Can a Person Know Something They Cannot Prove?

I believe that a person can know some things without proving them while others need to be proved. It is a matter of what they claim to know and the perspective you take in analysing their proposition. I will discuss the possibility of knowing something without being able to prove it and also the possibility that if something can not be proven then the knower does not know what he/she claims to know.
After many attempts in defining what it is to 'know' something, and finding that it is difficult to do so completely and without flaw, I have decided to simply say that to 'know' something is to believe that a fact is true. This belief must come from prior experiences, acquaintances, perceptions, emotions, etc. that a person has had. …