Primary voters dealt defeats Tuesday to heavily publicized political names, including Rudy Giuliani's son in New York and a pro-Donald Trump election conspiracy theorist in Colorado.

Tina Peters, a Colorado election official under indictment over efforts to bolster Trump's claims of voter fraud, headed for a third place finish in a Republican primary for Secretary of State.

In New York, U.S. Rep. Lee Zeldin, R-N.Y., won the GOP gubernatorial primary over Andrew Giuliani, son of former New York Mayor and Trump adviser Rudy Giuliani. Zeldin now faces a fall race against Gov. Kathy Hochul, who easily won the Democratic primary.

The states of Illinois, Oklahoma, and Utah also held primaries. In Illinois, two members of the U.S. House lost primaries to other incumbents who had been placed in the same newly drawn congressional districts.