Q: Why is a conjecture considered reasonable but not proven?

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a theorem

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

From Wikipedia ("Prime triplet"): "Similarly to the twin prime conjecture, it is conjectured that there are infinitely many prime triplets." So, it seems that nobody really knows for sure. "It is conjectured" means that it seems reasonable to suppose that there are infinitely many, but that it hasn't been proven yet.

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.

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Never

theorem

a theorem

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.

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.

theorem

There are no proven dangers, only rumor and conjecture.

It is a proposition or a belief that has not yet been proven.

Theorem

There is need for a conjecture. It is an easily proven fact that an even number minus an even number is always an even number.

There have been many attempts to try and prove it but so far none of these succeeded

A statement that might be true (based on some research or reasoning), but is not proven. Like a hypothesis, but not stated in as formal, or testable, way. So a conjecture is like an educated guess. Example: I heard the sound of a plastic bag, so I conjecture there might be some food!