Common year starting on Friday

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. 2021, the current year, is a common year starting on a Friday in the Gregorian calendar. The last such year was 2010 and the next such year will be 2027 in the Gregorian calendar,[1] or, likewise, 2005, 2011 and 2022 in the obsolete Julian calendar. The century year, 2100, will also be a common year starting on Friday in the Gregorian calendar. See below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; the only Friday the 13th in this common year occurs in August. Leap years starting on Thursday share this characteristic, but also have another one in February. In this common year, February is rectangular in ISO 8601 calendar, U.S. Independence Day and Halloween are on a Sunday, Thanksgiving Day is on November 25, and Christmas is on a Saturday. However, 1582 was not included because the Gregorian calendar was introduced on October 15 of that year. This is one of the three possible common years in which an end of century year can begin on, the most recent being 1700 and the next one being 2100.

Calendars

Calendar for any common year starting on Friday,
presented as common in many English-speaking areas

ISO 8601-conformant calendar with week numbers for
any common year starting on Friday (dominical letter C)

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	January
53					01	02	03
01	04	05	06	07	08	09	10
02	11	12	13	14	15	16	17
03	18	19	20	21	22	23	24
04	25	26	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	February
05	01	02	03	04	05	06	07
06	08	09	10	11	12	13	14
07	15	16	17	18	19	20	21
08	22	23	24	25	26	27	28

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	March
09	01	02	03	04	05	06	07
10	08	09	10	11	12	13	14
11	15	16	17	18	19	20	21
12	22	23	24	25	26	27	28
13	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	April
13				01	02	03	04
14	05	06	07	08	09	10	11
15	12	13	14	15	16	17	18
16	19	20	21	22	23	24	25
17	26	27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	May
17						01	02
18	03	04	05	06	07	08	09
19	10	11	12	13	14	15	16
20	17	18	19	20	21	22	23
21	24	25	26	27	28	29	30
22	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	June
22		01	02	03	04	05	06
23	07	08	09	10	11	12	13
24	14	15	16	17	18	19	20
25	21	22	23	24	25	26	27
26	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	July
26				01	02	03	04
27	05	06	07	08	09	10	11
28	12	13	14	15	16	17	18
29	19	20	21	22	23	24	25
30	26	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	August
30							01
31	02	03	04	05	06	07	08
32	09	10	11	12	13	14	15
33	16	17	18	19	20	21	22
34	23	24	25	26	27	28	29
35	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	September
35			01	02	03	04	05
36	06	07	08	09	10	11	12
37	13	14	15	16	17	18	19
38	20	21	22	23	24	25	26
39	27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	October
39					01	02	03
40	04	05	06	07	08	09	10
41	11	12	13	14	15	16	17
42	18	19	20	21	22	23	24
43	25	26	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	November
44	01	02	03	04	05	06	07
45	08	09	10	11	12	13	14
46	15	16	17	18	19	20	21
47	22	23	24	25	26	27	28
48	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	December
48			01	02	03	04	05
49	06	07	08	09	10	11	12
50	13	14	15	16	17	18	19
51	20	21	22	23	24	25	26
52	27	28	29	30	31

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 does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Friday[1]
Decade	1st	2nd		3rd		4th	5th		6th	7th	8th		9th	10th
16th century	prior to first adoption (proleptic)													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

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). A leap year has two adjoining dominical letters (one for January and February and the other for March to December, as 29 February has no letter). 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
Decade	1st		2nd		3rd		4th		5th		6th		7th		8th		9th		10th
15th century	1406		1417		1423		1434		1445		1451		1462		1473	1479	1490		—
16th century	1501	1507	1518		1529		1535		1546		1557		1563		1574	1585		1591		—
17th century	1602		1613	1619	1630		—		1641	1647	1658		1669		1675		1686		1697
18th century	1703		1714		1725		1731		1742		1753	1759	1770		—		1781	1787	1798
19th century	1809		1815		1826		1837		1843		1854		1865		1871		1882		1893	1899
20th century	1910		—		1921	1927	1938		1949		1955		1966		1977		1983		1994
21st century	2005		2011		2022		2033	2039	2050		—		2061	2067	2078		2089		2095

References

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

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

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