2 questions, actually.

[Yinzer]

First, what do they call the years occuring between B.C. and A.D.?

Second, I heard a bit about the switch from the julian calendar to the gregorian calendar (c1700), but just how many days difference is there?

[Hippy]

In what we now call AD 523 Dionysius Exiguus (in English known as Denis the Little), a monk from Scythia, a canon in the Roman curia, was assigned was to prepare calculations of future dates for Easter. At that time it was customary to count years since the reign of emperor Diocletian; but in his calculations Dionysius chose to number the years since the birth of Christ, rather than honour the pagan Diocletian.

 

Dionysius (wrongly) fixed Jesus' birth with respect to Diocletian's reign in such a manner that it fell on 25 December in the 753rd year since the founding of Rome (AUC, ab urbe condita), thus making the current era (AD, anno domini) start with AD 1 on 1 January 754 AUC.

 

When people started dating years before 754 AUC using the term "Before Christ," they used year 1 BC to immediately precede AD 1 with no intervening year zero.

 

Some people claim that the venerable Bede (673-735) introduced BC dating. Although Bede seems to have used the term on at least one occasion, it is generally accepted that BC dates were not generally used until the middle of the 17th century.

 

The Julian calendar was introduced by Julius Caesar in 45 BC, but its calculation of the year length was wrong and in 1582 a revision, called by Pope Gregory XIII, corrected the drift. The main changes were: drop 10 days from October 1582; change leap years so that not all years ending in "00" are leap; and change the beginning of the year to 1 January from 25 March. This was adopted immediately in Catholic countries, but Protestant countries made the change later. England changed in 1752, with eleven days removed from September. The additional day was needed because the old and new calendars disagreed on whether 1700 was a leap year, so the old calendar had to be adjusted by one more day.

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[Yinzer]

Oh my, how do you know so much?! Well thanks for the great answer.
Cheers!