Common Year Starting On Thursday
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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.

Calendars

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


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

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, alongside with 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 does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.

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 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

  1. ^ a b c Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 2017.

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