Under the Gregorian calendar, what days can never be Easter?

Obviously, October 31 can't be Easter any year whatsoever. Indeed no day in October can be Easter. But can February 28 be Easter? What about February 29? May 1? Is there a single consecutive range of days that can't be Easter, like say for example April 17 wrapping around past December to January and over to March 12?

Bonus question: using the Julian calendar as it was observed in Russia until 1918, does the answer to this question change merely by a simple transposition?

• Commented Apr 6, 2015 at 0:17
• @Lucian Do you have a more reliable source than that? Even if those Wikipedia articles are technically correct, the writing looks awful. Commented Apr 7, 2015 at 2:44
• Since the Julian calendar shifts with respect to the mean tropical year (hence with respect to the equinoctes) by one day every 128 years, there is no day in the Julian calendar that isn't eventually an Easter. Commented Jul 14, 2015 at 23:53
• @Eric Yes, of course, which is why I wrote "as it was observed in Russia until 1918." I can't promise you David's bounty, but I do hope someone comes along to give a better answer so that Dave doesn't have to reluctantly let the system auto-award it to the reluctant mathematician. Commented Jul 15, 2015 at 0:41

Easter is defined (on the Gregorian calendar) as "the first Sunday following the first full moon after the spring equinox". The spring equinox ranges from Mar 20-21. The lunar cycle is 29.53 days. The dominical ranges from 1-7. Thus, Easter will be no later than Apr 25. The earliest is Mar 22.

• So then each day between March 22 and April 25 (inclusive) will be Easter at least once within the next four centuries? Commented Apr 7, 2015 at 2:41
• This calculation will work most of the time. In some religions, observers watch for the full moon and then name the date. Their full moon can be different from the astronomical full moon. (human error?) Commented Jul 11, 2015 at 21:28
• The Catholic Church computes Easter using the ecclesiastical full moon, a straightforward (though somewhat verbose) formula that obviates any need for observation or for detailed computation of when the Moon actually becomes full. Commented Jul 11, 2015 at 22:27
• (loosely stated) the first full moon on or after the vernal equinox; also, if that calculation coincides with Passover, then Easter will be a week later.
– DDS
Commented Jun 28, 2019 at 6:30
• @mlchristians, is there any evidence that Easter is moved when it coincides with Passover? I've seen various calculations for the date of Easter, and can't see any evidence that Passover itself is calculated, let alone that it causes Easter to be moved. Commented Feb 8, 2021 at 14:45

TL;DR: Gregorian Easters (eventually) fall on each date in [22 March, 25 April]. Greek Orthodox (Julian) Easters (eventually) fall on each date in the year, including 29 February.

In the years 1919 through 2285, the following years will be the first occurrence of Easter (Gregorian) for each date:

• 22 March, 2285
• 23 March, 2008
• 24 March, 1940
• 25 March, 1951
• 26 March, 1967
• 27 March, 1921
• 28 March, 1937
• 29 March, 1959
• 30 March, 1975
• 31 March, 1929
• 1 April, 1923
• 2 April, 1961
• 3 April, 1983
• 4 April, 1920
• 5 April, 1931
• 6 April, 1947
• 7 April, 1985
• 8 April, 1928
• 9 April, 1939
• 10 April, 1955
• 11 April, 1971
• 12 April, 1925
• 13 April, 1941
• 14 April, 1963
• 15 April, 1979
• 16 April, 1922
• 17 April, 1927
• 18 April, 1954
• 19 April, 1981
• 20 April, 1919
• 21 April, 1935
• 22 April, 1962
• 23 April, 2000
• 24 April, 2011
• 25 April, 1943

Consequently, every date in the range given by @reluctant mathematician in his answer occurs by 2285.

We could credibly argue whether 22 March will ever actually be a Gregorian Easter since the shortening of times that calendars in use suggests that the Gregorian calendar may be replaced by that time. No other dates are Easters through they year 10000 under the Gregorian Calendar.

Greek Orthodox Easter is celebrated according to the Julian Calendar. (This may or may not be the same calendar as in use in Russia up to 1918, I am unable to get definitive data from the implementation described below.) It takes about 10000 years for this calendar to shift just under three months, so I used the same method but on a time window from 1919 to 50000. This gives the table of all 366 dates (including 29 February in 42460):

