The 2011 Â£1 coin, which features Edinburgh, is the rarest to be put into circulation by the Royal Mint.
Recent sales on eBay and other such websites have seen the coin sell for between Â£15 and Â£20.
Only 935,000 of these coins were issued back in 2011 - in the context of pound coins this is a very low number and it is notoriously rare to receive one in change.
The coin scores a maximum 100 points on Change Checker's scarcity index.
It is believed the Edinburgh coin will become increasingly difficult to find when, along with all the other old Â£1 coins, it is taken out of circulation next month. Anyone lucky enough to own one of the coins is advised not to cash in until after it is removed from circulation.
Change Checker calculated that anyone looking for an Edinburgh coin would have to sift through approximately 3,000 Â£1 coins to find one.
The old Â£1 coin will be replaced by the new 12 sided coin which was introduced into circulation earlier this year.