Good god man yeah need to at least use 1600. Because you've sanded an almost perfect mirror finish with 400 grit you will now need to lap with an 800 grit, then 1200, then the 1600. If you go straight to 1600 the tiny scratches from the 400 grit wont come out unless you rub for a L O N G time. Best if you go even higher on the grits too. Its such a tiny surface area shouldn't take too long.

Also - I'm not sure as I don't have *ANY* experience lapping CPU's but might be worth getting some Tin Oxide or similar polish and then polishing with a polishing wheel on a Dremel. Will get it mirror smooth but again i'm no expert in CPU's just making knives and polishing stones and jewelry so take my advice on the polish with a grain of salt. If its a perfectly even smooth surface you want though that'd be the way to do it :)

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*Edit: Tin Oxide not Titanium Oxide

*Edit2: for those concerned about sand paper you can also just use a piece of hardened glass or a slab of granite or anything smooth and flat and then buy grits of silicon carbide. If you buy a 400 grit carbide, mix it with some olive oil, then put a teaspoon on the plate and start sanding away it will break down over use until it is eventually a very fine grit (say 2000 or so).

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Im in AUS but I see Amazon sells it:

https://www.amazon.com/Silicon-Carbide-Powder-400-Grit/dp/B007BRD6YC

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