The first day of the Jewish Passover feast is given according to the Julian calendar up to and including 1582 (AM 5342/43) and according to the Gregorian calendar from 1583 (AM 5343/44) onwards. Note that the Jewish Paschal Full Moon always falls on 14 Nisan.
The Gaussian algorithm for calculating the first day of the Jewish Passover feast (15 Nisan) is equivalent with the method currently employed in the rabbinic (or cyclic) Jewish calendar, which according to tradition was introduced by Hillel the Patriarch (Hillel II) in AD 358/359 (AM 4119). However, there is evidence (cf. Stern, 2001) that up to the 10th century AD several versions of the Jewish calendar existed simultaneously and textual evidence suggests that some of the underlying parameters and postponement rules currently employed in the rabbinic Jewish calendar were probably not introduced until the mid-10th century AD.
The Julian Easter algorithm should not be used before c. AD 530 as it differs slightly from the computations of the Christians of Alexandria and from the 532-year cycle of Victorius of Aquitaine that was used in the western parts of Europe up to the 8th century AD. Of course there will also be differences with the Easter dates computed from the earlier Paschal tables (based on 16- and 84-year cycles) that were previously adopted in the Western Roman Empire.
Note: A slightly different Easter reckoning is followed to this day by some Eastern Orthodox Churches, notably the Armenian Orthodox Church, the Syrian Orthodox Church (known as the Jacobites) and the Church of the East (known as the Nestorians). The latter are also known as the Non-Chalcedonian churches and, as the Armenian Orthodox Church, are located near the eastern border of the former Byzantine Empire.
These churches place the Paschal Full Moon on 6 April (instead of 5 April) when the Golden Number is 1 and when this happens to fall on a Sunday (i.e. when the Dominical Letter is E) Easter Sunday is observed a week later on 13 April (instead of 6 April). This happens four times in each 532-year cycle and since the introduction of the Dionysian Easter reckoning this has occurred in 570, 665, 760, 1007, 1102, 1197, 1292, 1539, 1634 (23 April New Style), 1729 (24 April NS) and 1824 (25 April NS). The next cases (up to 2500) will be in 2071 (26 April NS), 2166 (27 April NS), 2261 (28 April NS) and 2356 (29 April NS).
Gregorian Easter Sunday dates are only defined for the years following the Gregorian calendar reform in 1582. In the default mode the Easter/Passover calculator therefore does not output Gregorian Easter Sunday dates before 1583 as these are meaningless for chronological purposes, but if so desired the calculator can also output proleptic Gregorian calendar dates.
Assuming no change in the current rules for calculating the dates for Passover and Easter Sunday in the Jewish and Gregorian calendars, the Easter/Passover calculator should produce valid results up to at least AD 9999.
Note: The Easter/Passover calculator should NOT be used to date key events in the life of Jesus Christ or that of other early Christians as it is based on strictly cyclical algorithms that were not introduced until many centuries later.