A change of thinking

Calculus Level 5

\[\displaystyle \left\lceil \sum _{ n=1 }^{ \infty }{ \left( \sum _{ p=2 }^{ x }{ \dfrac { 1000 }{ { n }^{ p } } } \right) } \right\rceil =1000x\]

Find the smallest positive integer value of \(x\) which satisfies the given equation.


(This problem is original.)
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