Will DDR3-8500MHz work on the 2011 Mac Mini?

No, Macs cannot use slowed RAM that what they come with.

Intell said:

No, Macs cannot use slowed RAM that what they come with.

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Not to argue but are you sure about that. the intel processor in the 2011 mac mini is rated for 1066 or 1333 ram it also does 1600 ram and 1866 ram at least people on this site say that it does.

I'm starting to think the OP got his numbers wrong. 10660mhz seems far too fast for modern ram speeds. While a Mac can use faster ram than its stock speed, they will refuse to boot if slower ram is installed.

Intell said:

I'm starting to think the OP got his numbers wrong. 10660mhz seems far too fast for modern ram speeds. While a Mac can use faster ram than its stock speed, they will refuse to boot if slower ram is installed.

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PC-10666 is the standard RAM for the new Mac minis.

I'm guessing that PC-8500 should work, but there may be stability issues...

Personally, I'd send it back and get RAM that was at least 1333MHz, but I take a conservative approach to RAM speeds in Macs, trying to match speeds in all cases. Following this approach has meant I've never had any RAM-related issues, even using ValueRAM and other cheap stuff.