The rare gold penny, which features a portrait of King Henry III, is one of just eight in the world.
The piece is an example of the first ever English gold coin and 52,000 were produced.
But these were quickly withdrawn because it was deemed too heavy.
The banking error meant the gold it was made from was worth more than the coin itself.
This made the coins financially unviable as the holders could get more money from melting them down for gold rather than using them as currency.
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Virtually all of them were smelted and were replaced with correctly weighed pennies in 1257.
Today only eight of the coins exist, with all but three of them held by institutions.
One of the three in private hands has been put up for sale and is set to fetch £500,000.
It is being sold by an anonymous collector who has owned it for 21 years.
Cristiano Bierrenbach, of the numismatic department at US-based Heritage Auctions, said: “These gold pennies were the first gold coins made in England.
“King Henry III tried to establish a trade conversion value for a coin to match the Ducat coin which was used on mainland Europe.
“He ordered the creation of a gold coin for his kingdom to be struck at twice the weight of a silver penny.
“But the issue was ultimately unsuccessful. The coins had a standard weight of 3.5 grammes but an error was made and the coin was made too heavy, about 4.2 grammes.
“After that the coin was pulled from circulation and they were melted down and more gold pennies were struck at the correct weight.
“It is incredibly rare to come across one of these. It is a big ticket item and we expect it to go for higher than the estimate.”
The coin depicts King Henry seated on a throne wearing robes. He has a sceptre in his right hand and an orb in his left.
The reverse features a long cross and the name Willem on LVND. This is William of Gloucester who was the King’s goldsmith and ultimately responsible for the error.
It is being sold on January 8.
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