Leap year starting on Thursday

A leap year starting on Thursday is any year with 366 days (i.e. it includes 29 February) that begins on Thursday 1 January, and ends on Friday 31 December. Its dominical letters hence are DC. The most recent year of such kind was 2004 and the next one will be 2032 in the Gregorian calendar[1] or, likewise, 2016 and 2044 in the obsolete Julian calendar.

Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths: those two in this leap year occur in February and August.

Calendars

Calendar for any leap year starting on Thursday,
presented as common in many English-speaking areas
January
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
February
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
29  
 
March
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
April
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
May
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
June
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
27282930  
 
July
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
August
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
September
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
2627282930  
 
October
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
November
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
282930  
 
December
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 
ISO 8601-conformant calendar with week numbers for
any leap year starting on Thursday (dominical letter DC)
January
Wk Mo Tu We Th Fr Sa Su
01 01020304
02 05060708091011
03 12131415161718
04 19202122232425
05 262728293031  
   
February
Wk Mo Tu We Th Fr Sa Su
05 01
06 02030405060708
07 09101112131415
08 16171819202122
09 23242526272829
   
March
Wk Mo Tu We Th Fr Sa Su
10 01020304050607
11 08091011121314
12 15161718192021
13 22232425262728
14 293031  
   
April
Wk Mo Tu We Th Fr Sa Su
14 01020304
15 05060708091011
16 12131415161718
17 19202122232425
18 2627282930  
   
May
Wk Mo Tu We Th Fr Sa Su
18 0102
19 03040506070809
20 10111213141516
21 17181920212223
22 24252627282930
23 31  
June
Wk Mo Tu We Th Fr Sa Su
23 010203040506
24 07080910111213
25 14151617181920
26 21222324252627
27 282930  
   
July
Wk Mo Tu We Th Fr Sa Su
27 01020304
28 05060708091011
29 12131415161718
30 19202122232425
31 262728293031  
   
August
Wk Mo Tu We Th Fr Sa Su
31 01
32 02030405060708
33 09101112131415
34 16171819202122
35 23242526272829
36 3031  
September
Wk Mo Tu We Th Fr Sa Su
36 0102030405
37 06070809101112
38 13141516171819
39 20212223242526
40 27282930  
   
October
Wk Mo Tu We Th Fr Sa Su
40 010203
41 04050607080910
42 11121314151617
43 18192021222324
44 25262728293031
   
November
Wk Mo Tu We Th Fr Sa Su
45 01020304050607
46 08091011121314
47 15161718192021
48 22232425262728
49 2930  
   
December
Wk Mo Tu We Th Fr Sa Su
49 0102030405
50 06070809101112
51 13141516171819
52 20212223242526
53 2728293031  
   

Applicable years

Gregorian Calendar

Leap years that begin on Thursday, along with those that start on Monday or Saturday, occur least frequently: 13 out of 97 (≈ 13.402%) total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is 3.25% (13 out of 400).

For this kind of year, the corresponding ISO year has 53 weeks, and the ISO week 10 (which begins March 1) and all subsequent ISO weeks occur earlier than in all other years, and exactly one week earlier than common years starting on Friday, for example, June 20 falls on week 24 in common years starting on Friday, but on week 25 in leap years starting on Thursday, despite falling on Sunday in both types of year. That means that moveable holidays may occur one calendar week later than otherwise possible, e.g. Gregorian Easter Sunday in week 17 in years when it falls on April 25 and which are also leap years, falling on week 16 in common years.[2]

Gregorian leap years starting on Thursday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
17th century 1604163216601688
18th century 172817561784
19th century 182418521880
20th century 192019481976
21st century 2004203220602088
22nd century 212821562184
23rd century 222422522280
24th century 232023482376
25th century 2404243224602488
26th century 252825562584
27th century 262426522680

400 year cycle

century 1: 4, 32, 60, 88

century 2: 128, 156, 184

century 3: 224, 252, 280

century 4: 320, 348, 376

Julian Calendar

Like all leap year types, the one starting with 1 January on a Thursday occurs exactly once in a 28-year cycle in the Julian calendar, i.e. in 3.57% of years. As the Julian calendar repeats after 28 years that means it will also repeat after 700 years, i.e. 25 cycles. The year's position in the cycle is given by the formula ((year + 8) mod 28) + 1).

Julian leap years starting on Thursday
Decade 1st2nd3rd4th5th6th7th8th9th10th
15th century 142814561484
16th century 1512154015681596
17th century 162416521680
18th century 1708173617641792
19th century 182018481876
20th century 1904193219601988
21st century 2016204420722100
22nd century 212821562184

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States


References

  1. Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
  2. Leap years when Easter Sunday falls on April 25 are only possible years when Easter Sunday can fall on week 17.
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