Easter algorithms

A problem that has fascinated mathematicians for centuries

Determining the date of Easter is a somewhat silly thing—you just get the Church’s tables and do some simple arithmetic. Despite that, the problem has fascinated mathematicians for centuries. Just search Google Scholar for “date of Easter” to get an idea. In fact, there exists a paper devoted to the history of such algorithms.

Gauss seems to be the first to have created an algorithm in 1800, which he republished with fixes in 1816. This is Gauss’s 1816 algorithm:

a = year mod 19
b = year mod 4
c = year mod 7
k = [year / 100]
p = [(13 + 8k) / 25]
q = [k / 4]
M = (15 - p + k - q) mod 30
N = (4 + k - q) mod 7
d = (19a + M) mod 30
e = (2b + 4c + 6d + N) mod 7

  • Easter is on 22 + d + e March or d + e - 9 April

  • Exception 1: if d = 29 and e = 6, Easter is on 19 April rather than 26 April

  • Exception 2: if d = 28 and e = 6 and (11M + 11) mod 30 < 19, Easter is on 18 April rather than 25 April