For a composite positive integer $x$, denote by $pd(x)$ the smallest positive difference between any two prime divisors of $x.$ Find the smallest possible value of $pd(x)$ for composite $x$ of the form $x=n^{100}+n^{99}+\cdots+n+1,$ where $n$ is a positive integer.

**Details and assumptions**

You may refer to a list of primes.

For example, since $429 = 3 \times 11 \times 13$, $pd(429) = | 13 - 11 | = 2$.

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