Editing Doomsday rule (section)

==400-year cycle of anchor days==
{| class="wikitable mw-collapsible mw-collapsed" style="clear:right;float:right;margin:0.5em 1em 0.5em 0;text-align:center"
! colspan=4 | Julian centuries
! style="text-align:right" | -1600J<br/>  -900J<br/>  -200J<br/>  500J<br/> 1200J<br/> 1900J<br/> 2600J<br/> 3300J
! style="text-align:right" | -1500J<br/>  -800J<br/>  -100J<br/>  600J<br/> 1300J<br/> 2000J<br/> 2700J<br/> 3400J
! style="text-align:right" | -1400J<br/>  -700J<br/>     0J<br/>  700J<br/> 1400J<br/> 2100J<br/> 2800J<br/> 3500J
! style="text-align:right" | -1300J<br/>  -600J<br/>   100J<br/>  800J<br/> 1500J<br/> 2200J<br/> 2900J<br/> 3600J
! style="text-align:right" | -1200J<br/>  -500J<br/>   200J<br/>  900J<br/> 1600J<br/> 2300J<br/> 3000J<br/> 3700J
! style="text-align:right" | -1100J<br/>  -400J<br/>   300J<br/> 1000J<br/> 1700J<br/> 2400J<br/> 3100J<br/> 3800J
! style="text-align:right" | -1000J<br/>  -300J<br/>   400J<br/> 1100J<br/> 1800J<br/> 2500J<br/> 3200J<br/> 3900J
|-
! colspan=4 {{Diagonal split header 2|1={{indent|2}}Years|2=<span style="{{writing-mode|v1}}">Gregorian<br/>centuries</span>}}
! valign="top" scope="col" style="text-align:right" |-1600<br /> -1200<br />  -800<br />  -400<br />   0<br /> 400<br />  800<br /> 1200<br /> 1600<br /> 2000<br /> 2400<br /> 2800<br /> 3200<br /> 3600
! valign="top" scope="col" style="text-align:right" |
! valign="top" scope="col" style="text-align:right" |-1500<br /> -1100<br />  -700<br />  -300<br /> 100<br /> 500<br />  900<br /> 1300<br /> 1700<br /> 2100<br /> 2500<br /> 2900<br /> 3300<br /> 3700
! valign="top" scope="col" style="text-align:right" |
! valign="top" scope="col" style="text-align:right" |-1400<br /> -1000<br />  -600<br />  -200<br /> 200<br /> 600<br /> 1000<br /> 1400<br /> 1800<br /> 2200<br /> 2600<br /> 3000<br /> 3400<br /> 3800
! valign="top" scope="col" style="text-align:right" |
! valign="top" scope="col" style="text-align:right" |-1300<br /> -900<br />   -500<br />  -100<br /> 300<br /> 700<br /> 1100<br /> 1500<br /> 1900<br /> 2300<br /> 2700<br /> 3100<br /> 3500<br /> 3900
|-style="background:#EEF"
!scope="row" | 00 || 28 || 56 || 84
| Tue. || Mon. || Sun. || Sat. || Fri. || Thu. || Wed.
|-
!scope="row" | 01 || 29 || 57 || 85
| Wed. || Tue. || Mon. || Sun. || Sat. || Fri. || Thu.
|-
!scope="row" | 02 || 30 || 58 || 86
| Thu. || Wed. || Tue. || Mon. || Sun. || Sat. || Fri.
|-
!scope="row" | 03 || 31 || 59 || 87
| Fri. || Thu. || Wed. || Tue. || Mon. || Sun. || Sat.
|-style="background:#EEF"
!scope="row" | 04 || 32 || 60 || 88
| Sun. || Sat. || Fri. || Thu. || Wed. || Tue. || Mon.
|-
!scope="row" | 05 || 33 || 61 || 89
| Mon. || Sun. || Sat. || Fri. || Thu. || Wed. || Tue.
|-
!scope="row" | 06 || 34 || 62 || 90
| Tue. || Mon. || Sun. || Sat. || Fri. || Thu. || Wed.
|-
!scope="row" | 07 || 35 || 63 || 91
| Wed. || Tue. || Mon. || Sun. || Sat. || Fri. || Thu.
|-style="background:#EEF"
!scope="row" | 08 || 36 || 64 || 92
| Fri. || Thu. || Wed. || Tue. || Mon. || Sun. || Sat.
|-
!scope="row" | 09 || 37 || 65 || 93
| Sat. || Fri. || Thu. || Wed. || Tue. || Mon. || Sun.
|-
!scope="row" | 10 || 38 || 66 || 94
| Sun. || Sat. || Fri. || Thu. || Wed. || Tue. || Mon.
|-
!scope="row" | 11 || 39 || 67 || 95
| Mon. || Sun. || Sat. || Fri. || Thu. || Wed. || Tue.
|-style="background:#EEF"
!scope="row" | 12 || 40 || 68 || 96
| Wed. || Tue. || Mon. || Sun. || Sat. || Fri. || Thu.
|-
!scope="row" | 13 || 41 || 69 || 97
| Thu. || Wed. || Tue. || Mon. || Sun. || Sat. || Fri.
|-
!scope="row" | 14 || 42 || 70 || 98
| Fri. || Thu. || Wed. || Tue. || Mon. || Sun. || Sat.
|-
!scope="row" | 15 || 43 || 71 || 99
| Sat. || Fri. || Thu. || Wed. || Tue. || Mon. || Sun.
|-style="background:#EEF"
!scope="row" | 16 || 44 || 72 ||
| Mon. || Sun. || Sat. || Fri. || Thu. || Wed. || Tue.
|-
!scope="row" | 17 || 45 || 73 ||
| Tue. || Mon. || Sun. || Sat. || Fri. || Thu. || Wed.
|-
!scope="row" | 18 || 46 || 74 ||
| Wed. || Tue. || Mon. || Sun. || Sat. || Fri. || Thu.
|-
!scope="row" | 19 || 47 || 75 ||
| Thu. || Wed. || Tue. || Mon. || Sun. || Sat. || Fri.
|-style="background:#EEF"
!scope="row" | 20 || 48 || 76 ||
| Sat. || Fri. || Thu. || Wed. || Tue. || Mon. || Sun.
|-
!scope="row" | 21 || 49 || 77 ||
| Sun. || Sat. || Fri. || Thu. || Wed. || Tue. || Mon.
|-
!scope="row" | 22 || 50 || 78 ||
| Mon. || Sun. || Sat. || Fri. || Thu. || Wed. || Tue.
|-
!scope="row" | 23 || 51 || 79 ||
| Tue. || Mon. || Sun. || Sat. || Fri. || Thu. || Wed.
|-style="background:#EEF"
!scope="row" | 24 || 52 || 80 ||
| Thu. || Wed. || Tue. || Mon. || Sun. || Sat. || Fri.
|-
!scope="row" | 25 || 53 || 81 ||
| Fri. || Thu. || Wed. || Tue. || Mon. || Sun. || Sat.
|-
!scope="row" | 26 || 54 || 82 ||
| Sat. || Fri. || Thu. || Wed. || Tue. || Mon. || Sun.
|-
!scope="row" | 27 || 55 || 83 ||
| Sun. || Sat. || Fri. || Thu. || Wed. || Tue. || Mon.
|-
|}

