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A Long Count is simply an expression of a total number of days elapsed since a given epoch. As they appear in the literature, Long Count dates are written left-to-right, in order of decreasing unit size, with units separated by periods.
As an example, the Long Count written as 9.16.5.0.0 represents a total of 1,413,000 days (9144000 + 167200 + 5360 + 020 + 01).
One occasionally encounters inscriptions in which larger units are written. The Maya apparently conceived of the Long Count as a kind of odometer in which all units were initially set to 13. The ball court at Koba bears a date in which the Long Count portion is written as 13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.0.0.0.0. Recording dates in this format allowed the Maya to claim understanding of, and therefore intellectual control over, very large spans of time and thereby helped legitimize the dynastic claims of the rulers.
The Long Count can be used like a linear day count from an epoch, but it should be remembered that it, too, is a cyclic count. What appears to be a straight line is actually a circle of very large radius.
These three elements are combined to create a complete date. The combination is done in two steps. First, the tzolkin and haab are combined to create a date in the Calendar Round. The prime factors of 365 are (1, 5, 73) and of 260 are (1, 22, 5, 13). The least common multiple is therefore (221373 =) 18,980, which is the number of days in one Calendar Round. This period of time is equivalent to 52 vague years. Each day in this cycle is designated by a combination of tzolkin and haab date. Each such day had certain characteristics and divinatory attributes.
Second, a Long Count number is expressed as the number of days since a certain epoch was counted. The epoch used for virtually all Maya dates is a date expressed as 4 Ahau 8 Cumhu in the Calendar Round and which corresponds to a Western date of 11 August 3114 B.C. (Gregorian).
A complete Maya date, then, is a combination of a Long Count number and a Calendar Round date. An example might be a date like 9.11.11.9.17 9 Caban 5 Pop, an actual example from Dos Pilas. Note that if the epoch is known, then the zero point for the Long Count is known, and the Calendar Round date can be reconstructed from the Long Count. The concept behind a complete Maya date is similar to that used for an ISO period, since it involves a starting date (the assumed epoch), a duration (the Long Count), and an ending date (partially expressed by the Calendar Round date).
Virtually all known Maya dates are based on the epoch of 4 Ahau 8 Cumhu. The epoch is not stated, but inferred, from the Long Count and the Calendar Round date. In a few cases, the calculated epoch is not the standard one. There are a few known instances of mistakes among the inscriptions (e.g., two errors appear in the accession date on the Tablet of the Cross at Palenque). Whether the Maya used a different epoch in a few instances or made errors in recording dates in these cases is not known.
The dating system used by the Maya evolved over time. The first dates recorded simply used the tzolkin. The haab was added about 200 years later. Finally, in the Classical Period, the Long Count was added. In the general decline, which occurred

 
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