I moved about 6 hours away from this guy I'm completely in love with, but it's been only about a month since I've lived here & my boyfriend (boyfriend honestly doesn't even explain what he means to me) doesn't think I want him as bad as I do. How do I "prove" to him exactly how I feel. I want him more than anything in the world, I love him with everything I am and never want to lose him. What can I do to prove it

It is not an issue of you proving to him how much you need him, it's the fact that he is not mature enough and is showing this in his insecurity of you being so far away.Not a bad thing and not a good thing either. I feel it is an undesirable personality trait. By being far away from him, you will be finding out little things about him that you may not appreciate in a partner.

Sometimes long distance relationships cannot withstand the test of time.

Tick

I moved about 6 hours away from this guy I'm completely in love with, but it's been only about a month since I've lived here & my boyfriend (boyfriend honestly doesn't even explain what he means to me) doesn't think I want him as bad as I do. How do I "prove" to him exactly how I feel. I want him more than anything in the world, I love him with everything I am and never want to lose him. What can I do to prove it

Why does he think this? Has he told you any specifics?

This is an old classic male ploy to try and get a girl to have sex. If you really love me you will do ANYTHING I ask you to ,to prove it right. This is a possibility.

How old are you two? That could help in being more specific.

Why did you move away?

I have to agree with Tickle. Long distance relationships usually don't work out too well and most will break in due time. But, if he loves you the way you love him, he will grow to show you just how much you mean to him.
Perhaps going out of your way to send him a card saying either a cute poem or just saying 'I love you' would help. Even calling him up to talk about nothing would show him you'll sacrifice time just to hear his voice. Sending small things to him could help.
How old you guys? This might help get more specific answers.