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!
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Any proposition, which is based on partial information, is a conjecture. It can be sensible or nonsense. The statement "the ancient Egyptians were really from Mars" is a valid conjecture.