# Prime Time

Let $$P$$ and $$Q$$ be positive primes such that $\large 2^{P - 1} + 5PQ = Q^2 + 4P^2 + 7$ If the ordered pairs satisfying the equation are $$(P_1, Q_1)$$, $$(P_2, Q_2)$$, $$(P_3, Q_3)$$, $$\cdots$$ $$(P_n, Q_n)$$ for some positive integer $$n$$, find the value of $$\displaystyle \sum_{k = 1}^{n} (P_k + Q_k)$$.

This problem is part of the set "Symphony"

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