Originally Posted By: grelber
Originally Posted By: artie505
...
That seems like it might make grelber's "2" disappear.


Not after the fact. I tried that after the 2 appeared; it apparently only works for future updates. It won't 'erase' what came before (unless and until the updates denoted are downloaded and installed — or so I presume). So that's another dead end.

That really got me thinking that the "2" must be cached somewhere on your iMac, so I went looking and found /Library/Preferences/com.apple.SoftwareUpdate.plist which includes

Code:
<key>LastUpdatesAvailable</key>
	<integer>0</integer>


which, I believe, is where your "2" lives, and I think this procedure will get rid of it:
  1. Navigate to System Prefs > App Store.
  2. Make sure that "Automatically check for updates" is NOT checked.
  3. Quit System Prefs.
  4. Navigate to /Library/Preferences/com.apple.SoftwareUpdate.plist.
  5. Trash it. (You'll probably be asked to authenticate with your Admin password.)
  6. Empty the trash.
  7. Shut down.
  8. Start up.
Hopefully, your "2" will be gone.

FULL DISCLOSURE:
  • On the one hand, there's enough data stored on your iMac for macOS to recreate at least part of the trashed file. (The rest requires App Store access.)
  • But on the other hand, System Prefs .plists are notorious for not regenerating after being trashed.
  • On the third hand, though, Software Update is a dead issue in your instance, so you've got nothing to lose but your "2".
More: I forgot to mention that I more or less confirmed my theory by changing my "0" to a "1" and then launching the App Store and actually seeing the "1" revert to a "0" in the open .plist as I watched.

The new Great Equalizer is the SEND button.

In Memory of Harv: Those who can make you believe absurdities can make you commit atrocities. ~Voltaire