The mintage of the 1860-S $3 has been debated over the years, as reflected in David Akers' writeup below. The official Mint Reports show a mintage of 7,000 coins, but that figure was reduced by 2,592 coins believed to have been melted before release because they were lightweight. Researcher R.W. Julian recently (Summer 2017) corrected the record by noting that the 2,592 coins were a group of underweight $3 gold pieces found by former Mint Director Henry Linderman on a visit to the San Francisco Mint in October 1869. Apparently, this group of coins had been "sweated" either mechanically or chemically. Sweating was a nefarious practice by which small amounts of gold were removed surreptitiously from a coin for profit, after which the sweated coins were returned to circulation. Thus, this was not a case of poorly-made 1860-S Three Dollar gold pieces; rather, the 2,592 coins were of unknown date and mint that had been gathered up at the San Francisco Mint for analysis and eventual destruction. The net result is that the official mintage of 7,000 coins for the 1860-S $3 is correct.
Julian, R.W. "Mintage figure error crept into numismatic literature 50 years ago". The Centinel, Summer 2017 (Volume 65, Number 2), pp. 46-50.