# Triple Primes.

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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