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▲ ndsipa_pomu 4 days ago

It'd also be an end to the project and would make the conjecture far less interesting.

▲kevinventullo 4 days ago | parent [-]

IMO it would make the conjecture far more interesting, as it would be a surprise to most people who have thought about the problem.

Many natural questions would arise, starting with “Is this the only counterexample?”

▲ndsipa_pomu 4 days ago | parent [-]

Possibly, but it would join other false conjectures such as Euler's sum of powers conjecture - posed in 1769 and no counterexample found until 1966. There's only been three primitive counterexamples found so far.

(I got that from https://math.stackexchange.com/questions/514/conjectures-tha... which features some other false conjectures that may be of interest to you)

▲charlieyu1 3 days ago | parent [-]

Not even the same implications. All empirical evidence strongly support the Goldbach conjecture. Any counterexample would mean an entire field of Mathematics has to be rewritten.