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Around the year 1800, the German mathematician Carl Friedrich Gauss (1777 – 1855) introduced formulas for calculating the dates for Christian Easter and the Jewish Passover. These formulas made chonological calculations much easier.

The procedure for calculating the date of the Jewish Passover (Nissan 15) is as follows:

1) A=R+3660,

where “A” is the year according to the Jewish calendar; “R” is the year NE.

2) a= (12A+17) mod 19,

where “mod 19” is the remainder of the division by 19.

3) b=A mod 4.

4) M+m= (32,0440933+1,5542418a+0,25b-0,00317779A),

where “M” is the integer part, and “m” is the fractional part.

5) c= (M+3A+5b+5) mod 7.

So, three variants are possible:

1) is c=1, a> b and m≥0.63287037, then the Jewish Passover (Nissan 15) falls on M+2 March in the Julian calendar.

2) if c=2, 4 or 6, and also when c=0, a> 11 and m≥0,89772376, then the Jewish Passover falls on M+1 March.

3) in all other cases it falls on M in March.

If the resulting value is greater than the number of days in March, you should subtract 31. The result will correspond to a date in April.

For example, let us calculate the date for the Jewish Passover in 2016:

1) A=5776.

2) a=17.

3) b=0.

4) M+m=40,11128886.

M=40, m=0,11128886.

5) c=6.

Since c=6, you should add 1 to M=40 and subtract 31. So, in 2016, the Jewish Passover (Nissan 15) falls on April 10 in the Julian calendar, which corresponds to April 23 in the Gregorian calendar. As noted above, the 24-hour day in the Jewish calendar begins at sunset. That is why the 15th of Nissan in this case begins in the evening of April 9 and ends in the evening of April 10.

The procedure for calculating the date of Christian Easter using the Gauss formula is as follows:

1) a=R mod 19,

where “R” is the year NE; “mod 19” is the remainder after the division by 19.

2) b=R mod 4.

3) c=R mod 7.

4) d= (19a+15) mod 30.

5) e= (2b+4c+6d+6) mod 7.

Three variants are possible:

1) if the sum of (d+e) does not exceed 9, then Christian Easter falls on March (22+d+e).

2) is (d+e) ≥10, then Easter falls on April (d+e-9).

For example, let us calculate the date for Easter in 2016:

1) a=2.

2) b=0.

3) c=0.

4) d=23.

5) e=4.

Since (d+e) exceeds 9, let us calculate (d+e-9) =18. So, in 2016, Orthodox Christian Easter falls on April 18 of the Julian calendar, which corresponds to May 1 in the Gregorian calendar.