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365,242 or 365,243 depending upon what particular day you start counting.

365 x 1000 = 365,000, but you need to add extra days for the leap days:

25 leap days will occur during centuries whose final year is evenly divisible by 400 (e.g. 1901-2000 had 25 leap days); otherwise 24 leap days will occur (e.g.1801-1900 had 24 leap days).

Therefore 10 centuries will include 8 or 7 centuries with 24 leap days and 2 or 3 centuries with 25 leap days respectively.

24 x 8 + 25 x 2 = 242 and so 365,000 + 242 = 365,242, or

24 x 7 + 25 x 3 = 243 and so 365,000 + 243 = 365,243

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