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The numbers in the filename aren't random! They usually correspond to the: Post or Video ID Cache/Server Identifier

It often starts with something like scontent.fxxx.fbcdn.net . Download 10000000 657713119039362 2509505574370057596 mp4

Right-click on the video player and select "Save Video As..." You can then rename it from the long string of numbers to something more memorable. The numbers in the filename aren't random