the 10 days of October 5-14, in 1582, never existed

"implementing the new [Gregorian] calendar came in October 1582, when 10 days were dropped from the calendar to bring the vernal equinox from March 11 back to March 21. The church had chosen October to avoid skipping any major Christian festivals. So, in countries that adopted the new calendar, the Feast of St. Francis of Assisi on October 4, 1582, was directly followed by October 15."

• https://www.britannica.com/story/ten-days-that-vanished-the-switch-to-the-gregorian-calendar
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Ten Days That Vanished: The Switch to the Gregorian Calendar | Britannica

When it comes to calendars, small errors can add up over time.

Encyclopedia Britannica