Since in the Gregorian calendar there are 146,097 days, or exactly 20,871 seven-day weeks, in 400 years, the anchor day repeats every four centuries. For example, the anchor day of 1700–1799 is the same as the anchor day of 2100–2199, i.e. Sunday.

The full 400-year cycle of doomsdays is given in the adjacent table. The centuries are for the Gregorian and [[proleptic Gregorian calendar]], unless marked with a J for Julian. The Gregorian leap years are highlighted.

Negative years use [[astronomical year numbering]]. Year 25BC is −24, shown in the column of −100J (proleptic Julian) or −100 (proleptic Gregorian), at the row 76.

{|class="wikitable" style="margin:1em auto;text-align:center"
|+ '''Frequency of Gregorian Doomsday in the 400-year cycle per weekday and year type'''
|-
! !!scope="col"|Sunday!!scope="col"|Monday!!scope="col"|Tuesday!!scope="col"|Wednesday!!scope="col"|Thursday!!scope="col"|Friday!!scope="col"|Saturday
!!scope="col"|Total
|-
!scope="row" style="text-align:left"|Non-leap years
| 43 || 43 || 43 || 43 || 44 || 43 || 44 || '''303'''
|-
!scope="row" style="text-align:left"|Leap years
| 13 || 15 || 13 || 15 || 13 || 14 || 14 || '''97'''
|-style="font-weight:bold"
!scope="row" style="text-align:left"|Total
| 56 || 58 || 56 || 58 || 57 || 57 || 58 || '''400'''
|}

A leap year with Monday as doomsday means that Sunday is one of 97 days skipped in the 400-year sequence. Thus the total number of years with Sunday as doomsday is 71 minus the number of leap years with Monday as doomsday, etc. Since Monday as doomsday is skipped across February 29, 2000, and the pattern of leap days is symmetric about that leap day, the frequencies of doomsdays per weekday (adding common and leap years) are symmetric about Monday. The frequencies of doomsdays of leap years per weekday are symmetric about the doomsday of 2000, Tuesday.

The frequency of a particular date being on a particular weekday can easily be derived from the above (for a date from January 1 – February 28, relate it to the doomsday of the previous year).

For example, February 28 is one day after doomsday of the previous year, so it is 58 times each on Tuesday, Thursday and Sunday, etc. February 29 is doomsday of a leap year, so it is 15 times each on Monday and Wednesday, etc.

===28-year cycle===
Regarding the frequency of doomsdays in a Julian 28-year cycle, there are 1 leap year and 3 common years for every weekday, the latter 6, 17 and 23 years after the former (so with intervals of 6, 11, 6, and 5 years; not evenly distributed because after 12 years the day is skipped in the sequence of doomsdays).{{Citation needed|date=January 2008}} The same cycle applies for any given date from March 1 falling on a particular weekday.

For any given date up to February 28 falling on a particular weekday, the 3 common years are 5, 11, and 22 years after the leap year, so with intervals of 5, 6, 11, and 6 years. Thus the cycle is the same, but with the 5-year interval after instead of before the leap year.

Thus, for any date except February 29, the intervals between common years falling on a particular weekday are 6, 11, 11. See e.g. at the bottom of the page [[Common year starting on Monday]] the years in the range 1906–2091.

For February 29 falling on a particular weekday, there is just one in every 28 years, and it is of course a leap year.

===Julian calendar===
The [[Gregorian calendar]] is currently accurately lining up with astronomical events such as [[solstices]]. In 1582 this modification of the [[Julian calendar]] was first instituted. In order to correct for calendar drift, 10 days were skipped, so doomsday moved back 10 days (i.e. 3 weekdays): Thursday, October 4 (Julian, doomsday is Wednesday) was followed by Friday, October 15 (Gregorian, doomsday is Sunday). The table includes Julian calendar years, but the algorithm is for the Gregorian and proleptic Gregorian calendar only.

Note that the Gregorian calendar was not adopted simultaneously in all countries, so for many centuries, different regions used different dates for the same day.
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