TITLE: Results on the largest prime factor of $2^n+1$
QUESTION [7 upvotes]: A work of Cameron Stewart (the paper has appeared in Acta Mathematica),  proving a conjecture of Erdos, Stewart shows that 
the largest prime factor of $2^n-1$ is at least 
$n \times \exp\Big( \frac{\log n}{104 \log \log n}\Big)$ ,
if $n$ is large enough. 
Zsigmondy's theorem  is on the same topic.
I would like to know about the largest prime factor of $2^n+1$. I have searched, but most of the time result of the largest prime factor of $2^n-1$  appears. 
My questions is-

Is there any result regarding the largest prime factor of $2^n+1$ ?

if you know anything related to the problem, please inform.

REPLY [8 votes]: One has $2^n+1= \frac{2^{2n}-1}{2^n-1} = \prod_{d \mid 2n,~d\nmid n} \Phi_d(2,1)$. In particular, $\Phi_{2n}(2,1)$ divides $2^n+1$, and so the main theorem of Stewart's paper shows immediately that $P(2^n+1) > 2n \exp(\log(2n)/104\log\log(2n))$ for large $n$.