• 1 January, 33809
• 2 January, 33972
• 3 January, 33904
• 4 January, 34189
• 5 January, 34341
• 6 January, 34436
• 7 January, 34531
• 8 January, 34626
• 9 January, 34721
• 10 January, 34968
• 11 January, 35063
• 12 January, 35158
• 13 January, 35405
• 14 January, 35500
• 15 January, 35595
• 16 January, 35785
• 17 January, 35937
• 18 January, 36032
• 19 January, 36127
• 20 January, 36222
• 21 January, 36317
• 22 January, 36564
• 23 January, 36659
• 24 January, 36754
• 25 January, 37001
• 26 January, 37096
• 27 January, 37191
• 28 January, 37381
• 29 January, 37533
• 30 January, 37628
• 31 January, 37723
• 1 February, 37818
• 2 February, 37913
• 3 February, 38160
• 4 February, 38255
• 5 February, 38350
• 6 February, 38749
• 7 February, 38692
• 8 February, 38787
• 9 February, 38977
• 10 February, 39129
• 11 February, 39224
• 12 February, 39319
• 13 February, 39414
• 14 February, 39509
• 15 February, 39756
• 16 February, 39851
• 17 February, 39946
• 18 February, 40345
• 19 February, 40288
• 20 February, 40383
• 21 February, 40573
• 22 February, 40725
• 23 February, 40820
• 24 February, 40915
• 25 February, 41010
• 26 February, 41105
• 27 February, 41352
• 28 February, 41447
• 29 February, 42460
• 1 March, 41542
• 2 March, 41884
• 3 March, 42047
• 4 March, 41979
• 5 March, 42169
• 6 March, 42321
• 7 March, 42579
• 8 March, 42511
• 9 March, 42606
• 10 March, 42701
• 11 March, 43100
• 12 March, 43043
• 13 March, 43138
• 14 March, 43480
• 15 March, 43643
• 16 March, 43575
• 17 March, 43765
• 18 March, 43917
• 19 March, 44175
• 20 March, 44107
• 21 March, 44202
• 22 March, 44544
• 23 March, 44859
• 24 March, 44639
• 25 March, 44734
• 26 March, 45076
• 27 March, 45239
• 28 March, 45171
• 29 March, 45361
• 30 March, 45513
• 31 March, 45771
• 1 April, 45703
• 2 April, 45893
• 3 April, 46140
• 4 April, 2010
• 5 April, 1942
• 6 April, 1980
• 7 April, 1991
• 8 April, 1923
• 9 April, 1939
• 10 April, 1966
• 11 April, 1920
• 12 April, 1931
• 13 April, 1947
• 14 April, 1963
• 15 April, 1928
• 16 April, 1922
• 17 April, 1955
• 18 April, 1971
• 19 April, 1925
• 20 April, 1919
• 21 April, 1946
• 22 April, 1979
• 23 April, 1995
• 24 April, 1927
• 25 April, 1943
• 26 April, 1970
• 27 April, 1924
• 28 April, 1935
• 29 April, 1951
• 30 April, 1967
• 1 May, 1921
• 2 May, 1926
• 3 May, 1959
• 4 May, 1975
• 5 May, 1929
• 6 May, 1945
• 7 May, 2051
• 8 May, 1983
• 9 May, 2173
• 10 May, 2268
• 11 May, 2583
• 12 May, 2515
• 13 May, 2610
• 14 May, 2705
• 15 May, 3104
• 16 May, 3047
• 17 May, 3142
• 18 May, 3332
• 19 May, 3647
• 20 May, 3579
• 21 May, 3769
• 22 May, 3864
• 23 May, 4179
• 24 May, 4111
• 25 May, 4206
• 26 May, 4301
• 27 May, 4700
• 28 May, 4643
• 29 May, 4738
• 30 May, 4928
• 31 May, 5243
• 1 June, 5175
• 2 June, 5365
• 3 June, 5460
• 4 June, 5775
• 5 June, 5707
• 6 June, 5802
• 7 June, 5992
• 8 June, 6459
• 9 June, 6239
• 10 June, 6334
• 11 June, 6524
• 12 June, 6839
• 13 June, 6771
• 14 June, 6961
• 15 June, 7056
• 16 June, 7371
• 17 June, 7303
• 18 June, 7493
• 19 June, 7588
• 20 June, 8055
• 21 June, 7835
• 22 June, 7930
• 23 June, 8120
• 24 June, 8435
• 25 June, 8367
• 26 June, 8557
• 27 June, 8652
• 28 June, 8899
• 29 June, 8994
• 30 June, 9089
• 1 July, 9184
• 2 July, 9499
• 3 July, 9431
• 4 July, 9526
• 5 July, 9716
• 6 July, 10031
• 7 July, 9963
• 8 July, 10153
• 9 July, 10248
• 10 July, 10495
• 11 July, 10590
• 12 July, 10685
• 13 July, 10780
• 14 July, 11095
• 15 July, 11027
• 16 July, 11122
• 17 July, 11312
• 18 July, 11627
• 19 July, 11559
• 20 July, 11749
• 21 July, 11844
• 22 July, 12091
• 23 July, 12186
• 24 July, 12281
• 25 July, 12376
• 26 July, 12691
• 27 July, 12623
• 28 July, 12718
• 29 July, 12908
• 30 July, 13223
• 31 July, 13155
• 1 August, 13345
• 2 August, 13440
• 3 August, 13687
• 4 August, 13782
• 5 August, 13877
• 6 August, 13972
• 7 August, 14287
• 8 August, 14219
• 9 August, 14314
• 10 August, 14504
• 11 August, 14819
• 12 August, 14751
• 13 August, 14941
• 14 August, 15036
• 15 August, 15283
• 16 August, 15378
• 17 August, 15473
• 18 August, 15568
• 19 August, 15883
• 20 August, 15815
• 21 August, 15910
• 22 August, 16100
• 23 August, 16415
• 24 August, 16347
• 25 August, 16537
• 26 August, 16632
• 27 August, 16879
• 28 August, 16974
• 29 August, 17069
• 30 August, 17164
• 31 August, 17479
• 1 September, 17411
• 2 September, 17506
• 3 September, 17848
• 4 September, 18011
• 5 September, 17943
• 6 September, 18133
• 7 September, 18228
• 8 September, 18475
• 9 September, 18570
• 10 September, 18665
• 11 September, 18760
• 12 September, 19075
• 13 September, 19007
• 14 September, 19102
• 15 September, 19444
• 16 September, 19607
• 17 September, 19539
• 18 September, 19729
• 19 September, 19824
• 20 September, 20071
• 21 September, 20166
• 22 September, 20261
• 23 September, 20356
• 24 September, 20671
• 25 September, 20603
• 26 September, 20793
• 27 September, 21040
• 28 September, 21203
• 29 September, 21135
• 30 September, 21325
• 1 October, 21420
• 2 October, 21667
• 3 October, 21762
• 4 October, 21857
• 5 October, 21952
• 6 October, 22199
• 7 October, 22294
• 8 October, 22389
• 9 October, 22636
• 10 October, 22799
• 11 October, 22731
• 12 October, 22921
• 13 October, 23016
• 14 October, 23263
• 15 October, 23358
• 16 October, 23453
• 17 October, 23548
• 18 October, 23795
• 19 October, 23890
• 20 October, 23985
• 21 October, 24232
• 22 October, 24395
• 23 October, 24327
• 24 October, 24517
• 25 October, 24612
• 26 October, 24859
• 27 October, 24954
• 28 October, 25049
• 29 October, 25144
• 30 October, 25391
• 31 October, 25486
• 1 November, 25581
• 2 November, 25828
• 3 November, 25991
• 4 November, 25923
• 5 November, 26113
• 6 November, 26208
• 7 November, 26455
• 8 November, 26550
• 9 November, 26645
• 10 November, 26740
• 11 November, 26987
• 12 November, 27082
• 13 November, 27177
• 14 November, 27424
• 15 November, 27587
• 16 November, 27519
• 17 November, 27709
• 18 November, 27804
• 19 November, 28051
• 20 November, 28146
• 21 November, 28241
• 22 November, 28336
• 23 November, 28583
• 24 November, 28678
• 25 November, 28773
• 26 November, 29020
• 27 November, 29183
• 28 November, 29115
• 29 November, 29305
• 30 November, 29400
• 1 December, 29647
• 2 December, 29742
• 3 December, 29837
• 4 December, 29932
• 5 December, 30179
• 6 December, 30274
• 7 December, 30369
• 8 December, 30616
• 9 December, 30779
• 10 December, 30711
• 11 December, 30901
• 12 December, 31148
• 13 December, 31243
• 14 December, 31338
• 15 December, 31433
• 16 December, 31528
• 17 December, 31775
• 18 December, 31870
• 19 December, 31965
• 20 December, 32212
• 21 December, 32375
• 22 December, 32307
• 23 December, 32592
• 24 December, 32744
• 25 December, 32839
• 26 December, 32934
• 27 December, 33029
• 28 December, 33124
• 29 December, 33371
• 30 December, 33466
• 31 December, 33561

