A millennium is by definition "a period of 1000 years." The 3rd Millennium starts January 1st, year 2001 NOT year 2000 as many people believe, when using the Gregorian calendar. The reason why the 3rd Millennium / 21st Century starts in 2001 is because there was no year 0 (or AD 0, 0 BC). The year before 1 A.D. is defined as year 1 B.C., so year 0 was skipped. Because one Millennium is 1000 years, the first Millennium ends with year 1000. The next (2nd) Millennium starts 1000 years after the first, that is in year 1+1000 = 1001. And the 3rd one starts 1000 years later than the 2nd: 1001+1000 = 2001. The same procedure could be followed for centuries.