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Distribution of Easters
By Brad Rodgers on Sunday, March 31, 2002 - 02:49 am:

With what density does Easter fall in March? I've found the algorithm for calculating Easter's date (apparently due to Gauss), but I have no idea of an elegant way to calculate the density. Here is an algorithm

"All variables are integers and all remainders from division are dropped.

The algorithm uses the year, y, to give the month, m, and day, d, of Easter. The symbol × means multiply.


c = y / 100
n = y - 19 × ( y / 19 )
k = ( c - 17 ) / 25
i = c - c / 4 - ( c - k ) / 3 + 19 × n + 15
i = i - 30 × ( i / 30 )
i = i - ( i / 28 ) × ( 1 - ( i / 28 ) × ( 29 / ( i + 1 ) )× ( ( 21 - n ) / 11 ) )
j = y + y / 4 + i + 2 - c + c / 4
j = j - 7 × ( j / 7 )
l = i - j
m = 3 + ( l + 40 ) / 44
d = l + 28 - 31 × ( m / 4 )"

Thanks,

Brad

By Yatir Halevi on Saturday, April 13, 2002 - 02:33 pm:

Here is another algorithm, credited to Butcher.
Unlike the one given by Gauss, this method has no exception and is valid for all years in the Gregorian Calendar, hence from the year 1583 on.
the year is y.
a= y mod 19
b= y div 100
c= y mod 100
d= b div 4
e= b mod 4
f= (b+8) div 25
g= (b-f+1) div 3
h=(19a+b-d-g+15) mod 30
i= c div 4
k= c mod 4
l= (32+2e+2i-h-k) mod 7
m= (a+11h+22l) div 451
n= (h+l-7m+114) div 31
p= (h+l-7m+114) mod 31

n=number of month (3=march, 4=april)
p+1=day of that month upon which Easter Sunday falls.

And it has been found that, in the long run, the most frequent Greogrian Easter date is April 19.

Yatir

By Graeme Mcrae on Saturday, May 04, 2002 - 06:42 am:

I compared the two algorithms for the years 1583 through 31583 and found they give identical results, so I don't know what "exceptions" Yatir is talking about.

In the 30001 years I checked, the most common date is April 19, occurring 1159 times. (At first, I only checked 3001 years, and found that April 10 and April 15 were most common, occuring 116 times each.)

Here is the distribution of the 35 possible dates in the years 1583 through 31583:


date total rank %
03/22 144 35 0.48%
03/23 286 33 0.95%
03/24 429 32 1.43%
03/25 581 29 1.94%
03/26 696 28 2.32%
03/27 866 25 2.89%
03/28 979 22 3.26%
03/29 1016 6 3.39%
03/30 994 16 3.31%
03/31 994 16 3.31%
04/01 1012 10 3.37%
04/02 984 19 3.28%
04/03 1018 4 3.39%
04/04 977 23 3.26%
04/05 1016 6 3.39%
04/06 999 14 3.33%
04/07 1001 13 3.34%
04/08 1014 9 3.38%
04/09 977 23 3.26%
04/10 1019 3 3.40%
04/11 981 21 3.27%
04/12 1015 8 3.38%
04/13 994 16 3.31%
04/14 997 15 3.32%
04/15 1018 4 3.39%
04/16 983 20 3.28%
04/17 1011 11 3.37%
04/18 1043 2 3.48%
04/19 1159 1 3.86%
04/20 1002 12 3.34%
04/21 854 26 2.85%
04/22 725 27 2.42%
04/23 560 30 1.87%
04/24 437 31 1.46%
04/25 220 34 0.73%
Grand Total 30001 100.00%