Bipartite primes

Let \(p(n)\) denote binary representation of natural number \(n\).For example, \(p(7)=111\).

Let \(A(n) = (p(n+p(n))-n)\) for natural number \(n\).

For how many integers between \({3,10000}\) (both inclusive) is \(A(n)\) a positive prime number.

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