# Huge powers

First two consecutive prime numbers greater than $$10^7$$ are $$p_{1} = 10000019$$ and $$p_{2} = 10000079$$ respectively. Let $$p$$ be the smallest prime factor of $$S = p_{1}^2 + p_{2}^2-5$$. Also, let $$q$$ be the units digit of $$S$$. What is the value of $$p+q$$?

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