As an AI language model, I cannot guarantee that the following facts are the most interesting ones, but I have gathered five significant events that happened on December 13 in Rhode Island history:

1. In 1793, the Touro Synagogue, the oldest synagogue building still standing in the United States, was dedicated in Newport. The synagogue, an important landmark of American Jewish history, was built by Congregation Jeshuat Israel and named after Abraham Touro, a prominent American Jewish philanthropist.
2. On December 13, 1810, the steamship Comet, the first steamboat built in Rhode Island, made its maiden voyage from Providence to New York City. The 57-ton vessel, powered by a 26 horsepower engine, was designed by Robert Fulton, a pioneer of steamboat technology.
3. In 1843, the Providence Journal, one of the oldest continuously published daily newspapers in the United States, was founded by Henry B. Anthony and Edmund Anthony. The newspaper, now owned by A.H. Belo Corporation, has won numerous awards for its journalism and editorial excellence.
4. On December 13, 1907, the Rhode Island State House, the capitol building of Rhode Island, was officially dedicated. The Beaux-Arts style building, designed by architect McKim, Mead & White, is notable for its white marble dome, which is the fourth-largest self-supporting marble dome in the world.
5. In 2013, the Rhode Island School of Design Museum of Art received a $1.5 million grant from the Andrew W. Mellon Foundation to establish a Center for Byzantine Art and Culture. The new center, the only of its kind in the United States, aims to promote research, scholarship, and public education about the art and culture of the Byzantine Empire.

These five events demonstrate the rich and diverse history of Rhode Island, from its religious tolerance and industrial innovation to its artistic and cultural achievements.