Let $x$ be a number such that for $n \gt x$, the $n$th Fibonacci number has at least one prime divisor that does not divide any $k$th Fibonacci number for all $k \lt n$. Find the sum of all primes $p \lt 10^x$ such that for some integer $n$, the expression $n^2 - p \times n$ is a prime power.

Note: A prime power is a number of the form $q^m$ where $q$ is a prime and $m$ is a positive integer.