Is Sen. Orrin Hatch, (R-Utah) poised to lay undisputed claim to the title of “most senior Republican member. (Jacquelyn Martin/AP)

We learned of this spat three years ago, when Hatch’s press secretary at the time, Andrea Saul (now working for Mitt Romney) wanted a correction in a column.

“You have Sen. Lugar listed as the longest-serving Republican senator. Sen. Hatch is actually the longest-serving GOP senator,” she wrote, and photos of them in the Senate chamber clearly show Hatch “is in the first GOP seat, with Lugar behind him.”

But on their Web sites, each one claimed to be the “most senior Republican” and Lugar’s site even notes that he is most senior and that Hatch was the second-most. (You might see this matter as meaningless, but the senators obviously care.)

So we kept digging.

Both lawmakers were sworn in on the same day -- Jan. 3, 1977. There are numerous criteria set by the Senate Rules Committee for determining seniority when senators are sworn in on the same day. These include whether you’ve been in the House, or have been a governor or member of the Cabinet. If there is still a tie, senators are ranked in terms of their state’s population at the time of their swearing-in.

Under those rules, the edge would go to Lugar. The Senate historian’s office uses those rules to decide who’s senior for historical purposes, we were told, which is why Lugar is ranked 1,705th senator (out of a total of 1,911) and Hatch is 1,708. It’s also why Lugar has a lower Senate license plate number. (Ah, there’s a prize worth having.)

But the Republican caucus has the ultimate say on this and under GOP rules when Hatch and Lugar were first elected, the alphabet, not state size. Under those rules, Hatch is obviously No. 1.

Lugar’s defeat Tuesday — and Hatch’s very likely win in his primary next month and then in November — would put an end to the debate.

Hatch’s office declined to comment. But passersby thought they heard chants inside his office of “we’re number one.”