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Proleptic Gregorian calendar
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The proleptic Gregorian calendar is produced by extending the Gregorian calendar to dates preceding its official introduction in 1582. It has been defined in the international standard ISO 8601.
Most Maya scholars use the proleptic Gregorian calendar, especially when converting Long Count dates (first century BC to tenth century). It is also explicitly required for all dates before 1582 by ISO 8601:2004 (4.3.2.1), if the partners to information exchange agree. However, neither astronomers nor non-Maya historians generally use it.
For these calendars we can distinguish two systems of numbering years BC. Bede and later historians did not use the Latin zero, nulla, as a year, so the year preceding AD 1 is 1 BC. In this system the year 1 BC is a leap year (likewise in the proleptic Julian calendar). Mathematically, it is more convenient to include a year zero and represent earlier years as negative, for the specific purpose of facilitating the calculation of leap years BC. This is the convention used in astronomical year numbering and in the international standard date system, ISO 8601. In these systems, the year 0 is a leap year.
Note that the Julian calendar was in actual use from AD 1 until 1582 or later (see From Julian to Gregorian), so historians and astronomers prefer to use the actual Julian calendar during that period. Likewise, the proleptic Julian calendar is used to specify dates before AD 1, the first common year that did not follow a quadrennial leap year (leap years between 45 BC and 1 BC were irregular, see Leap year error). But when seasonal dates are important, the proleptic Gregorian calendar is sometimes used, especially when discussing cultures that did not use the Julian calendar.
The proleptic Gregorian calendar is sometimes used in computer software to simplify the handling of older dates. For example, it is the calendar used by MySQL [1] and by CIM.
Difference between Julian and proleptic Gregorian calendar dates
Before the introduction of the Gregorian calendar, the difference between Julian and proleptic Gregorian calendar dates were as follows:
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