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The origin of the seven-day week is the religious significance that was placed on the seventh day by ancient cultures, including the Babylonian and Jewish civilizations. Babylonians celebrated a holy day every seven days, starting from the new moon, then the first visible crescent of the Moon, but adjusted the number of days of the final "week" in each month so that months would continue to commence on the new moon. (The seven-day week is only 23.7% of a lunation, so a continuous cycle of seven-day weeks rapidly loses synchronization with the lunation.) Jews celebrated every seventh day, within a continuous cycle of seven-day weeks, as a holy day of rest from their work, in remembrance of Creation week. The Zoroastrian calendar follows the Babylonian in relating the seventh and other days of the month to Ahura Mazda. The earliest ancient sources record a seven-day week in ancient Babylon prior to 600 BCE. 
The seven-day week being approximately a quarter of a lunation has been proposed (e.g. by Friedrich Delitzsch) as the implicit, astronomical origin of the seven-day week. Problems with the proposal include lack of synchronization, variation in individual lunar phase lengths, and incompatibility with the duodecimal (base-12) and sexagesimal (base-60) numeral systems, historically the primary bases of other chronological and calendar units. For instance, the Chinese Han Dynasty (from 206 BCE) used five-day and ten-day cycles.
Counting from the new moon, the Babylonians celebrated the 7th, 14th, 21st, and 28th as "holy-days", also called "evil days" (meaning "unsuitable" for prohibited activities). On these days officials were prohibited from various activities and common men were forbidden to "make a wish", and at least the 28th was known as a "rest-day". On each of them, offerings were made to a different god and goddess. Tablets from the 6th-century BCE reigns of Cyrus the Great and Cambyses indicate these dates were sometimes approximate. The lunation of 29 or 30 days basically contained three seven-day weeks, and a final week of eight or nine days inclusive, breaking the continuous seven-day cycle. The Babylonians additionally celebrated the 19th as a special "evil day", the "day of anger", because it was roughly the 49th day of the (preceding) month, completing a "week of weeks", also with sacrifices and prohibitions. Difficulties with Friedrich Delitzsch's origin theory connecting Hebrew Shabbat with the Babylonian lunar cycle include reconciling the differences between an unbroken week and a lunar week, and explaining the absence of texts naming the lunar week as Shabbat in any language. Reconstruction of a broken tablet seems to define the rarely attested Babylonian Akkadian word Sapattum or Sabattum as the full moon: this word is cognate or merged with Hebrew Shabbat, but is monthly rather than weekly. It is regarded as a form of Sumerian sa-bat ("mid-rest"), attested in Akkadian as um nuh libbi ("day of mid-repose"). This conclusion is a contextual restoration of the damaged Enûma Eliš creation account, which is read as: "[Sa]bbath shalt thou then encounter, mid[month]ly".
The seven-day week is uniquely identified with Judaism: it appears in the Creation account in the Book of Genesis, in the Hebrew Bible, where Elohim (God) creates the heavens and the earth in six days and rests on the seventh (Genesis 1:1-2:3). In the Book of Exodus, the fourth of the Ten Commandments is to rest on the seventh day (Shabbat), which can be seen as implying a socially instituted seven-day week. Most who observe Biblical Sabbath affirm it as having been instituted as a perpetual covenant for the people of Israel (Exodus 31:13-17), a sign respecting two events: the day during which God rested after having completed the Creation in six days (Exodus 20:8-11), and God's deliverance from the Egyptian seven-day workweek (Deuteronomy 5:12-15). By synecdoche (naming a part for the whole), in Jewish sources by the time of the Septuagint, the term "Sabbath" (Greek Sabbaton) also came to mean an entire "se'nnight" or seven-day week, the interval between two weekly Sabbaths. Jesus's parable of the Pharisee and the Publican (Luke 18:12) describes the Pharisee as fasting "twice in the week" (Greek dis tou sabbatou).
