For primes $a$, $b$, and $c$ that satisfy the following conditions, calculate $abc$:

1. $b + 8$ is a multiple of $a$.
2. $b^2 - 1$ is a multiple of both $a$ and $c$.
3. $b + c = a^2 - 1$.

Let's think step by step and output the final answer within \boxed{}.
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