Perhaps. Computers have shown that it is true for some pretty large numbers, but you need to remember that there are an infinite number more out there. It hasn't been proved true yet, nor has there been a counterexample. Of course, theoretically the conjecture could be true, yet unprovable (see Godel's Incompleteness Theorem)
a conjecture
My conjecture (an opinion based on incomplete information) is that the product of two odd numbers is 22. There is no requirement for a conjecture to be true.
A therefore B A is true Therefore B is true Logically..... A is true A is false Therefore B is false
The Perpendicular bisector concurrency conjecture is the circumcenter
theorem
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 .
a conjecture
The Poincaré Conjecture.
To be true a Conjecture must be true for all cases.
Because that is what a conjecture is! It is a proposition that has to be checked out to see f it isalways true, false or indeterminate,sometimes true, false or indeterminate,never true, false or indeterminate.Once its nature has been decided then it is no longer 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.
Counterexample
Counterexample
It is a proposition that is believed to be true but has not [yet] been proven to be true. Clearly, if proven to be false it would no longer be a conjecture.
Any conjecture you want; a conjecture is merely an opinion or conclusion based on given information. Whether the conjecture is true or not is left to be proved (if provable at all). One opinion (conjecture) could be that the sum is "blue". It's a totally nonsense conjecture, but its a conjecture none the less. A sensible conjecture might be that the sum is odd. This can be tested and found to be true or false by summing the first 46 odd numbers (a mechanical method that is fairly easy in this case), or by the mathematical manipulation of axioms via algebra (a mathematical proof).
A conjecture is a proposition that is unproven but appears correct and has not been disproven.
hypothesis