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If Goldbach's conjecture is false but the smallest counterexample has 10^1000 digits, would we be unable to ever prove or disprove it?

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如果哥德巴赫猜想是错的，但最小的反例也有 10^1000 位数，那我们岂不是永远无法证明也无力证伪？

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Zhihu Hot ListLast observed #8 · 1.3M heat

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Ranking history & source details

First recorded Sep 15, 2026, 8:34 AM CST · latest Sep 15, 2026, 8:34 AM CST. Ranks reflect attention on each platform.

Retained daily observations
Day	Platform	Best rank	Last rank
2026-09-15	Zhihu Hot List	#8	#8