Prime Divisors Positive Difference

Number Theory Level 5

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