Good question.  

I don't really know.  The first stage would be to see what those numbers might correspond to in the sky.  Generally, I have been looking at much shorter time-frames.  

The longest cycle I have encountered so far is (one fifth of) 25 800 years (the cycle of precession of the equinoxes) and at this point I can not really justify this--because I do not have an explanation for the one fifth.  And the longest cycle that I have come across that is sure is a 112-year eclipse cycle (actually 1385  months) in an account of the markings on a brass bowl recovered from Arabia and dating from Mohammedian times or possibly earlier (brass is hard to date).  The 56-year cycle of the Dragon against the year can be confidently adduced to the ring of hollow stones at Stonehenge.  This is not an eclipse cycle, but is instead relevant to the elevation of the Moon's path in the sky.  

The Fates are kind.