This is a proposal for a replacement to the traditional Gregorian calendar, which was adopted by Western cultures in 1582 to replace the Julian calendar from Roman times. I submit this proposal for feedback, suggestions, and inquiry into prior proposals of a similar or identical nature.

Below is a reproduction of https://github.com/rickhull/compsci/blob/master/RationalPrimeCalendar.md

Rational Prime Calendar

A rational basis for a calendar upon 61 day periods

The Gregorian calendar is a 400-year-old hack job. February's weird. July-August breaks the pattern, and no one can remember which months have 31 days. But there's a better way, hidden in prime factorization.

Considerations

Solar day (roughly 24 hours for the earth to rotate)
Solar year (365.2425 solar days for the earth to orbit the sun)
Lunar cycle (29.53 days for 8 distinct moon phases, roughly 12x annually)

It's impossible to coordinate or synchronize these 3 cycles perfectly. But we can devise a system to accommodate them and minimize tradeoffs. We also want to consider historical calendars, particularly the current Gregorian calendar and less so the prior Julian calendar.

Approach

If a solar year is considered to be 366 days, this factors to 61 * 3 * 2, which naturally suggests (6) 61-day periods, or alternately (61) 6-day periods. Perhaps we should have 6 day weeks, but that will be for another proposal.

We can split each 61-day period into alternating months of 30 and 31 days, in either order. This provides some alignment with the lunar cycle as well as traditional calendars.

The Prime Insight

61 is prime; indivisible, mathematically fundamental
Each of 6 periods of 61 days can be split into pairs of months, 30 + 31
12 months matches the lunar cycle of roughly 30 days
12 months allows clean divisibility by 4 (seasons, business quarters)
12 months matches tradition
Resist entropy: a regular pattern of pairs in a predictable order

Leap Year

We can retain the Gregorian approach to leap years, which solves the problem of accounting for the remaining 0.2425 days in a solar year as years go by. We'll pick one month out of twelve that will have an extra day roughly every 4 years. If 366 days is our starting basis, then the leap month will have a one-day deficit in most years.

Specifics

For explication, a leap year is considered the base case, and a "normal year" is handled specially, in some sense, ...

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