Here's what Wiley Sword has to say in "Sharpshooter: Hiram Berdan, his famous Sharpshooters and their Sharps Rifles."
"Generally, the one constant premise in evaluating a possible Berdan Sharps rifle is its inspection by John Taylor. Bear in mind that other inspector's initials may appear on the barrel, such as 'O W A.' for O. W. Ainsworth, brought over from Colt as sub inspector..." Here Sword lists numerous serial numbers. He cautions, "The actual Berdan Sharpshooter documented number suggests that these rifles were issued randomly, and no correlation with serial number exists as to the unit of issue. Both the 1st and 2nd U.S. Sharpshooters are known to have carried rifles in the 54000, 55000, 56000, 57000 serial ranges. Accordingly, those Berdan Sharps issued subsequently to the Andrew Sharpshooters, Col. L of the 1st Minnesota, and the Pennsylvania Bucktails (42nd Pa. Vol. Inf.) are believed to be similarly randomly numbered within the above estimated range. Certain Sharps rifles of slightly higher numbers than #57574 may have some possibility of association with the Berdan Sharpshooters. Because of the rush to complete the Berdan special order it is possible that a few rifles at the tail end of production went out without the double set triggers, which were very time consuming to make. At least one rifle of signle trigger type has been reported with John Taylor inspector marks (#57743). This may involve a replacement stock or trigger mechanism, and until further evidence is presented no final conclusinon seems possible on this aspect..."
Any other history on your gun? Who was the first in your family and how did he acquire it?