Before You Buy an NVME for Your 2013 Mac Pro 6,1 Make Sure It Really Is an Upgrade:
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I just bought a "new to me" 2013 Mac Pro 6,1 that was manufactured in 2016 with a 1TB drive already in it.
The Ebay Seller had several others that had 256GB drives so I assumed this one was upgraded later or something.
Turns out, it has the 1TB APPLE SSD SM1024G drive in it already. This is about as fast as you're going to get.
Results above are mine. Some ads tout "up to 1565MB/s read and 1354MB/s write" which as you can see are in the same ballpark.
Now, if you need more storage, sure, then you might get a little more speed with a current tech drive.
If you have an original drive then please download BlackMagic's Disk Speed Test (it's free) from the app store and report your speed and drive in the comments below (you can get drive model from "About This Macc-=>System Report-=>Hardware -=>Storage"
I'd be interested if the later manufactured computers had the smaller drives still but with faster speeds.
If you're buying an NVME, you'll need a little adapter. Personally, I'd get a regular NVME drive vs. the special 'Just for Macs' drives that have a slightly different interface. OWC and other places sell these.
Also, you won't be able to do 'hand me downs' to PCs etc. that use the industry standard interface if you buy an 'Apple Only' drive.
There could some twiddling, such as if you need a firmware update for the SSD you buy (SK Hynix P31 Gold for example.)
The NVME adapter you want is a Sintech brand:
The Q&A on Amazon specifically mentions the 2013 Mac Pro and the articles I've read also mention it specifically.
Can't go wrong with a Samsung drive, most likely: https://amzn.to/3E5ryLk
If you're not getting the read speeds above, I'd upgrade to an NVME drive using the Sintech adapter.
But check first. If you have a later manufacure date 2013 Mac Pro 6,1 you may already have the fastest drive available.