1300 + ~700 = ~2000. Uh oh."
The astronomers in some of these linked articles say that the next best chance for a (somewhat predictable) comet swarm is about the year 3,000.
So it averaged 600-700 years 4 times in a row but it's going to take a 2500 year break between 500 A.D. and 3000 A.D.?