in last place with just 4.5 percent of the vote.
In the Democratic primary, political novice Hoffman edged out longtime politician David Schapira. Schapira, a former Tempe councilman and state legislator, bowed out and later endorsed Hoffman in a Facebook post.
Hoffman is a 32-year-old speech therapist. She worked in the Peoria Unified School District until May, at which time she left her job to campaign full-time.
Clarification: This article has been updated to state the reason why Riggs did not run for re-election in 1998. He chose to run for Senate in California instead.