However my slashdot number, which I've had nearly 20 years, I know nothing more than it begins with 2.
The modern numbers I remember are my mobile phone number, my wife's, and my passport numbers (phone numbers as we've had them over a decade and all of them because I have to write them on forms so much). The only other numbers that spring to mind are my staff number at work (used in various forms, had since 2003) and my bank numbers (needed to log on)
If you use a number a lot, you learn it. If you don't (like usernames which are saved) you forget it. I can barely remember my credit card pin as I use contactless so much, but muscle memory seems to work there.
I was (am?) 72167,3530. Does that make my ID older or newer than yours?
Then people will be buying/selling UUIDS which are easier to pronounce or memorize. People will always consider patterns more valuable.
1) Short number.
2) Repeating digits like say only containing 2 or 3 numbers.
One of these was great, but both? Jackpot.
You could add a third factor: keypad pattern. It never occurred to me I'd use keypad to remember the number TBH, but IIRC one of my friends did care about that. I'm actually frightened by that option in Android I kid you not; I am frightened I forget the pattern!
Of my own numbers discounting the starting 1 (I personally did not care about that one but I know others did) one ended with 0's and the other one only contained 2 different digits with one being twice the other one. Extremely easy to remember.
UUIDs were also my first idea, but I have the feeling that sharing them (i.e. to invite a new friend) would be cumbersome. I wonder if a new system akin to what3words.com could help there.
Oldschool Battle.net had a 16 alphanumeric characters with underscore allowed and that was that. At least for Warcraft 3 it's been the case since 2002 for a very long time (until quite recently last year they allowed fancy symbols in usernames).
You also had to login at least once every 3 months or Blizzard purged your account.
Of course, yes. I doubt this problem came up with the original Battle.net accounts :-)
The weakness lies partly in ICQ: they allowed to easily find all these people using @hotmail.com e-mail address and even showed this information. Sure, you could disable being part of this feature (IIRC it was called "yellow pages" or something akin to it) but still.
The other part of the weakness is exactly the very issue of domain squatting, username squatting, e-mail squatting or whatever you want to call it. I understand Microsoft wants to save space on their e-mail servers back in the early '00s but: former username should be frozen and their e-mail could be either bounced or silently rejected to /dev/null or whatever's the Windows equiv.
Blizzard's WoW has the rule that you you can only get a username from an inactive account. An inactive account is an account which did not play the previous expansion. That's their compromise. To be fair, it is not like people use WoW usernames for password recovery.
As for using numbers as username: that is what UNIX does under the hood, it is what Facebook does under the hood as well, it is what Blizzard's WoW does under the hood as well, and what T9 converts to as well, and ICQ did as well in contrast to MSN. Turns out people are lousy at remembering a bunch of numbers. So they resort to 26 character system of letters, or 36 character system of letters plus numbers. (Some services are more or less strict.) So, no, using numbers as human-usable UUID is not a solution but using it under the hood is totally OK.
ICQ did that. Though it still led to interesting results, because lower numbers were thought to be more valuable, and people were buying/selling those.
Perhaps a random numbers with the same number of digits or UUIDs may work without such issues. :)