The Dexter Silver Dollar, 1804 was not minted in 1804. The US Mint did mint silver dollars in 1804 but they were dated 1803, rather than make a new mold. Dexter purchased his coin in 1885 from the Chapman Brothers Auction then sued for authenticity. The US Mint settled the matter. Yes, they had minted the coins in 1834 but only a few. 15 specimens are known. They were gifts.
Dexter had a painting commissioned to celebrate his authentic coin. He also punched a small "D" in one of the clouds on the back of the coin, forever marking it as his.
In a recent auction, 1989, the coin sold for $990,000.