0
No.
Let the four numbers be (n-1), n, (n+1), (n+2).
Their sum is 4n + 2 = 2(2n + 1)
If 2000 is the sum of four consecutive integers, then:
2(2n+1) = 2000
⇒ 2n + 1 = 1000
⇒ 2n = 999
but 999 is odd, not even and so n cannot be an integer; therefore 2000 is not the sum of four consecutive integers.
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