# A question on pure math research for integer factorization

I'm interested in integer factorization for a project I'm working on (no it doesn't involve RSA) and I've notice that the majority of papers seemed to be focused on algorithms. Applications aside, I haven't seen a great deal of recent theoretical work on factorization.

If someone could link a few papers focusing on the theory of factorization instead of algorithms, then I'd be most appreciative.

Edit:

First, it seems I accidently deleted the well thought out and rigorous reply. I am truly sorry and I hope that it can be recovered. My apologizes.

Second, let me refine my query a bit. I am research patterns of integer factorization looking for a general recursive relationship: give an integer factorization M for an arbitrary integer N, what can we say about N+1's factorization?

Most IF research is focused on finding particular IFs to break the RSA cryptosystem. I could care less about the speed of factorization as I'm looking for general results to help me prove something related to IF.

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I'm sorry I think I deleted your comment. I feel terrible about it – Charles Hoskinson Mar 23 '13 at 23:39

Given the factorization of $n$, we can say next-to-nothing about the factorization of $n+1$. We can say no prime that divides $n$ also divides $n+1$; we can say that if $2$ doesn't divide $n$, then it does divide $n+1$; that's about it. If, say, $n$ is prime, $n+1$ could have hundreds of factors, or it could be twice a prime.