a theorem
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There is no conjecture about the sum of the first 30 positive even numbers. The answer can be derived and proven. A statement that has been proven is no longer a conjecture.
There have been many attempts to try and prove it but so far none of these succeeded
A conjecture is a statement that is believed to be true, but has yet to be proven. Conjectures can often be disproven by a counter example and are then referred to as false conjectures.
One possible conjecture is that the product of two odd integers is 8. A conjecture does not have to be true, nor does it have to be sensible. It must be testable, though. Many conjectures were initially thought to be sensible and true but later proven to be false. And when the false nature is fully understood, in retrospect they no longer appear sensible either!
The Poincaré Conjecture.