The argument Jewish to CalendarChange converts between Western (Gregorian) dates and Jewish dates. The Gregorian date of Israel's independence is May 14, 1948:

Because the Jewish calendar has a leap month preceding Passover, the Wolfram Language uses a numbering starting with Nisan, the month of Passover:

Israel's independence was declared on the 5th of Iyar, 5708.

In Wolfram Language numbering, Tishrei, the first month of the Jewish year, is number 7.

By definition, Yom Kippur cannot fall on a Friday or Sunday:

Because of the leap month, Jewish dates can vary by up to a month in the Western calendar. The Western and Jewish anniversaries of Israel's independence differ greatly:

The Jewish calendar follows a 19-year cycle. Western and Jewish anniversaries will correspond almost exactly every 19 years:

A program which returns the Western (Gregorian) date of Passover for a given Western year:

A program which returns the Western (Gregorian) date of Yom Kippur for a given Western year:

A program which returns the Western date of the Jewish holiday Lag Ba'Omer for a given Western year:

Because it is a solar and lunar calendar (the year follows the seasons and the months keep track of the phases of the moon), the Jewish calendar has an extra leap month seven times every 19 years. This leap month occurs in spring, and is the month preceding Passover. It is therefore appropriate to count the Jewish months starting with Nisan, the month of Passover, as follows:

Since the Jewish year begins in the fall, this numeration of months will not always follow an increasing order; that is, later dates in the same year may have a smaller number for the month:

For this reason, some calendar functions will still work with the Calendar->Jewish option, but will not follow the same rules. DaysBetween can return a positive number even if the second date is lexicographically smaller (smaller in the canonical Wolfram Language ordering):

DaysPlus can return a lexicographically smaller (smaller in the canonical Wolfram Language ordering) result for a later date: