The Trime was a three cent coin. There is a great article here at clevelandfed.org explaining how it came into being as a direct result of postage rates in 1851 dropping from 5 cents to 3 cents due to competitive pressure from private delivery companies. It also does a fair job of explaining the monetary crisis the U.S. faced as a result of the Gold Rush and minting coins out of precious metals.
According to 1847USA.com, On May 1, 1861 the letter rate was 3¢ if it stayed East of the Rockies, and 10¢ if it crossed the Rockies, both regardless of distance, effectively eliminating the 3000 mi. distinction. This distinction was dropped as of July 1, 1863.
The smallest coin ever minted by the United States, the Trime was created in response to a lack of small denomination coins to make change, and fit perfectly with postage rates. It was nicknamed a “fish-scale” and there are great images of it at coinauctionshelp.com.
According to the article at clevlandfed.org, there were cent and half-cent coins, but they were not recognized formally as legal tender until 1864 and were not widely available off the East Coast, so they were not very popular.
It is commonly believed that Benjamin Franklin designed the first penny, the “Fugio” , and, according to the U.S. Mint, the penny was one of the first coins minted in 1792. Always check your sources!
Also according to the article at clevelandfed.org:
“A customer who offered a gold dollar
in payment for a small article would
receive in exchange perhaps ten or
fifteen 3-cent pieces and a half-dozen
almost unrecognizable reals and
medios. A Philadelphia paper refers
derisively to shopkeepers scooping up
3-cent pieces with a ladle to make
change for a $5 bank-note.”
I guess that’s what happens when someone owes you 166 coins in change.
By the way, medios and reals were Spanish currencies.