Indicator sequence/Prime numbers/Exercise

Let the sequence ${}{\left(x_{n}\right)}_{n\in \mathbb {N} }$ be given by

${}x_{n}={\begin{cases}1,\,{\text{ falls }}n{\text{ is a prime number }}\,,\\0\,{\text{ else}}\,.\end{cases}}\,$

1. Determine ${}x_{117}$ and ${}x_{127}$.
2. Does this sequence converge in ${}\mathbb {Q}$?

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