Let $$\large f(n)=n^{(n^n)}+n^n+1$$
Checking $f(n)$ for $2\le n\le 100$, I noticed that $f(n)$ has a small prime factor except for $n=12,53$ and $60$
For $n=53$, I found the prime factor $7074407$ , but for $n=12$ and $n=60$, I did not find a prime factor yet. The numbers are too large to apply a primilaty test, so we need trial division.
Do $f(12)$ and $f(60)$ have a "small" prime factor, or are those numbers candidates for very large primes ?