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Is the bound achieved by his proof actually 70000000? That looks like a suspiciously round number. Why can't they tell us the exact bound that he achieved? (Pre
by pjdorrell 13y ago
Is the bound achieved by his proof actually 70000000? That looks like a suspiciously round number. Why can't they tell us the exact bound that he achieved? (Presumably some slightly smaller number?)
- vlasev 13y agoIn math you often don't need super precise bounds. I think it just happens that 70m works. If you try harder you can probably find something more accurate. IMO even a bound like 100m is good because it's a finite number.
- pjdorrell 13y agoNo, actually any proof that supplies a bound must also have some least bound that can be derived from that proof. It could be a calculation that starts from the bound, or it could be some calculation with a result that tells you what the bound is. To me it seems very unlikely that the actual bound was exactly 70000000 in either case. It _could_ be that some super-expensive calculation is required for each candidate bound, and Zhang guessed 70000000 as a starting point and did the calculation for that number, which succeeded, but he didn't bother repeating it for any smaller numbers because it would cost him too much. But if that was the case, that would be interesting in itself.