[ndsipa_pomu]

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]

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.