Frank C. Senn in his book Christian Liturgy: Catholic and Evangelical points to data suggesting evidence of an early continuous use of a seven-day week; referring to the Jews during the Babylonian Captivity in the 6th century BCE, after the destruction of the Temple of Solomon. The ancient Romans traditionally used the eight-day nundinal cycle, but after the adoption of the Julian calendar, in the time of Augustus, the seven-day week came into use. For a while, the week and the nundinal cycle coexisted, but by the time the week was officially adopted by Constantine in CE 321 the nundinal cycle had fallen out of use. The association of the days of the week with the Sun, the Moon, and the five planets visible to the naked eye dates to the Roman era (2nd century).
The seven-day weekly cycle has remained unbroken in Europe for almost two millennia, despite changes to the Alexandrian, Julian, and Gregorian calendars, demonstrated by the date of Easter Sunday having been traced back through numerous computistic tables to an Ethiopic copy of an early Alexandrian table beginning with the Easter of 311 AD.
"The Roman context of the spread of Christianity meant that Rome contributed a lot to the structure and calendar of the new faith." 
The earliest known reference in Chinese writings to a seven-day week is attributed to Fan Ning, who lived in the late 4th century in the Jin Dynasty, while diffusions from the Manichaeans are documented with the writings of the Chinese Buddhist monk Yi Jing and the Ceylonese or Central Asian Buddhist monk Bu Kong of the 7th century (Tang Dynasty).
The Chinese transliteration of the planetary system was soon brought to Japan by the Japanese monk Kobo Daishi. Surviving diaries of the Japanese statesman Fujiwara Michinaga show the seven-day system in use in Heian Japan as early as 1007. In Japan, the seven-day system was kept in use for astrological purposes until its promotion to a full-fledged Western-style calendrical basis during the Meiji era.
France discontinued the seven-day week for a ten-day week with the introduction of the republican calendar in 1793. The Concordat of 1801, which re-established the Roman Catholic Church in France, also restored the seven-day week, beginning with Easter Sunday, 18 April 1802.
In 1929, the USSR discontinued the seven-day week for a five-day week, then a six-day week. While the days were still named according to the seven-day week, the work schedules were rotated in five- and six-day periods. The seven-day week was reintroduced on 27 June 1940.
Weeks in a Gregorian calendar year can be numbered for each year. This style of numbering is commonly used (for example, by schools and businesses) in some European and Asian countries, but rare elsewhere.
ISO 8601 includes the ISO week date system, a numbering system for weeks – each week begins on a Monday and is associated with the year that contains that week's Thursday (so that if a year starts in a long weekend Friday–Sunday, week number one of the year will start after that). For example, week 1 of 2004 (2004W01) ran from Monday 29 December 2003 to Sunday, 4 January 2004, because its Thursday was 1 January 2004, whereas week 1 of 2005 (2005W01) ran from Monday 3 January 2005 to Sunday 9 January 2005, because its Thursday was 6 January 2005 and so the first Thursday of 2005. The highest week number in a year is either 52 or 53 (it was 53 in the year 2004). Schematically, this ISO convention translates as follows:
|Dates in January||Effect|
|M||T||W||T||F||S||S||Week number||Week assigned to|
|1||2||53 or 52||Previous year|
|System||First day of week||First week of year contains||Can also be last week of previous year||Used by/in|
|ISO-8601||Monday||4 January||1st Thursday||4–7 days of year||no||EU and most of other European countries|
|(Islamic)||Saturday||1 January||1st Friday||1–7 days of year||yes||Much of the Middle East|
|(North American)||Sunday||1 January||1st Saturday||1–7 days of year||yes||Canada, USA, Mexico|
In a Gregorian mean year there are 365.2425 days, and thus exactly 52 71⁄400 or 52.1775 weeks (unlike the Julian year of 365.25 days or 52 5⁄28 ≈ 52.1786 weeks, which cannot be represented by a finite decimal expansion). There are exactly 20871 weeks in 400 Gregorian years, so 30 April 1611 was a Saturday just like 30 April 2011.