To start, it is impossible to prove that anyone exists beyond your own consciousness. In philosophy, this issues has become known as the problem of other minds. That being said, the problem that you have presented falls prey to a rule of thumb for many philosophers known as Occam's Razor. This idea was presented by William of Ockam in the 14th century and it states that in discussing a problem in philosophy, one should reject the answer with the most assumptions. Your statement that asks the reader to "prove that you exist" requires many more assumptions than if I were to say that I exist due to my empirical knowledge of the world. Therefore I exist