The following partial factorization
http://factordb.com/index.php?id=1100000001285565404
was used by factordb to prove this number ($\ 32^{2133}+4^{2133}+1\ $) to be prime.
http://factordb.com/index.php?query=32%5E2133%2B4%5E2133%2B1
What confuses me : I only know a variant of the p-1-method , where $n-1=FG$ where $F$ is completely factored and we have $F>G$. This is apparently not the case in the given factorization.
So how could factordb prove the primality with the $p-1$-method ?