Common year starting on Thursday
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[1] or, likewise, 2010 and 2021 in the obsolete Julian calendar, see below for more. This common year contains the most Friday the 13ths; specifically, the months of February, March, and November. Leap years starting on Sunday share this characteristic.
From February until March in this type of year is also the shortest period (one month) that occurs within a Friday the 13th.
Contents
1 Calendars
2 Applicable years
2.1 Gregorian Calendar
2.2 Julian Calendar
3 References
Calendars
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Applicable years
Gregorian Calendar
In the (currently used) Gregorian calendar, 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 does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.
| 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 | |||||
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.
| 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 | 1663 | 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
| 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 | 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 % | ||||||||
^ abc Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"""""""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
