It's hard to tell if the later terms will truly converge on 1.057934 or not. They're heading in that direction, but the convergence is painfully slow. Oh, labels. Yes, the purple line is for the coefficients of solving the 580x580 system, then 560, 540, 520, 500, 480, and 440 (skipped 460, will fill in later). Yellow is 440.
The convergence is slow, but I would not be surprised if we eventually got there, by the time we'd solved the million by million system, etc. Obviously, this will have to remain hypothetical, because even a supercomputer would have trouble solving a several thousand system using exact rational math. Beyond that is out of the reach of all the distributed computing in the world (we're talking five orders of magnitude above what my system can handle, just to get to 6,000!!!). The best we could hope for is to used floating point math with maybe millions of bits of precision, and let a distributed effort try to solve. Probably not worth it anyway, even if we could organize such a feat.
The convergence is slow, but I would not be surprised if we eventually got there, by the time we'd solved the million by million system, etc. Obviously, this will have to remain hypothetical, because even a supercomputer would have trouble solving a several thousand system using exact rational math. Beyond that is out of the reach of all the distributed computing in the world (we're talking five orders of magnitude above what my system can handle, just to get to 6,000!!!). The best we could hope for is to used floating point math with maybe millions of bits of precision, and let a distributed effort try to solve. Probably not worth it anyway, even if we could organize such a feat.
~ Jay Daniel Fox