Not just that, but this paticulary problem is also famous for crazy people claiming they have a proof. Until some mathmatician agrees with the proof (or even just indicates it is interesting), this is a non story.
Yeah. The "proof" of theorem 2 being just a handwavy do the first proof again, but use Q_2 and normalize the result after each step to a simple fraction, which will only increase c_1.
That really sounds suspicious to me. Why not just solve this version directly with these changes. That should have been a more straightforward proof.