It is of course exceedingly unlikely that any calendrical system, even the Julian system, will remain in use until 46140, the first (Gregorian) year Easter will fall on (Gregorian) 3 April.

Appendix

I used the Mathematica functions EasterSunday[] and EasterSundayGreekOrthodox[]. As of Version 10, these functions were crippled by Wolfram. Mathematica documentation claims "As of Version 10.0, calendar functionality is built into the Wolfram Language". However, there is no equivalent facility, nor is there documentation of a workaround. I have consequently used https://mathematica.stackexchange.com/questions/75281/eastersunday-replacement-in-mathematica-10 to workaround Wolfram's stupidity.

The Greek Orthodox version of the above was created using

dates = DataPacletsCalendarDataDumpEasterSundayGreekOrthodox /@ Range[1919, 50000]
days = Sort[DeleteDuplicates[dates[[All, {2, 3}]]]]
findDates[day_] := Select[dates, #[[2]] == day[[1]] && #[[3]] == day[[2]] &][[1]]
result = findDates /@ days)
Length[result]
Max[result[[All, 1]]]
months = {"January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"}
StringJoin @@ (" * " <> ToString[#[[3]]] <> " " <> months[[#[[2]]]] <> ", " <> ToString[#[[1]]] <> "\n" &) /@ result

• Side question: if humans are still living on this planet in 2285, what sort of calendar do you think they'll be using? Stardates? Or just some tweaks on the Gregorian calendar just major enough to be considered different from Gregorian? Commented Jul 15, 2015 at 21:11
• @DavidR. : We could just keep using Gregorian to 2285, but it seems likely that something will change. Perhaps the fallout of global water warfare will return us to "Year 10 of Thog's rule" calendars. Optimistically, I like to imagine at some point the economic costs of civil time and astronomical calendars will drive the move to atomic timekeeping, eschewing of timezones, and some sort of uniformization of the calendar (i.e. all units a fixed multiple of other units). Commented Jul 15, 2015 at 22:31