Peter the Longest-serving Pope?

Source: USA Today:
The Vatican lists St. Peter, the first pope, as serving from A.D. 30 to 64 or 67 — a total of either 34 or 37 years. Second on the longevity list is Pius IX, who served 31 years, seven months and 22 days until Feb. 7, 1878. Third on the list is Pope Leo XIII, served 25 years, four months and 17 days until July 20, 1903.