WASHINGTON -- Old inns along the Revolutionary War trails boast of George Washington sleeping there. But coin experts say they have found the first silver piece minted by the United States -- one likely held by the most en vogue of Founding Fathers, Alexander Hamilton.

David McCarthy figured the silver coin had to be one-of-a-kind after spotting it in the auction catalogue.

Its front features the all-seeing eye of God, surrounded by rays of light. The rays shoot out toward 13 stars -- one for each of the colonies that had rebelled against Great Britain. A similar coin bore two words in Latin above the starburst: "Nova Constellatio," or "new constellation" to describe the infant United States. But this silver piece bore no inscription at all. It was the first clue that the coin was something singular, said McCarthy, a senior researcher for the coin and collectibles firm Kagin's.

He had a hunch it was the first coin ever minted by the U.S. government in 1783 -- the prototype for a plan discussed by both Hamilton and Thomas Jefferson that arguably shaped the course of the nation. McCarthy staked his company's money to buy the coin for $1.18 million at the 2013 auction. After nearly four years of late nights sifting through the papers of the Founding Fathers and studying the beading on the coin's edges, he is now making an exhaustive case that this silver piece is indeed the first American coin, the precursor of what ultimately would circulate a decade later as the U.S dollar.

The coin is on display this week at the World's Fair of Money in Denver.

"You've used the progeny of this one coin in every transaction you've done in your life, whether it's a bitcoin, a dollar or a euro," McCarthy said."

McCarthy published the details of his findings in the August issue of the coin journal, The Numismatist, as well as in a post on Medium. He vetted and refined his findings over the years with other top experts such as John Dannreuther, a rare coin dealer who found identifying marks on another coin that indicates that it had to have been struck days or even weeks later from the same steel dies.

"I'm 99.9999 per cent certain this is the first U.S. coin," Dannreuther said.

It was well-known among collectors that a first coin existed. Robert Morris, the Philadelphia merchant who financed the American Revolution, recorded its existence in his diary on April 2, 1783.

As first Superintendent of Finance of the United States, Morris wrote he received a delivery of "a Piece of Silver Coin being the first that has been struck as an American Coin." Hamilton visited Morris a week later and the two corresponded on the "subject of the Coin." The continental Congress was then presented with a fuller set of coins on April 22, which was then forwarded to Jefferson for his thoughts.

Both Hamilton and Jefferson -- now popularly known as rivals from the musical "Hamilton" -- embraced the idea that the U.S. currency should be in units of 10.

The coin purchased by McCarthy had a back with a wreath identifying it as a "500" quint, essentially the forerunner of the half-dollar. It had initially been found in 1860, about 15 years after the similar coin with the "new constellation" inscription. Because the new constellation coin was found earlier, experts labeled McCarthy's coin as "Type 2." Over the years, that label was mistakenly believed to refer to the coin being struck after the one with the inscription.

"You have this powerful word '2' that implies something and it hijacked everyone's ability to see what was right in front of them," said McCarthy, 44.

The day of the 2013 auction in Schaumburg, Illinois, McCarthy sat in his hotel room with his files and air conditioning cranked on high. He methodically convinced his boss, Donald Kagin, that the coin up for auction was the nation's first. It was a nuanced case since other dealers claimed it was a forgery. But the initial explanation was that mints tended to add inscriptions to the steel dies used to make coins after having engraved the images.

So McCarthy bid on the silver coin -- and then began the research needed to make his case ironclad. He searched through the National Archives for records, only to learn that the microfilm of original documents didn't correspond to the actual files.

His eureka moment came in a New York hotel room while reviewing the original receipts for the steel dies used to make the coins. There had been a total of 10 dies made by a blacksmith, but the receipts showed that 12 dies had been engraved by two different artisans. This suggested that two of the dies had been recycled and refined after the first coin had been struck. He compared the beadings on the edges of the different coins, as well as a dent in the eye at the centre of the inscripted "500" coin and its plain cousin. The evidence all pointed to him having uncovered the nation's first coin.

Jeff Garrett, president of the American Numismatic Association, called the research "really, really good." His organization publishes The Numismatist journal.

In terms of the coin's possible value, Garrett said the closest comparison was a 1794 silver dollar that sold for more than $10 million four years ago. But the allure of coins isn't just their rarity or metal content but the history that comes embedded to them as they pass through the ages.

"People always ask, how could a coin be worth a $1 million or $5 million?" Garrett said. "I always say it's because of the stories."