As was pointed out to me (thanks, Flonne!), Tiny Empires 3000 has send the end of its first millenium. As its clock ticked over from December, 3999, it went back to January, 3000. This puts the cyclical time at 1,000 years-- 36,000 minutes -- 600 hours -- 25 days -- or about 3 and a half weeks. A bit longer, probably, since a 3 minute year tends to slide a bit long due to processing lag.