Common year starting on Saturday explained

A common year starting on Saturday is any non-leap year (i.e. a year with 365 days) that begins on Saturday, 1 January, and ends on Saturday, 31 December. Its dominical letter hence is B. The most recent year of such kind was 2022 and the next one will be 2033 in the Gregorian calendar[1] or, likewise, 2023 and 2034 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 one in this common year occurs in May.

From July of the year that precedes this year until September in this type of year is the longest period (14 months) that occurs without a Tuesday the 13th.

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, alongside Sunday, Monday, Wednesday or Friday, 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 Saturday. The 28-year sub-cycle will break at a century year which is not divisible by 400 (e.g. it broke at the year 1900 but not at the year 2000).

!colspan=2
1st !2nd 3rd 4th 5th 6th 7th 8th 9th 10th
16th centuryprior to first adoption (proleptic) 1594
17th century1695
18th century1791
19th century- 1898
20th century1994
21st century2095
2191
- 2298
24th century2394
25th century2495
400-year cycle
0–995 11 22 33 39 50 61 67 78 89 95
100–199101 107 118 129 135 146 157 163 174 185 191
200–299203 214 225 231 242 253 259 270 281 287 298
300–399310 321 327 338 349 355 366 377 383 394

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 in the Church of England, as 29 February has no letter). Each of the seven two-letter sequences occurs 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 10, 16 and 27 of the cycle are common years beginning on Saturday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Saturday.

Decade!colspan=2
1st !2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century1491
16th century1575 <-- Wikipedia year articles refer to Gregorian years from 1582 --> 1586 1597
17th century1603 1614 1625 1631 1642 1653 1659 1670 1681 1687 1698
18th century1709 1715 1726 1737 1743 1754 1765 1771 1782 1793 1799
19th century1810 1821 1827 1838 1849 colapan21855 1866 1877 1883 1894
20th century1905 1911 1922 1933 1939 1950 1961 1967 1978 1989 1995
21st century2006 2017 2023 2034 2045 2051 2062 2073 2079 2090

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.