CNN

A banner on the Wyoming GOP's Web site encourages applicants for the state's vacant Senate seat.

WASHINGTON (CNN) - After U.S. Senator Craig Thomas died of leukemia earlier this month, Republican leaders in his home state of Wyoming decided to employ a wide-open application process to find potential candidates for his vacant seat.

Any registered Republican who was a resident of Wyoming and met the age limit for a senator (at least 30) could throw his or her cowboy hat into the ring by filling out a two-page job application and submitting it to state party headquarters.

By Thursday's deadline, 31 people applied, including a host of current and former state legislators, two doctors, seven ranchers, a minister, a radio announcer and the manager of a truck stop company.

"Grassroots democracy is alive and well in Wyoming," said Fred Parady, the chairman of the state GOP, in a statement. "We have an energized citizenry and an eager group of applicants."

Sunday, the entire herd of candidates will be invited to take the stage at Casper College for a candidates' forum, which will be broadcast statewide. Parady said party leaders were still "finalizing procedures" for handling the large field of Senate hopefuls. After Sunday's forum, the GOP central committee will meet Tuesday to pick the three finalists to send to Gov. David Freudenthal, who will pick a new senator from the list.

Two of the candidates hail from families that are no stranger to the U.S. Senate State Rep. Colin Simpson of Cody is the son of former Sen. Alan Simpson and grandson of former Sen. Milward Simpson. Matt Mead of Jackson, who resigned last week from his post as U.S. attorney to seek Thomas' seat, is the grandson of former Sen. Cliff Hansen.

Some of the other higher-profile figures in the field of 27 men and four women are Tom Sansonetti, a Cheyenne lawyer who was once Thomas' chief-of-staff; former State Treasurer Cynthia Lummis; and Randall Luthi, a former state House speaker who is now deputy director of the U.S. Fish and Wildlife Service in Washington.

However, one name not on the list is Wyoming's lone U.S. House member, seven-term Rep. Barbara Cubin, who announced shortly after Thomas' death she would not try to move over to the Senate. And although there was speculation about the possibility in local media, Lynne Cheney, wife of Vice President Dick Cheney, also did not apply.

– CNN's Richard Shumate