What is the smallest prime factor of the number
$$N\ :=\ 14^{14^{14}}+13\ ?$$
The number of digits of $N$ is $12,735,782,555,419,983$ (The number of digits of $N$ has itself $17$ digits). The first digits of $N$ are $1698324865652...$ and the last digits are $...6015154651149$
It is hopeless to apply a primilaty test for $N$ because $N$ is far too large. I applied trial division and found no prime factor below $6\times 10^9$.
I do not think that there are any better methods to find a factor of such a number than trial division, so I invite number-theory-enthusiasts to join in the search for prime factors.