Is there list of composite Mersenne numbers with their factorization?

Question

Here is a list of known Mersenne primes.

http://mathworld.wolfram.com/news/2009-06-07/mersenne-47/

I'm looking for a list of composite Mersenne numbers(when $p$ is prime $2^p-1$ isn't) with their factorizations for larger $p$.($p<43112609 $)

Answer 1

The 'cunningham project' at this website lists factors for $2^n-1, \text{ odd }n<1300$ http://homes.cerias.purdue.edu/~ssw/cun/

Answer 2

According to the information at Mersenne prime Wikipedia page, up to the 44th Mersenne prime it is actually known that there are no other primes before. Thus for $p \le 32582657$ the composite ones are exactly those not in the list yielding primes.

Usually there will be no complete factorizations known, and in many cases it'll be impossible to come up with them.