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, 1988, 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.

In this leap year, Martin Luther King Jr. Day is on January 19, Valentine's Day is on a Saturday, Presidents' Day is on February 16, the leap day is on a Sunday, Saint Patrick’s Day is on a Wednesday, Memorial Day is on its latest possible date, May 31, Juneteenth is on a Saturday, U.S. Independence Day and Halloween are on a Sunday, Labor Day is on September 6, Columbus Day is on October 11, Election Day in the United States is on its earliest possible date, November 2nd, Thanksgiving is on November 25, and Christmas is on a Saturday.

CalendarsEdit

Calendar for any leap year starting on Thursday,
presented as common in many English-speaking areas
January
Su Mo Tu We Th Fr Sa
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30 31
 
February
Su Mo Tu We Th Fr Sa
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29  
 
March
Su Mo Tu We Th Fr Sa
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31  
 
April
Su Mo Tu We Th Fr Sa
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30
 
May
Su Mo Tu We Th Fr Sa
01
02 03 04 05 06 07 08
09 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31  
June
Su Mo Tu We Th Fr Sa
01 02 03 04 05
06 07 08 09 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30  
 
July
Su Mo Tu We Th Fr Sa
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30 31
 
August
Su Mo Tu We Th Fr Sa
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31  
 
September
Su Mo Tu We Th Fr Sa
01 02 03 04
05 06 07 08 09 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30  
 
October
Su Mo Tu We Th Fr Sa
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31  
November
Su Mo Tu We Th Fr Sa
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30  
 
December
Su Mo Tu We Th Fr Sa
01 02 03 04
05 06 07 08 09 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30 31  
 
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 01 02 03 04
02 05 06 07 08 09 10 11
03 12 13 14 15 16 17 18
04 19 20 21 22 23 24 25
05 26 27 28 29 30 31  
   
February
Wk Mo Tu We Th Fr Sa Su
05 01
06 02 03 04 05 06 07 08
07 09 10 11 12 13 14 15
08 16 17 18 19 20 21 22
09 23 24 25 26 27 28 29
   
March
Wk Mo Tu We Th Fr Sa Su
10 01 02 03 04 05 06 07
11 08 09 10 11 12 13 14
12 15 16 17 18 19 20 21
13 22 23 24 25 26 27 28
14 29 30 31  
   
April
Wk Mo Tu We Th Fr Sa Su
14 01 02 03 04
15 05 06 07 08 09 10 11
16 12 13 14 15 16 17 18
17 19 20 21 22 23 24 25
18 26 27 28 29 30  
   
May
Wk Mo Tu We Th Fr Sa Su
18 01 02
19 03 04 05 06 07 08 09
20 10 11 12 13 14 15 16
21 17 18 19 20 21 22 23
22 24 25 26 27 28 29 30
23 31  
June
Wk Mo Tu We Th Fr Sa Su
23 01 02 03 04 05 06
24 07 08 09 10 11 12 13
25 14 15 16 17 18 19 20
26 21 22 23 24 25 26 27
27 28 29 30  
   
July
Wk Mo Tu We Th Fr Sa Su
27 01 02 03 04
28 05 06 07 08 09 10 11
29 12 13 14 15 16 17 18
30 19 20 21 22 23 24 25
31 26 27 28 29 30 31  
   
August
Wk Mo Tu We Th Fr Sa Su
31 01
32 02 03 04 05 06 07 08
33 09 10 11 12 13 14 15
34 16 17 18 19 20 21 22
35 23 24 25 26 27 28 29
36 30 31  
September
Wk Mo Tu We Th Fr Sa Su
36 01 02 03 04 05
37 06 07 08 09 10 11 12
38 13 14 15 16 17 18 19
39 20 21 22 23 24 25 26
40 27 28 29 30  
   
October
Wk Mo Tu We Th Fr Sa Su
40 01 02 03
41 04 05 06 07 08 09 10
42 11 12 13 14 15 16 17
43 18 19 20 21 22 23 24
44 25 26 27 28 29 30 31
   
November
Wk Mo Tu We Th Fr Sa Su
45 01 02 03 04 05 06 07
46 08 09 10 11 12 13 14
47 15 16 17 18 19 20 21
48 22 23 24 25 26 27 28
49 29 30  
   
December
Wk Mo Tu We Th Fr Sa Su
49 01 02 03 04 05
50 06 07 08 09 10 11 12
51 13 14 15 16 17 18 19
52 20 21 22 23 24 25 26
53 27 28 29 30 31  
   

Applicable yearsEdit

Gregorian CalendarEdit

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 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
17th century 1604 1632 1660 1688
18th century 1728 1756 1784
19th century 1824 1852 1880
20th century 1920 1948 1976
21st century 2004 2032 2060 2088
22nd century 2128 2156 2184
23rd century 2224 2252 2280
24th century 2320 2348 2376
25th century 2404 2432 2460 2488
26th century 2528 2556 2584
27th century 2624 2652 2680

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 CalendarEdit

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 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1428 1456 1484
16th century 1512 1540 1568 1596
17th century 1624 1652 1680
18th century 1708 1736 1764 1792
19th century 1820 1848 1876
20th century 1904 1932 1960 1988
21st century 2016 2044 2072 2100
22nd century 2128 2156 2184

ReferencesEdit

  1. ^ a b 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.