Common year starting on Thursday

Encyclopedia

A common year starting on Thursday is any non-leap year (i.e. a year with 365 days) 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, 2010 and 2021 in the obsolete Julian calendar, see below for more. This is the only common year with three occurrences of Friday the 13th; specifically, the months of February, March, and November. Leap years starting on Sunday share this characteristic and with the exception of skipped leap years, a leap year that begins on a Sunday falls exactly three years either side of two consecutive common years starting on Thursday – for example 2012 between 2009 and 2015.

From February until March in this type of year is also the shortest period (one month) that runs between two instances of Friday the 13th. In 2015, for example, the three Friday the 13ths of that year occurred in February, March and November. In this common year, February is rectangular in calendar where week starts on Sunday, U.S. Independence Day and Halloween are on a Saturday, Memorial Day is on its earliest possible date, May 25, Labor Day is on its latest possible date, September 7, Thanksgiving is on November 26, and Christmas is on a Friday. This common year is also the only one where Memorial Day and Labor Day are not 14 weeks (98 days) apart: they are 15 weeks (105 days) apart in this common year. Leap years starting on Wednesday share this characteristic.

Calendars

Calendar for any common year starting on Thursday,
presented as common in many English-speaking areas
January
Su Mo Tu We Th Fr Sa
1 2 3
4 5 6 7 8 9 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
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
March
Su Mo Tu We Th Fr Sa
1 2 3 4 5 6 7
8 9 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
1 2 3 4
5 6 7 8 9 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
1 2
3 4 5 6 7 8 9
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
1 2 3 4 5 6
7 8 9 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
1 2 3 4
5 6 7 8 9 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
1
2 3 4 5 6 7 8
9 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
1 2 3 4 5
6 7 8 9 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
1 2 3
4 5 6 7 8 9 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
1 2 3 4 5 6 7
8 9 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
1 2 3 4 5
6 7 8 9 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 common year starting on Thursday (dominical letter D)
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
March
Wk Mo Tu We Th Fr Sa Su
09 01
10 02 03 04 05 06 07 08
11 09 10 11 12 13 14 15
12 16 17 18 19 20 21 22
13 23 24 25 26 27 28 29
14 30 31
April
Wk Mo Tu We Th Fr Sa Su
14 01 02 03 04 05
15 06 07 08 09 10 11 12
16 13 14 15 16 17 18 19
17 20 21 22 23 24 25 26
18 27 28 29 30
May
Wk Mo Tu We Th Fr Sa Su
18 01 02 03
19 04 05 06 07 08 09 10
20 11 12 13 14 15 16 17
21 18 19 20 21 22 23 24
22 25 26 27 28 29 30 31
June
Wk Mo Tu We Th Fr Sa Su
23 01 02 03 04 05 06 07
24 08 09 10 11 12 13 14
25 15 16 17 18 19 20 21
26 22 23 24 25 26 27 28
27 29 30
July
Wk Mo Tu We Th Fr Sa Su
27 01 02 03 04 05
28 06 07 08 09 10 11 12
29 13 14 15 16 17 18 19
30 20 21 22 23 24 25 26
31 27 28 29 30 31
August
Wk Mo Tu We Th Fr Sa Su
31 01 02
32 03 04 05 06 07 08 09
33 10 11 12 13 14 15 16
34 17 18 19 20 21 22 23
35 24 25 26 27 28 29 30
36 31
September
Wk Mo Tu We Th Fr Sa Su
36 01 02 03 04 05 06
37 07 08 09 10 11 12 13
38 14 15 16 17 18 19 20
39 21 22 23 24 25 26 27
40 28 29 30
October
Wk Mo Tu We Th Fr Sa Su
40 01 02 03 04
41 05 06 07 08 09 10 11
42 12 13 14 15 16 17 18
43 19 20 21 22 23 24 25
44 26 27 28 29 30 31
November
Wk Mo Tu We Th Fr Sa Su
44 01
45 02 03 04 05 06 07 08
46 09 10 11 12 13 14 15
47 16 17 18 19 20 21 22
48 23 24 25 26 27 28 29
49 30
December
Wk Mo Tu We Th Fr Sa Su
49 01 02 03 04 05 06
50 07 08 09 10 11 12 13
51 14 15 16 17 18 19 20
52 21 22 23 24 25 26 27
53 28 29 30 31

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, alongside Tuesday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-four common years per cycle or exactly 11% start on a Thursday. The 28-year sub-cycle only spans across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Thursday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
16th century prior to first adoption (proleptic) 1587 1598
17th century 1609 1615 1626 1637 1643 1654 1665 1671 1682 1693 1699
18th century 1705 1711 1722 1733 1739 1750 — 1761 1767 1778 1789 1795
19th century 1801 1807 1818 1829 1835 1846 1857 1863 1874 1885 1891
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
22nd century 2105 2111 2122 2133 2139 2150 — 2161 2167 2178 2189 2195

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 3, 14 and 20 of the cycle are common years beginning on Thursday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Thursday.

Julian common years starting on Thursday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1405 1411 1422 1433 1439 1450 — 1461 1467 1478 1489 1495
16th century 1506 1517 1523 1534 1545 1551 1562 1573 1579 1590 —
17th century 1601 1607 1618 1629 1635 1646 1657 1683 1674 1685 1691
18th century 1702 1713 1719 1730 — 1741 1747 1758 1769 1775 1786 1797
19th century 1803 1814 1825 1831 1842 1853 1859 1870 — 1881 1887 1898
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

References

Gregorian year types per leap cycle by Dominical letter (DL) and Doomsday (DD)
Year starts Common years Leap years
1 Jan Count Ratio 31 Dec DL DD Count Ratio 31 Dec DL DD Count Ratio
Sun 58 14.50 % Sun A Tue 43 10.75 % Mon AG Wed 15 3.75 %
Sat 56 14.00 % Sat B Mon 43 10.75 % Sun BA Tue 13 3.25 %
Fri 58 14.50 % Fri C Sun 43 10.75 % Sat CB Mon 15 3.75 %
Thu 57 14.25 % Thu D Sat 44 11.00 % Fri DC Sun 13 3.25 %
Wed 57 14.25 % Wed E Fri 43 10.75 % Thu ED Sat 14 3.50 %
Tue 58 14.50 % Tue F Thu 44 11.00 % Wed FE Fri 14 3.50 %
Mon 56 14.00 % Mon G Wed 43 10.75 % Tue GF Thu 13 3.25 %
∑ 400 100.0 % 303 75.75 % 97 24.25 %
  1. ^ Jump up to:a b 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.