Leap year starting on Thursday

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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.

Contents

This is the only year in which February has five Sundays, as the leap day adds that extra Sunday.

This is the only leap year with three occurrences of Tuesday the 13th: those three in this leap year occur three months (13 weeks) apart: in January, April, and July. Common years starting on Monday share this characteristic, in the months of February, March, and November.

Along with it's common year counterpart, the gap between July of this year until the next common year (14 months) is the longest time between Tuesday the 13th's, so from July of this year until September of the next year, as in 2004-05 or 2032-33 for example. This also applies for common years starting on Friday, unless the next leap year falls on a Saturday, in this case, the gap is reduced to only 11 months, as in 2027-28 for example.

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.

If this year occurs, the leap day falls on a Sunday (similar to its common year equivalent), transitioning it from what it would appear to be a common year starting on Thursday to the next common year after the previous one, so March 1 would start on a Monday, like it would be on its common year equivalent (March to December of this type of year aligns with the common year equivalent, that should've happened 5 years earlier in order for this type of leap year to start due to the cyclical nature of the calendar.) The previous leap year would have to have been on a Saturday due to the Gregorian Calendar's cyclical nature.

Calendars

Calendar for any leap year starting on Thursday,
presented as common in many English-speaking areas
January
SuMoTuWeThFrSa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
February
SuMoTuWeThFrSa
01020304050607
08091011121314
15161718192021
22232425262728
29 
 
March
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
28293031 
 
April
SuMoTuWeThFrSa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
May
SuMoTuWeThFrSa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031 
June
SuMoTuWeThFrSa
0102030405
06070809101112
13141516171819
20212223242526
27282930 
 
July
SuMoTuWeThFrSa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
August
SuMoTuWeThFrSa
01020304050607
08091011121314
15161718192021
22232425262728
293031 
 
September
SuMoTuWeThFrSa
01020304
05060708091011
12131415161718
19202122232425
2627282930 
 
October
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 
November
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
282930 
 
December
SuMoTuWeThFrSa
01020304
05060708091011
12131415161718
19202122232425
262728293031 
 
ISO 8601-conformant calendar with week numbers for
any leap year starting on Thursday (dominical letter DC)
January
WkMoTuWeThFrSaSu
0101020304
0205060708091011
0312131415161718
0419202122232425
05262728293031 
  
February
WkMoTuWeThFrSaSu
0501
0602030405060708
0709101112131415
0816171819202122
0923242526272829
  
March
WkMoTuWeThFrSaSu
1001020304050607
1108091011121314
1215161718192021
1322232425262728
14293031 
  
April
WkMoTuWeThFrSaSu
1401020304
1505060708091011
1612131415161718
1719202122232425
182627282930 
  
May
WkMoTuWeThFrSaSu
180102
1903040506070809
2010111213141516
2117181920212223
2224252627282930
2331 
June
WkMoTuWeThFrSaSu
23010203040506
2407080910111213
2514151617181920
2621222324252627
27282930 
  
July
WkMoTuWeThFrSaSu
2701020304
2805060708091011
2912131415161718
3019202122232425
31262728293031 
  
August
WkMoTuWeThFrSaSu
3101
3202030405060708
3309101112131415
3416171819202122
3523242526272829
363031 
September
WkMoTuWeThFrSaSu
360102030405
3706070809101112
3813141516171819
3920212223242526
4027282930 
  
October
WkMoTuWeThFrSaSu
40010203
4104050607080910
4211121314151617
4318192021222324
4425262728293031
  
November
WkMoTuWeThFrSaSu
4501020304050607
4608091011121314
4715161718192021
4822232425262728
492930 
  
December
WkMoTuWeThFrSaSu
490102030405
5006070809101112
5113141516171819
5220212223242526
532728293031 
  

Applicable years

Gregorian Calendar

Leap years that begin on Thursday, along with those starting on Monday and 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 thus 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]
Decade1st2nd3rd4th5th6th7th8th9th10th
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 252825562584
27th century 262426522680
400-year cycle
0–994326088
100–199128156184
200–299224252280
300–399320348376

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
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1428 1456 1484
16th century 1512 1540 1568 1596
17th century 1624 1652 1680
18th century1708173617641792
19th century182018481876
20th century1904193219601988
21st century2016204420722100
22nd century212821562184

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States


Related Research Articles

The International Fixed Calendar is a proposed calendar reform designed by Moses B. Cotsworth, first presented in 1902. The International Fixed Calendar divides the year into 13 months of 28 days each. A type of perennial calendar, every date is fixed to the same weekday every year. Though it was never officially adopted at the country level, the entrepreneur George Eastman instituted its use at the Eastman Kodak Company in 1928, where it was used until 1989. While it is sometimes described as the 13-month calendar or the equal-month calendar, various alternative calendar designs share these features.

<span class="mw-page-title-main">Week</span> Time unit equal to seven days

A week is a unit of time equal to seven days. It is the standard time period used for short cycles of days in most parts of the world. The days are often used to indicate common work days and rest days, as well as days of worship. Weeks are often mapped against yearly calendars, but are typically not the basis for them, as weeks are not based on astronomy.

A common year starting on Sunday is any non-leap year that begins on Sunday, 1 January, and ends on Sunday, 31 December. Its dominical letter hence is A. The most recent year of such kind was 2023 and the next one will be 2034 in the Gregorian calendar, or, likewise, 2018 and 2029 in the obsolete Julian calendar, see below for more.

