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These two methods start producing different dates after about year 3515.



That's interesting. I'm not sure of the significance of that year or how that relates to the algorithm in Meeus' book. This web page talks about the date algorithms in Meeus' book in some detail but the math is beyond me - http://mysite.verizon.net/aesir_research/date/jdimp.htm. The Julian day conversion algorithm here is the same one used by SQLite.




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