# Three twin primes

We define a twin prime as a pair of prime numbers whose absolute difference is precisely 2.

Let $$p,q$$ and $$r$$ be odd prime numbers such that $$p,q$$ are twin primes and $$r$$ is a twin prime with some prime.

Given that $$\dfrac{p^2+q}2 = r$$ and $$p<r-p< q < r < p^2$$, find the product $$pqr$$.

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