Ten days in October 1582 simply never happened
The Julian calendar had drifted ten days out of step with the seasons, so Pope Gregory XIII's reform deleted them outright: Thursday 4 October 1582 was followed by Friday 15 October. Catholic countries switched immediately; Britain held out until 1752, by which point it had to skip eleven days, and Russia didn't convert until 1918.
— Wikipedia contributors, Gregorian calendar — Introduced 1582