A common year starting on Friday is any non-leap year that begins on Friday, 1 January, and ends on Friday, 31 December. Its dominical letter hence is C. The most recent year of such kind was 2021 and the next one will be 2027 in the Gregorian calendar, or, likewise, 2022 and 2033 in the obsolete Julian calendar, see below for more. This common year is one of the three possible common years in which a century year can begin on, and occurs in century years that yield a remainder of 100 when divided by 400. The most recent such year was 1700 and the next one will be 2100.

A common year starting on Monday is any non-leap year that begins on Monday, 1 January, and ends on Monday, 31 December. Its dominical letter hence is G. The most recent year of such kind was 2018 and the next one will be 2029 in the Gregorian calendar, or likewise, 2019 and 2030 in the Julian calendar, see below for more. This common year is one of the three possible common years in which a century year can begin on and occurs in century years that yield a remainder of 300 when divided by 400. The most recent such year was 1900 and the next one will be 2300.

Dominical letters or Sunday letters are a method used to determine the day of the week for particular dates. When using this method, each year is assigned a letter depending on which day of the week the year starts. The Dominical letter for the current year 2024 is GF.

A leap year starting on Sunday is any year with 366 days that begins on Sunday, 1 January, and ends on Monday, 31 December. Its dominical letters hence are AG. The most recent year of such kind was 2012 and the next one will be 2040 in the Gregorian calendar or, likewise 2024 and 2052 in the obsolete Julian calendar.

A common year starting on Tuesday is any non-leap year that begins on Tuesday, 1 January, and ends on Tuesday, 31 December. Its dominical letter hence is F. The most recent year of such kind was 2019 and the next one will be 2030, or, likewise, 2014 and 2025 in the obsolete Julian calendar, see below for more.

A leap year starting on Monday is any year with 366 days that begins on Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letters hence are GF. The current year, 2024, is a leap year starting on Monday in the Gregorian calendar. The last such year was 1996 and the next such year will be 2052 in the Gregorian calendar or, likewise, 2008 and 2036 in the obsolete Julian calendar. 29 February falls on Thursday.

A common year starting on Wednesday is any non-leap year that begins on Wednesday, 1 January, and ends on Wednesday, 31 December. Its dominical letter hence is E. The most recent year of such kind was 2014, and the next one will be 2025 in the Gregorian calendar or, likewise, 2015 and 2026 in the obsolete Julian calendar, see below for more. This common year is one of the three possible common years in which a century year can begin on, and occurs in century years that yield a remainder of 200 when divided by 400. The most recent such year was 1800 and the next one will be 2200.

A leap year starting on Tuesday is any year with 366 days that begins on Tuesday, 1 January, and ends on Wednesday, 31 December. Its dominical letters hence are FE. The most recent year of such kind was 2008 and the next one will be 2036 in the Gregorian calendar or, likewise 2020 and 2048 in the obsolete Julian calendar.

A common year starting on Saturday is any non-leap year that begins on Saturday, 1 January, and ends on Saturday, 31 December. Its dominical letter hence is B. The most recent year of such kind was 2022 and the next one will be 2033 in the Gregorian calendar or, likewise, 2023 and 2034 in the obsolete Julian calendar. See below for more.

A common year starting on Thursday is any non-leap year that begins on Thursday, 1 January, and ends on Thursday, 31 December. Its dominical letter hence is D. The most recent year of such kind was 2015 and the next one will be 2026 in the Gregorian calendar or, likewise, 2021 and 2027 in the obsolete Julian calendar, see below for more.

A leap year starting on Saturday is any year with 366 days that begins on Saturday, 1 January, and ends on Sunday, 31 December. Its dominical letters hence are BA. The most recent year of such kind was 2000 and the next one will be 2028 in the Gregorian calendar or, likewise 2012 and 2040 in the obsolescent Julian calendar. In the Gregorian calendar, years divisible by 400 are always leap years starting on Saturday. The most recent such occurrence was 2000 and the next one will be 2400, see below for more.

A leap year starting on Friday is any year with 366 days that begins on Friday 1 January and ends on Saturday 31 December. Its dominical letters hence are CB. The most recent year of such kind was 2016 and the next one will be 2044 in the Gregorian calendar or, likewise, 2000 and 2028 in the obsolete Julian calendar.

A leap year starting on Wednesday is any year with 366 days that begins on Wednesday 1 January and ends on Thursday 31 December. Its dominical letters hence are ED. The most recent year of such kind was 2020 and the next one will be 2048 in the Gregorian calendar, or likewise, 2004 and 2032 in the obsolete Julian calendar, see below for more.

The determination of the day of the week for any date may be performed with a variety of algorithms. In addition, perpetual calendars require no calculation by the user, and are essentially lookup tables. A typical application is to calculate the day of the week on which someone was born or a specific event occurred.

The ISO week date system is effectively a leap week calendar system that is part of the ISO 8601 date and time standard issued by the International Organization for Standardization (ISO) since 1988 and, before that, it was defined in ISO (R) 2015 since 1971. It is used (mainly) in government and business for fiscal years, as well as in timekeeping. This was previously known as "Industrial date coding". The system specifies a week year atop the Gregorian calendar by defining a notation for ordinal weeks of the year.

The Hanke–Henry Permanent Calendar (HHPC) is a proposal for calendar reform. It is one of many examples of leap week calendars, calendars that maintain synchronization with the solar year by intercalating entire weeks rather than single days. It is a modification of a previous proposal, Common-Civil-Calendar-and-Time (CCC&T). With the Hanke–Henry Permanent Calendar, every calendar date always falls on the same day of the week. A major feature of the calendar system is the abolition of time zones.

References

  1. 1 2 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.