Common year starting on Friday

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A common year starting on Friday is any non-leap year (i.e. a year with 365 days) 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, [1] 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.

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Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th: the only one in this common year occurs in August. Leap years starting on Thursday share this characteristic, but also have another one in February.

From July of the year that precedes this year (as well as Leap years starting on Wednesday) until September in this type of year is the longest period (14 months) that occurs without a Friday the 17th, like recently 2020. Leap years starting on Tuesday share this characteristic, from August of the common year that precedes it to October in that type of year, like in 2007 and 2008. This type of year also has the longest period (also 14 months) without a Tuesday the 13th, from July of this year until September of the next common year (that being on Saturday), the most recent of this being 2021 and 2022, unless the next year is a leap year (which is also a Saturday), so years like 2028, then the period is reduced to only 11 months.

Leap years starting on Thursday also share this exact criteria. Common years starting on Tuesday also share this characteristic, from August from that year until October of the leap year that succeeds the common year (Leap years starting on Wednesday in this case)

This is the one of two types of years overall where a rectangular February is possible, in places where Monday is considered to be the first day of the week. Common years starting on Thursday share this characteristic, but only in places where Sunday is considered to be the first day of the week.

Additionally, this type of year has three months (February, March and November) beginning exactly on the first day of the week, in areas which Monday is considered the first day of the week. Leap years starting on Monday share this characteristic on the months of January, April and July.

Calendars

Calendar for any common year starting on Friday,
presented as common in many English-speaking areas
January
SuMoTuWeThFrSa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31 
February
SuMoTuWeThFrSa
010203040506
07080910111213
14151617181920
21222324252627
28 
 
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 common year starting on Friday (dominical letter C)
January
WkMoTuWeThFrSaSu
53010203
0104050607080910
0211121314151617
0318192021222324
0425262728293031
  
February
WkMoTuWeThFrSaSu
0501020304050607
0608091011121314
0715161718192021
0822232425262728
 
  
March
WkMoTuWeThFrSaSu
0901020304050607
1008091011121314
1115161718192021
1222232425262728
13293031 
  
April
WkMoTuWeThFrSaSu
1301020304
1405060708091011
1512131415161718
1619202122232425
172627282930 
  
May
WkMoTuWeThFrSaSu
170102
1803040506070809
1910111213141516
2017181920212223
2124252627282930
2231 
June
WkMoTuWeThFrSaSu
22010203040506
2307080910111213
2414151617181920
2521222324252627
26282930 
  
July
WkMoTuWeThFrSaSu
2601020304
2705060708091011
2812131415161718
2919202122232425
30262728293031 
  
August
WkMoTuWeThFrSaSu
3001
3102030405060708
3209101112131415
3316171819202122
3423242526272829
353031 
September
WkMoTuWeThFrSaSu
350102030405
3606070809101112
3713141516171819
3820212223242526
3927282930 
  
October
WkMoTuWeThFrSaSu
39010203
4004050607080910
4111121314151617
4218192021222324
4325262728293031
  
November
WkMoTuWeThFrSaSu
4401020304050607
4508091011121314
4615161718192021
4722232425262728
482930 
  
December
WkMoTuWeThFrSaSu
480102030405
4906070809101112
5013141516171819
5120212223242526
522728293031 
  

This is the only year type where the nth "Doomsday" (this year Sunday) is not in ISO week n; it is in ISO week n-1.

Applicable years

Gregorian calendar

In the (currently used) Gregorian calendar, alongside Sunday, Monday, Wednesday or Saturday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-three common years per cycle or exactly 10.75% start on a Friday. The 28-year sub-cycle only spans across century years divisible by 400, e.g. 1600, 2000, and 2400.

For this kind of year, the ISO week 10 (which begins March 8) and all subsequent ISO weeks occur later than in all other years, and exactly one week later than Leap years starting on Thursday. Also, the ISO weeks in January and February occur later than all other common years, but leap years starting on Friday share this characteristic in January and February, until ISO week 8.

Gregorian common years starting on Friday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic) 1582 1593 1599
17th century 1610 1621 1627 1638 1649 1655 1666 1677 1683 1694 1700
18th century 1706 1717 1723 1734 1745 1751 1762 1773 1779 1790
19th century 1802 1813 1819 1830 1841 1847 1858 1869 1875 1886 1897
20th century 1909 1915 1926 1937 1943 1954 1965 1971 1982 1993 1999
21st century 2010 2021 2027 2038 2049 2055 2066 2077 2083 2094 2100
22nd century 2106 2117 2123 2134 2145 2151 2162 2173 2179 2190
23rd century 2202 2213 2219 2230 2241 2247 2258 2269 2275 2286 2297
24th century 2309 2315 2326 2337 2343 2354 2365 2371 2382 2393 2399
400-year cycle
0–9910212738495566778394
100–199100106117123134145151162173179190
200–299202213219230241247258269275286297
300–399309315326337343354365371382393399

Julian calendar

In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks). This sequence occurs exactly once within a cycle, and every common letter thrice.

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). Years 4, 15 and 26 of the cycle are common years beginning on Friday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Friday.

Julian common years starting on Friday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century 1406 1417 1423 1434 1445 1451 1462 1473 1479 1490
16th century 1501 1507 1518 1529 1535 1546 1557 1563 1574 15851591
17th century16021613161916301641164716581669167516861697
18th century17031714172517311742175317591770178117871798
19th century18091815182618371843185418651871188218931899
20th century1910192119271938194919551966197719831994
21st century20052011202220332039205020612067207820892095

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States

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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 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.

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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.

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References

  1. 1 2 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.