Powerful Prime Numbers

Number Theory Level pending

Let \(M\) be a \(2015 \times 2015\) matrix with elements defined as

\(M_{p,q} = 2^{(p+1)\times(q+1)}-1\), where \(p,q\) are integers with \(0<p,q \leq 2015\).

How many elements of \(M\) are prime.

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