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Why was a week set at 7 days?

Base data: time. 1 week = 7 days = 604,800 sec.

There are various other possible origins apart from the Bible

The seven-day week is often said to emanate from the Bible. There is also a story that the ancient Babylonians thought of dividing periods into durations of seven days due to the waxing and waning of the moon. There is another story that it was because the number of planets known in the solar system at that time, apart from the earth, was seven.