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I used a Real Look screen protector for a few days.
It covered the on screen scratches pretty well and didn't hinder the screens brilliance in any way that I saw visible.
The installation took a good 30 minutes of fiddling and cleaning and wipes it was really frustrating as it had to be a perfect fit or else air bubble would ensue. When on the screen there wasn't one speck of dust on the screen and not one bubble it was immaculate.
The only problem with the screen protector was that after just a few days in my pocket with keys and change at times there were already scratches on it. I pealed it off upset in the money I had spent for only a few days and it had already scratched. I am now running the phone completely naked no screen protector or case and there are only minimal scratches on the screen when shown in light.
They aren't visible when the screen comes on.
In all the screen is Corning Gorilla Glass

Do you really need a screen protector, though? I have a Kindle Fire and my son (who's eight) has an iPod Touch and we haven't had any scratches at all on the glass after a few months. Isn't the glass on the Vivid similar?