Theorem — The set {1, . . . , 7824} can be partitioned into two parts, such that no part contains a Pythagorean triple, while this is impossible for {1, . . . , 7825}.
Yeah, when I saw "200 terabytes" I thought it was going to be about the Erdős discrepancy problem, since that's been making the rounds in the popular press, but turns out that only required 13 gigabytes for the 2010 proof.
I'm glad that Terry seems to have found a different proof. I attended a discussion of it during last week's Mathematical Congress of the Americas here in Mtl, and I think they were saying that Terry's proof seems correct.
https://arxiv.org/pdf/1605.00723.pdf