Facebook no longer allows direct viewing of full-size profile pictures via a simple, predictable URL for privacy and security reasons. However, here are the most common URL patterns that (and may still work for public profiles or your own photos):
I have seen users lose their Facebook accounts because they entered their credentials into a "profile picture viewer" site. The scammer then changed the email and password instantly. facebook profile picture viewer url
Finding a Facebook profile picture's direct URL or viewing it in high resolution is straightforward, whether you are using a mobile device or a computer. How to Find Your Facebook Profile Picture URL historically worked Facebook no longer allows direct viewing