I love this girl with everything I have I have never in my life velt so about a girl but she just stole my haert. But she is like 4 years younger then me is it wrong?

It is not wrong to love her. You just can't date or see her now. If you wait till she is at least 4 years older and her parents approve or 5 years when she is 18, there is no problem at all.

Right now the maturity level ( don't even start explaining why she is different) would make it too wrong

Next my other worry is of course you can't :LOVE someone that fast, you can be in "heat" from your hormones, and that is sort of sick thinking of a 13 year old child like that.

In the US, laws about getting involved with a younger person vary by state, but in all states, once you are 18 you are an adult and can be arrested. Laws about involvement (sexual intercourse) vary a lot by state if you are both under 18.
Whether you actually have sex or just see each other romantically doesn't matter, if adults want you to stop seeing each other and you don't.

How do you know her? How long have you known her? Do you know her feelings for you?

It isn't wrong now. Yes it is different but as you get older it won't matter. I have an example to prove it. My grandma got married at 18 and my grandad was 28. There is only 4 years between you and 10 between my grandparents so it doesn't matter.

It does matter.

Your grandmother was an adult when she married your grandpa. The age difference didn't matter because they were both adults.

The poster is 17 (almost an adult) and the girl is 13 (a child). Even though there's less of an age difference between the poster and your grandparents, it's still legally wrong for the poster to date this child, whereas your grandparents relationship was fine.

When the poster is 24 and the girl is 20, then no problem. Even when the girl is 18 and the poster 22, no problem. But at 17 and 13, it's a huge problem. He could end up in jail.

You got that half right. It IS wrong now, but when they are older it won't matter.

And your so-called proof is no proof at all. When did your grandparents marry, 50-60 years ago? A bit of a different time. And as Alty pointed at she was an adult.