If $n=\prod\_{i=1}^{k} p\_i^{e\_i}$ is a prime factorization of integer $n$.



> Is there a quick way to find the prime factorization of $n+1$?


Or the only way to do it is recalculating the whole factorization?


Any references and/or articles on this problem?



Prime factorization of n+1
Check out the literature on Fermat numbers, $2^{2^n}+1$. If factoring $m$ helped you factor $m+1$, these numbers would be a cinch, but they're not. 


