Common Year Starting On Saturday - Wikipedia

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Gregorian Calendar

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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).

Gregorian common years starting on Saturday
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
16th century prior to first adoption (proleptic) 1583 1594
17th century 1605 1611 1622 1633 1639 1650 — 1661 1667 1678 1689 1695
18th century 1701 1707 1718 1729 1735 1746 1757 1763 1774 1785 1791
19th century 1803 1814 1825 1831 1842 1853 1859 - 1870 1881 1898
20th century — 1910 1921 1927 1938 1949 1955 1966 1977 1983 1994
21st century 2005 2011 2022 2033 2039 2050 — 2061 2067 2078 2089 2095
22nd century 2101 2107 2118 2129 2135 2146 2157 2163 2174 2185 2191
23rd century 2203 2214 2225 2231 2242 2253 2259 - 2270 2281 2298
24th century — 2310 2321 2327 2338 2349 2355 2366 2377 2383 2394
25th century 2405 2411 2422 2433 2439 2450 — 2461 2467 2478 2489 2495
400-year cycle
0–99 5 11 22 33 39 50 61 67 78 89 95
100–199 101 107 118 129 135 146 157 163 174 185 191
200–299 203 214 225 231 242 253 259 270 281 287 298
300–399 310 321 327 338 349 355 366 377 383 394

Julian Calendar

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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 starting on Saturday.

Julian common years starting on Saturday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1401 1407 1418 1429 1435 1446 1457 1463 1474 1485 1491
16th century 1502 1513 1519 1530 — 1541 1547 1558 1569 1575 1586 1597
17th century 1603 1614 1625 1631 1642 1653 1659 1670 — 1681 1687 1698
18th century 1709 1715 1726 1737 1743 1754 1765 1771 1782 1793 1799
19th century 1810 — 1821 1827 1838 1849 1855 1866 1877 1883 1894
20th century 1905 1911 1922 1933 1939 1950 — 1961 1967 1978 1989 1995
21st century 2006 2017 2023 2034 2045 2051 2062 2073 2079 2090 —

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