It’s a simple question that is frequently debated among coin collectors: which coin is the most valuable in the world? The answer depends on who you ask and what measure you use. Even among seasoned numismatists, there is tremendous disagreement as to which coin is the most precious. What makes the question more interesting is that some of the rarest and most valuable pieces either haven’t traded hands in decades—or might never be sold ever.

One way of answering the question is to look at historic auction records. The current high water mark for a coin sold at auction is approximately $10mm; this was the price paid for a 1794 silver dollar in 2013. This piece is widely considered the very first silver dollar ever produced by the United States Mint; as such it carries tremendous historical significance. Although 75-100 of these 1794 dollars exist, this coin is clearly one of the finest and has one of the greatest stories in American numismatics. It is now part of a significant collection of US silver dollars.

Another contender is a unique 1907 prototype $20 Double Eagle designed by sculptor Augustus Saint-Gaudens and commissioned by Theodore Roosevelt. In a nutshell, Roosevelt wanted to revamp America’s gold coinage and hired Saint-Gaudens to overhaul the $20 Double Eagle. Saint-Gaudens went “all out” and produced this virtually stunning piece. Unfortunately, the exquisite design was impractical and difficult to strike, forcing the artist to go for a more modest motif. One virtually flawless specimen has survived; it last traded for approximately $500,000 in the mid-1980s but might fetch well over $10mm if offered for sale today.

One cannot ignore the wildly valuable and unusual rarities held by the Smithsonian Institute. Although these coins may never land in collectors’ hands, it’s great sport to speculate what these spectacular rarities might command in the private market. For example, the Smithsonian holds the very first $20 Double Eagle ever struck as well as the only two $50 “Half Union” gold pieces ever produced. These coins are valued at $10mm-$15mm each and, as best we can tell, will remain in the museum’s holdings for the foreseeable future.

Regardless of which coin is truly the most valuable, there are three common threads among all the candidates: rarity, beauty and history. The world’s most prized coins combine exquisite stories, dazzling visual appear and extreme scarcity. These coins may be well beyond the average collector’s reach, but they are fascinating to study and—for those lucky enough to visit the Smithsonian—fascinating to view in person.