Any theorem was a conjecture before its formal proof was accepted by the community. Thus the importance of conjectures is a proxy to the importance of theorems:

Any theorem was a conjecture before its formal proof was accepted by the community. Thus the importance of conjectures is a proxy to the importance of theorems: they are proto-theorems. The fact that the human mind is capable of searching for new mathematical theorems specifically here instead of there, is quite interesting. It's as if a skilled mathematician has knowledge that is bigger than math itself. Penrose used this as argument for the special nature of consciousness, wrongly - it probably makes more sense to remember how the way the human mind is not exact and produces errors all the time plays a huge role in a creative process. And luckily we can amend the human mind by social processes that help eliminating errors again. This way, a conjecture can be thought of as a claim to truth in a competitive environment and that would explain why proving the truth is regarded so much higher.