Let the start of the epoch be floor(exp(365.2425/2)) days before January 1, 2000. This date in the extreme long past causes all prime days to currently occur with average spacing about half a year. If a calendar year has multiple prime days, choose the first one as the Ancient Prime Day for the year. (The average spacing of half a year was chosen to decrease the likelihood of two Ancient Prime Days occurring very close to each other around a New Year.) If a year has no prime days, repeat the date of the last year that had a prime day, unless that year had multiple prime days, then use the next unused date, cycling through multiple times if necessary.
This is another idea for Modern computus.
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