it was important because it hasn't been solved
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Goldbach's Conjecture suggests that every even integer greater than 2 is the sum of two prime numbers. It was stated in 1984 and proved in 1996 .
Counterexample
The Poincaré Conjecture.
One possible conjecture is that their sum is 27. The conjecture is patently false, but that does not stop it being a conjecture.
My conjecture is that the sum is 67. A conjecture does not have to be true, or even plausible. You should be able to test it. If it is found to be true then in is no longer a conjecture, if it is found to be false, it is rejected - and so no longer a conjecture. If it cannot be proved either way, it remains a conjecture.