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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