Common year starting on Thursday explained

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, 2021 and 2027 in the obsolete Julian calendar, see below for more.

This is the only common year with three occurrences of Friday the 13th: those three in this common year occur in February, March, and November. Leap years starting on Sunday share this characteristic, for the months January, April and July. 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. Additionally, this is the one of only two types of years overall where a rectangular February is possible, in places where Sunday is considered to be the first day of the week. Common years starting on Friday share this characteristic, but only in places where Monday is considered to be the first day of the week.

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.

This type of year has 53 weeks in the week-day format of the ISO 8601 standard.

Decade!colspan=2
1st !2nd 3rd 4th 5th 6th 7th 8th 9th 10th
16th centuryprior to first adoption (proleptic) 1598
17th century1699
18th century1795
19th century1891
20th century1998
21st century2099
22nd century2195
2291
2398
25th century2499
400-year cycle
0–999 15 26 37 43 54 65 71 82 93 99
100–199105 111 122 133 139 150 161 167 178 189 195
200–299201 207 218 229 235 246 257 263 274 285 291
300–399303 314 325 331 342 353 359 370 381 387 398

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!colspan=2
1st !2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century1495
16th century1579 <-- Wikipedia year articles refer to Gregorian years from 1582 --> 1590
17th century1601 1607 1618 1629 1635 1646 1657 1683 1674 1685 1691
18th century1702 1713 1719 1730 1741 1747 1758 1769 1775 1786 1797
19th century1803 1814 1825 1831 1842 1853 1859 1870 1881 1887 1898
20th century1909 1915 1926 1937 1943 1954 1965 1971 1982 1993 1999
21st century2010 2021 2027 2038 2049 2055 2066 2077 2083 2094

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States

Notes and References

  1. Web site: The Mathematics of the ISO 8601 Calendar . Robert van Gent . Utrecht University, Department of Mathematics . 2017 . 20 July 2017.