When determining the date of the birth of Christ, Dionysious Exiguus forgot that Caesar Augustus had ruled under the name of Octavian for four years, and thus made a four-year error.
Dionysius Exiguus (Dennis the Little) was a Scythian monk and prominent scholar who lived in Rome and who had access to the state and church archives including many records now lost to us. It is true that Julius Caesar's grandnephew Octavian ruled as part of a triumvirate under his own name for four years, and was not proclaimed emperor Caesar Augustus until after he defeated the combined forces of Antony and Cleopatra at the navel battle of Actium in September, 31 B.C., but this was common knowledge. Schoolboys were expected to know the story, and a prominent historian working in Rome would not have made such a simple blunder.
Dionysius carefully selected the year we would call I B.C. for the birth of Christ, and set the date at December 25th as was customary in his time, and commenced the Christian Era with January 1, 1 A.D. (six days later) to agree with the stars of the ordinary Roman year, and was probably not far from the mark.