I see no evidence at all that you've made any kind of breakthrough. Current beli...

I see no evidence at all that you've made any kind of breakthrough. Current belief in the factoring world is that the GNFS is the fastest way to factor integers - are you claiming you can do better?

From http://en.wikipedia.org/wiki/RSA_numbers#RSA-2048 :

    RSA-2048 has 617 decimal digits (2,048 bits).
    It is the largest of the RSA numbers and carried
    the largest cash prize for its factorization,
    US$200,000. The largest factored RSA number is
    768 bits long (232 decimal digits), and the
    RSA-2048 may not be factorizable for many years
    to come, unless considerable advances are made
    in integer factorization or computational power
    in the near future.

And here from http://en.wikipedia.org/wiki/Integer_factorization_records :

    On December 12, 2009, a team including researchers
    from the CWI, the EPFL, INRIA and NTT in addition
    to the authors of the previous record factored
    RSA-768, a 232-digit semiprime.  They used the
    equivalent of almost 2000 years of computing on
    a single core 2.2 GHz AMD Opteron.

You're saying that a 4000 digit number may take 24 hours?

I'd be interested to see at least some evidence that you're doing something better before dedicating any time to your project.