# 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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