A=m*n and B=o*p, where m, n, o, p unknown large primes. Given C=m+o, is there an algorithm that simplifies factorization of products of primes?

Question

We have two known sums $A$ and $B$, of different unknown prime numbers:

$A=mn$

$B=op$

where $m, n, o, p$ are unknown large primes. For large primes the factorization of these primes is computationally very difficult.

If we know a third number $C$ such as $C=m+o$

Is there an algorithm that simplifies computational complexity for factorization of products of primes $A$ and $B$ using the sum $C$?