The katun of 7,200 days, twenty tuns or a little under twenty years, outlived the Long Count itself. After the Classic collapse the full five-place notation fell out of use in the northern lowlands, and what remained in the Postclassic and colonial period was the Short Count, a cycle of thirteen katuns named by the Tzolk'in day on which each ended.
Because a katun of 7,200 days is a multiple of twenty, it always ends on a day Ahau, and because thirteen numbers run against that fixed sign, thirteen katuns exhaust the possibilities before repeating. Thirteen katuns are 260 tuns, roughly 256 years, and the resulting cycle carries the same thirteen-by-twenty shape as the Tzolk'in in a different medium.
The Books of Chilam Balam, written in Yucatec Maya in the European alphabet after the conquest, record history and prophecy by katun in exactly this form, each katun carrying an expected character. The Short Count is genuinely shorter and genuinely ambiguous: a date given only by its katun repeats every 256 years, which is one of the standing difficulties in using those books as chronology.
The Short Count also explains a persistent confusion. A modern account that speaks of a thirteen-katun prophetic cycle is describing the Postclassic and colonial Yucatec system, not the Classic Long Count, and the two run on different principles: one repeats, the other does not. Conflating them produces claims about Classic Maya prophecy that the Classic sources do not contain.