Let \(n <11\) be a positive integer, and \(p_{1}, p_{2}, p_{3}, p\) are prime numbers such that \(p_{1} + p_{3}^{n}\) is prime.

If \(p_{1} +p_{2} = 3p, p_{2} + p_{3} =(p_{1}^{n})(p_{1} +p_{3})\) and \(p_{2} >9\) , then determine \(p_{1}p_{2}p_{3}^{n}\).

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