I know that after 100 years there are centennial celebrations, after 200 years bicentennial, tricentennial, etc.,
Similarly, are there terms for 2000, 3000, etc., years of celebration?
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Sure. Picking up where you left off, we have:
Anything beyond bimillenial is probably very uncommon at best, but you could likely follow the above naming convention and be understood. See more odd usages here.
For a thousand years, the word is millennial. For two thousand years, the word is bimillennial. See this Wikipedia article on anniversary names. I would imagine the same pattern goes for the higher thousands, e.g. trimillennial, quadrimillennial, and so forth.