# Testing primality for large numbers

The number $$121$$ is composite.
The number $$1211$$ is composite.
The number $$12111$$ is composite.
The number $$121111$$ is composite.

Let $$n$$ be the smallest positive integer such that $$12\underbrace{11...11}_{n \text{ times}}$$ is prime.

Find $$n$$.

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