The complexity of Integer Factorization is to my knowledge still an open problem, whereas deciding, whether a given integer is a prime number is known to be in $P$ and a proof is available online here: http://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf

It is however not known (cf e.g. http://en.wikipedia.org/wiki/Integer_factorization ), whether the Factorization Problem is in $FP$

Question: as the optimization variant of Integer Linear Programming is $NP$ hard and the study of the polytope of the associated $LP$ versions (i.e. integrality constraints removed) plays an important role, I would appreciate **references to the study of Integer Factorization Polytope**

It has been indicated to me, that the $ILP$ formulation of Integer Factorization poses no difficulty and so, I would expect, that the polytope that is associated to the relaxed $LP$ version should have been studied, at least in hope of being able to demonstrate that the problem is in $P$