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A comment on How many real numbers exist? New proof moves closer to an answer. Parent comment
https://en.m.wikipedia.org/wiki/Goldbach%27s_weak_conjecture
It was known to have at most finitely many counter-examples by the 1930’s, and by the 1950’s it was known that the largest counter-example had to be < 3^3^15. In 2002 that was lowered to about 10^1346. Still well out of reach of any computer!
Only in 2012 was an unconditional proof given.
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https://en.m.wikipedia.org/wiki/Goldbach%27s_weak_conjecture
It was known to have at most finitely many counter-examples by the 1930’s, and by the 1950’s it was known that the largest counter-example had to be < 3^3^15. In 2002 that was lowered to about 10^1346. Still well out of reach of any computer!
Only in 2012 was an unconditional proof given.