Common year starting on Wednesday

A common year starting on Wednesday is any non-leap year (a year with 365 days) that begins on Wednesday, 1 January, and ends on Wednesday, 31 December.^{[citation needed]} 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^[1] or, likewise, 2009, 2015 and 2026 in the obsolete Julian 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 June. Leap years starting on Tuesday share this characteristic. 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. In this common year, Martin Luther King Jr. Day is on January 20, Valentine's Day is on a Friday, President's Day is on February 17, Saint Patrick's Day is on Monday, Memorial day is on May 26, U.S. Independence Day is on a Friday, Labor Day is on its earliest possible date, September 1, Columbus Day is on October 13, Halloween is on a Friday, Veterans Day is on a Tuesday, Thanksgiving is on November 27, and Christmas is on a Thursday. This is the only type of year in which all dates fall on their respective weekdays 57 times in the 400 year Gregorian Calendar cycle.

Calendars[edit]

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

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

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

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

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

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

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

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

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

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

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	September
36	01	02	03	04	05	06	07
37	08	09	10	11	12	13	14
38	15	16	17	18	19	20	21
39	22	23	24	25	26	27	28
40	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	October
40			01	02	03	04	05
41	06	07	08	09	10	11	12
42	13	14	15	16	17	18	19
43	20	21	22	23	24	25	26
44	27	28	29	30	31

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

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

Applicable years[edit]

Gregorian Calendar[edit]

In the (currently used) Gregorian calendar, alongside Sunday, Monday, Friday 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 Wednesday. The 28-year sub-cycle only spans across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Wednesday^[1]
Decade	1st	2nd		3rd		4th	5th		6th		7th	8th		9th		10th
16th century	prior to first adoption (proleptic)													1586		1597
17th century	1603	1614		1625		1631	1642		1653	1659	1670	—		1681	1687	1698
18th century	1710	—		1721	1727	1738	1749		1755		1766	1777		1783		1794	1800
19th century	1806	1817		1823		1834	1845		1851		1862	1873	1879	1890		—
20th century	1902	1913	1919	1930		—	1941	1947	1958		1969	1975		1986		1997
21st century	2003	2014		2025		2031	2042		2053	2059	2070	—		2081	2087	2098
22nd century	2110	—		2121	2127	2138	2149		2155		2166	2177		2183		2194	2200
23rd century	2206	2217		2223		2234	2245		2251		2262	2273	2279	2290		—
24th century	2302	2313	2319	2330		—	2341	2347	2358		2369	2375		2386		2397

Julian Calendar[edit]

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 2, 8 and 19 of the cycle are common years beginning on Wednesday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Wednesday.

Julian common years starting on Wednesday
Decade	1st		2nd		3rd		4th		5th		6th		7th		8th		9th		10th
15th century	1410		—		1421	1427	1438		1449		1455		1466		1477		1483		1494
16th century	1505		1511		1522		1533	1539	1550		—		1561	1567	1578		1589		1595
17th century	1606		1617		1623		1634		1645		1651		1662		1673	1679	1690		—
18th century	1701	1707	1718		1729		1735		1746		1757		1763		1774		1785		1791
19th century	1802		1813	1819	1830		—		1841	1847	1858		1869		1875		1886		1897
20th century	1903		1914		1925		1931		1942		1953	1959	1970		—		1981	1987	1998
21st century	2009		2015		2026		2037		2043		2054		2065		2071		2082		2093	2099

References[edit]

Gregorian year types per leap cycle by Dominical letter (DL)^[2] and Doomsday (DD)
1 Jan	Count	Ratio	31 Dec	DL	DD	Count	Ratio	31 Dec	DL	DD	Count	Ratio
Year starts			Common years					Leap years
Sun	58	14.50 %	Sun	A	Tue	43	10.75 %	Mon	AG	Wed	15	03.75 %
Sat	56	14.00 %	Sat	B	Mon	43	10.75 %	Sun	BA	Tue	13	03.25 %
Fri	58	14.50 %	Fri	C	Sun	43	10.75 %	Sat	CB	Mon	15	03.75 %
Thu	57	14.25 %	Thu	D	Sat	44	11.00 %	Fri	DC	Sun	13	03.25 %
Wed	57	14.25 %	Wed	E	Fri	43	10.75 %	Thu	ED	Sat	14	03.50 %
Tue	58	14.50 %	Tue	F	Thu	44	11.00 %	Wed	FE	Fri	14	03.50 %
Mon	56	14.00 %	Mon	G	Wed	43	10.75 %	Tue	GF	Thu	13	03.25 %
∑	400	100.0 %				303	75.75 %				97	24.25 %

^ a b Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017. CS1 maint: discouraged parameter (link)
^ Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.

[math-1] Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017. CS1 maint: discouraged parameter (link)

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

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